in these cases it can happen that ab = ba ; then " inverse " typically implies that an element is both a left and right inverse. the notation f −1 is sometimes also used for the inverse function of the function f, which is for most functions not equal to the multiplicative inverse. for example, the multiplicative inverse 1 / ( sin x ) = ( sin x ) −1 is the cosecant of x, and not the inverse sine of x denoted by sin−1 x or arcsin x. the terminology difference reciprocal versus inverse is not sufficient to make this distinction, since many authors prefer the opposite naming convention, probably for historical reasons ( for example in french, the inverse function is preferably called the bijection reciproque ).


it affects the choice of comparable data for use in the analysis. it can also affect the method used to value the property. for example, tree value can contribute up to 27 % of property value.


in software engineering, cycle time is a software metric which estimates development speed in agile software projects. the cycle time measures how long it takes to process a given job - whether it's a client request, an order, or a defined production process stage. the crucial aspect of measuring the cycle time is considering only the active, operating processing time and discarding any idle, waiting, or service times occurring mid - process. according to the pmbok ( 7th edition ) by the project management institute ( pmi ), cycle time is the " total elapsed time from the start of a particular activity or work item to its completion.


in mathematics, a base - orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. for any two bases a { \ displaystyle a } and b { \ displaystyle b } there exists a feasible exchange bijection, defined as a bijection f { \ displaystyle f } from a { \ displaystyle a } to b { \ displaystyle b }, such that for every a ∈ a b { \ displaystyle a \ in a \ setminus b }, both ( a { a } ) ∪ { f ( a ) } { \ displaystyle ( a \ setminus \ { a \ } ) \ cup \ { f ( a ) \ } } and ( b { f ( a ) } ) ∪ { a } { \ displaystyle ( b \ setminus \ { f ( a ) \ } ) \ cup \ { a \ } } are bases. the property was introduced by brualdi and scrimger. a strongly - base - orderable matroid has the following stronger property : for any two bases a { \ displaystyle a } and b { \ displaystyle b }, there is a strong feasible exchange bijection, defined as a bijection f { \ displaystyle f } from a { \ displaystyle a } to b { \ displaystyle b }, such that for every x ⊆ a { \ displaystyle x \ subseteq a }, both ( a x ) ∪ f ( x ) { \ displaystyle ( a \ setminus x ) \ cup f ( x ) } and ( b f ( x ) ) ∪ x { \ displaystyle ( b \ setminus f ( x ) ) \ cup x } are bases.


in some implementations of software development processes, issues are investigated by quality assurance analysts a system is verified for correctness, and then assigned back to a member of the development team to resolve the identified issue. they can also be identified by system users during the user acceptance testing ( uat ) phase. issues can be recorded and communicated using issue or defect tracking systems. in the absence of a formal issue or defect tracking system, it is commonplace to simply use any form of written communication such as emails or instant messages to communicate the existence of a found issue.


in one version of airline scheduling the goal is to produce a feasible schedule with at most k crews. to solve this problem one uses a variation of the circulation problem called bounded circulation which is the generalization of network flow problems, with the added constraint of a lower bound on edge flows. let g = ( v, e ) be a network with s, t ∈ v as the source and the sink nodes.


differential variational inequalities were first formally introduced by pang and stewart, whose definition should not be confused with the differential variational inequality used in aubin and cellina ( 1984 ). differential variational inequalities have the form to find u ( t ) ∈ k { \ displaystyle u ( t ) \ in k } such that ⟨ v − u ( t ), f ( t, x ( t ), u ( t ) ) ⟩ ≥ 0 { \ displaystyle \ langle v - u ( t ), f ( t, x ( t ), u ( t ) ) \ rangle \ geq 0 } for every v ∈ k { \ displaystyle v \ in k } and almost all t ; k a closed convex set, where d x d t = f ( t, x ( t ), u ( t ) ), x ( t 0 ) = x 0. { \ displaystyle { \ frac { dx } { dt } } = f ( t, x ( t ), u ( t ) ), \ quad x ( t _ { 0 } ) = x _ { 0 }. } closely associated with dvis are dynamic / differential complementarity problems : if k is a closed convex cone, then the variational inequality is equivalent to the complementarity problem : k u ( t ) f ( t, x ( t ), u ( t ) ) ∈ k ∗. { \ displaystyle k \ ni u ( t ) \ quad \ perp \ quad f ( t, x ( t ), u ( t ) ) \ in k ^ { * }. }


in mathematical logic ( a subtopic within the field of formal logic ), two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa ; in other words, either both formulae are satisfiable or both are not. equisatisfiable formulae may disagree, however, for a particular choice of variables. as a result, equisatisfiability is different from logical equivalence, as two equivalent formulae always have the same models.


in the beginning of the agglomerative clustering process, each element is in a cluster of its own. the clusters are then sequentially combined into larger clusters, until all elements end up being in the same cluster. at each step, the two clusters separated by the shortest distance are combined. the function used to determine the distance between two clusters, known as the linkage function, is what differentiates the agglomerative clustering methods.


this is particularly common for discrete data. when this happens, the test procedure defined above is usually undefined because there is no way to uniquely rank the data. ( the sole exception is if there is a single sample x i { \ displaystyle x _ { i } } which is zero and no other zeros or ties. ) because of this, the test statistic needs to be modified.


( c ∈ c ). f ( a ) = c { \ displaystyle \ forall ( a \ in a ). \, \ exists! ( c \ in c ). f ( a ) = c }.


pca is used to identify a set of orthogonal basis vectors ( basis signals ) which capture as much as possible of the energy in the ensemble of observed samples. the vector space spanned by the basis vectors identified by the analysis is then the signal subspace. the underlying assumption is that information in speech signals is almost completely contained in a small linear subspace of the overall space of possible sample vectors, whereas additive noise is typically distributed through the larger space isotropically ( for example when it is white noise ).


a utility program ( movcpm ) was provided with system distribution that allowed relocating the object code to different memory areas. the utility program adjusted the addresses in absolute jump and subroutine call instructions to new addresses required by the new location of the operating system in processor memory. this newly patched version could then be saved on a new disk, allowing application programs to access the additional memory made available by moving the system components.


during the construction of the sequence, if a proof π j { \ displaystyle \ pi _ { j } } happens to be too large, π j + 1 { \ displaystyle \ pi _ { j + 1 } } is set to be the smallest proof in { π 1, π 2, …, π j } { \ displaystyle \ { \ pi _ { 1 }, \ pi _ { 2 }, \ ldots, \ pi _ { j } \ } }. for achieving a better compression / time ratio, a heuristic for variable selection is desirable. for this purpose, cotton defines the " additivity " of a resolution step ( with antecedents p { \ displaystyle p } and n { \ displaystyle n } and resolvent r { \ displaystyle r } ) : add ( r ) : = max ( | r | − max ( | p |, | n | ), 0 ) { \ displaystyle \ operatorname { add } ( r ) : = \ max ( | r | - \ max ( | p |, | n | ), 0 ) } then, for each variable v { \ displaystyle v }, a score is calculated summing the additivity of all the resolution steps in π { \ displaystyle \ pi } with pivot v { \ displaystyle v } together with the number of these resolution steps.


the binary logarithm has also been written as log n with a prior statement that the default base for the logarithm is 2. another notation that is often used for the same function ( especially in the german scientific literature ) is ld n, from latin logarithmus dualis or logarithmus dyadis. the din 1302, iso 31 - 11 and iso 80000 - 2 standards recommend yet another notation, lb n. according to these standards, lg n should not be used for the binary logarithm, as it is instead reserved for the common logarithm log10 n.


in mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0, { \ displaystyle a _ { 1 } x _ { 1 } + \ ldots + a _ { n } x _ { n } + b = 0, } where x 1, …, x n { \ displaystyle x _ { 1 }, \ ldots, x _ { n } } are the variables ( or unknowns ), and b, a 1, …, a n { \ displaystyle b, a _ { 1 }, \ ldots, a _ { n } } are the coefficients, which are often real numbers. the coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. to yield a meaningful equation, the coefficients a 1, …, a n { \ displaystyle a _ { 1 }, \ ldots, a _ { n } } are required to not all be zero.


in mathematics, an asymmetric relation is a binary relation r { \ displaystyle r } on a set x { \ displaystyle x } where for all a, b ∈ x, { \ displaystyle a, b \ in x, } if a { \ displaystyle a } is related to b { \ displaystyle b } then b { \ displaystyle b } is not related to a. { \ displaystyle a. }


most schema migration tools aim to minimize the impact of schema changes on any existing data in the database. despite this, preservation of data in general is not guaranteed because schema changes such as the deletion of a database column can destroy data ( i. e. all values stored under that column for all rows in that table are deleted ). instead, the tools help to preserve the meaning of the data or to reorganize existing data to meet new requirements. since meaning of the data often cannot be encoded, the configuration of the tools usually needs manual intervention.


this knowledge comes from repeated examinations over time that show changes from marketing initiatives ( from brand and competition ) and the evolution of consumers ’ needs. harold geneen in his groundbreaking book “ managing ” explains the role of an effective ceo : to repeatedly evaluate performance numbers on a continuous basis. only long term observation brings true insight of unanticipated changes and “ red flags ” in the data. all measurement systems are prone to misinterpretation and error.


the sscg sequence begins slower than scg, sscg ( 0 ) = 2, sscg ( 1 ) = 5, but then grows rapidly. sscg ( 2 ) = 3 × 2 ( 3 × 295 ) − 8 ≈ 3. 241704 × 1035775080127201286522908640065. its first and last 20 digits are 32417042291246009846... 34057047399148290040.


this allows for forward and reverse branches in code. the limited range of the branch instructions meant that, as code grew, the target addresses of some branches would become unreachable.


in some time - critical situations, failure to act may entail a continuously increasing cost over time, or a continuously decreasing probability over time of achieving the desired outcome. in real - time computing systems, this may be represented by time - utility functions.


minimal - rights : stronger than non - negativity : each claimant should get at least his minimal right, which is what's left if all other agents get their full claims : i : x i ≥ m i, where m i : = max ( 0, e − j = i c j ) { \ displaystyle \ forall i : x _ { i } \ geq m _ { i }, { \ text { where } } m _ { i } : = \ max ( 0, e - \ sum _ { j \ neq i } c _ { j } ) }. note that efficiency, non - negativity and claims - boundedness together imply minimal - rights. equal treatment of equals ( ete ) : two claimants with identical claims should get identical allocations : c i = c j x i = x j { \ displaystyle c _ { i } = c _ { j } \ implies x _ { i } = x _ { j } }.


with some precomputation, only a single multiplication per sector is required ( note that addition in a binary finite field is a simple bitwise addition, also known as xor ) : f ⊗ i = f ⊗ ( i 0 ⊕ δ ) = f ⊗ i 0 ⊕ f ⊗ δ { \ displaystyle f \ otimes i = f \ otimes ( i _ { 0 } \ oplus \ delta ) = f \ otimes i _ { 0 } \ oplus f \ otimes \ delta }, where f ⊗ δ { \ displaystyle f \ otimes \ delta } are precomputed for all possible values of δ { \ displaystyle \ delta }. this mode of operation needs only a single encryption per block and protects against all the above attacks except a minor leak : if the user changes a single plaintext block in a sector then only a single ciphertext block changes.


in search of " framework for modeling space systems architectures " peter shames and joseph skipper ( 2006 ) defined a " nominal set of views ", derived from ccsds rasds, rm - odp, iso 10746 and compliant with ieee 1471. this " set of views ", as described below, is a listing of possible modeling viewpoints. not all of these views may be used for any one project and other views may be defined as necessary. note that for some analyses elements from multiple viewpoints may be combined into a new view, possibly using a layered representation.


they are studied in the eight queens puzzle, where eight non - attacking queens are placed on a standard 8 × 8 { \ displaystyle 8 \ times 8 } chessboard. dominating sets represent arrangements of queens where every square is attacked or occupied by a queen ; five queens, but no fewer, can dominate the 8 × 8 { \ displaystyle 8 \ times 8 } chessboard. colourings of the graphs represent ways to colour each square so that a queen cannot move between any two squares of the same colour ; at least n colours are needed for an n × n { \ displaystyle n \ times n } chessboard, but 9 colours are needed for the 8 × 8 { \ displaystyle 8 \ times 8 } board.


in actual implementation, that is not two separate steps ; the dft replaces the dtft. so j. cooley ( pp. 77 – 78 ) describes the implementation as discrete finite fourier transform. or another name for the fourier series coefficients. or another name for one snapshot of a short - time fourier transform.


in more technical terms, roaming refers to the ability for a cellular customer to automatically make and receive voice calls, send and receive data, or access other services, including home data services, when travelling outside the geographical coverage area of the home network, by means of using a visited network. for example : should a subscriber travel beyond their cell phone company's transmitter range, their cell phone would automatically hop onto another phone company's service, if available. the process is supported by the telecommunication processes of mobility management, authentication, authorization and accounting billing procedures ( known as aaa or'triple a').


the rnn hierarchy can be " collapsed " into a single rnn, by " distilling " a higher level " chunker " network into a lower level " automatizer " network. in 1993, a chunker solved a deep learning task whose cap depth exceeded 1000. such history compressors can substantially facilitate downstream supervised deep learning. geoffrey hinton et al. ( 2006 ) proposed learning a high - level internal representation using successive layers of binary or real - valued latent variables with a restricted boltzmann machine to model each layer.


( b ) " instrument " means a negotiable instrument. ( c ) an order that meets all of the requirements of subsection ( a ), except paragraph ( 1 ), and otherwise falls within the definition of " check " in subsection ( f ) is a negotiable instrument and a check. ( d ) a promise or order other than a check is not an instrument if, at the time it is issued or first comes into possession of a holder, it contains a conspicuous statement, however expressed, to the effect that the promise or order is not negotiable or is not an instrument governed by this article.


in most of europe, lpd433 band is allowed for license - free voice communication in addition to pmr446. wireless network devices use wavebands as follows : ieee 802. 11 / wi - fi 2450 mhz and 5800 mhz bands bluetooth 2450 mhz band falls under wpanieee 802. 15. 4, zigbee and other personal area networks may use the 915 mhz and 2450 mhz ism bands because of frequency sharing between different allocations. wireless lans and cordless phones can also use bands other than those shared with ism, but such uses require approval on a country by country basis.


the name " uniform norm " derives from the fact that a sequence of functions { f n } { \ displaystyle \ left \ { f _ { n } \ right \ } } converges to f { \ displaystyle f } under the metric derived from the uniform norm if and only if f n { \ displaystyle f _ { n } } converges to f { \ displaystyle f } uniformly. if f { \ displaystyle f } is a continuous function on a closed and bounded interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the weierstrass extreme value theorem, so we can replace the supremum by the maximum. in this case, the norm is also called the maximum norm. in particular, if x { \ displaystyle x } is some vector such that x = ( x 1, x 2, …, x n ) { \ displaystyle x = \ left ( x _ { 1 }, x _ { 2 }, \ ldots, x _ { n } \ right ) } in finite dimensional coordinate space, it takes the form : ‖ x ‖ ∞ : = max ( | x 1 |, …, | x n | ). { \ displaystyle \ | x \ | _ { \ infty } : = \ max \ left ( \ left | x _ { 1 } \ right |, \ ldots, \ left | x _ { n } \ right | \ right ). }


{ \ displaystyle \ left | s _ { n } - \ ell \ right | < \ varepsilon. } if the series is convergent, the ( necessarily unique ) number ℓ { \ displaystyle \ ell } is called the sum of the series. the same notation k = 1 ∞ a k { \ displaystyle \ sum _ { k = 1 } ^ { \ infty } a _ { k } } is used for the series, and, if it is convergent, to its sum. this convention is similar to that which is used for addition : a + b denotes the operation of adding a and b as well as the result of this addition, which is called the sum of a and b. any series that is not convergent is said to be divergent or to diverge.


in the uk, ofcom requires that predictive dialers abandon fewer than 3 % of answered calls on a daily basis. ofcom also requires that if an agent is not available within 2 seconds the call is considered " abandoned " and an automated message is played. the automated message must identify the company making the call, the purpose of the call, a free phone or basic rate phone number to call back on and must not contain any form of marketing. a phone call to the return number must not be treated by the company as an opportunity to market, but to be removed from the calling list.


if the information word consists of n { \ displaystyle n } bits, then the berger code needs k = log 2 ( n + 1 ) { \ displaystyle k = \ lceil \ log _ { 2 } ( n + 1 ) \ rceil } " check bits ", giving a berger code of length k + n. ( in other words, the k { \ displaystyle k } check bits are enough to check up to n = 2 k − 1 { \ displaystyle n = 2 ^ { k } - 1 } information bits ). berger codes can detect any number of one - to - zero bit - flip errors, as long as no zero - to - one errors occurred in the same code word.


in some places and at some times, the one - and two - stroke variants have been used in the same contexts to distinguish between the u. s. dollar and other local currency, such as the former portuguese escudo. however, such usage is not standardized, and furthermore the two versions are generally considered mere graphic variants of the same symbol — a typeface design choice. computer and typewriter keyboards usually have a single key for that sign, and many character encodings ( including ascii and unicode ) reserve a single numeric code for it. indeed, dollar signs in the same digital document may be rendered with one or two strokes, if different computer fonts are used, but the underlying codepoint u + 0024 ( ascii 3610 ) remains unchanged.


electronic news gathering, including live via satellite interviews, reporters'live shots, and sporting events are all examples of radio or television content that is backhauled to a station or network before being made available to the public through that station or network. cable tv channels, particularly public, educational, and government access ( peg ) along with ( local origination ) channels, may also backhauled to cable headends before making their way to the subscriber. finished network feeds are not considered backhauls, even if local insertion is used to modify the content prior to final transmission.


in the case p = 2 { \ displaystyle \ textstyle p = 2 }, the inequality holds with a 2 = b 2 = 1 { \ displaystyle \ textstyle a _ { 2 } = b _ { 2 } = 1 }, and it reduces to the rule for the sum of variances of independent random variables with zero mean, known from elementary statistics : if e ( x i ) = 0 { \ displaystyle \ textstyle e \ left ( x _ { i } \ right ) = 0 } and e ( | x i | 2 ) < + ∞ { \ displaystyle \ textstyle e \ left ( \ left \ vert x _ { i } \ right \ vert ^ { 2 } \ right ) < + \ infty }, then v a r ( i = 1 n x i ) = e ( | i = 1 n x i | 2 ) = i = 1 n j = 1 n e ( x i x j ) = i = 1 n e ( | x i | 2 ) = i = 1 n v a r ( x i ). { \ displaystyle \ mathrm { var } \ left ( \ sum _ { i = 1 } ^ { n } x _ { i } \ right ) = e \ left ( \ left \ vert \ sum _ { i = 1 } ^ { n } x _ { i } \ right \ vert ^ { 2 } \ right ) = \ sum _ { i = 1 } ^ { n } \ sum _ { j = 1 } ^ { n } e \ left ( x _ { i } { \ overline { x } } _ { j } \ right ) = \ sum _ { i = 1 } ^ { n } e \ left ( \ left \ vert x _ { i } \ right \ vert ^ { 2 } \ right ) = \ sum _ { i = 1 } ^ { n } \ mathrm { var } \ left ( x _ { i } \ right ). }


in set theory, an honest leftmost branch of a tree t on ω × γ is a branch ( maximal chain ) ƒ ∈ such that for each branch g ∈, one has n ∈ ω : ƒ ( n ) ≤ g ( n ). here, denotes the set of branches of maximal length of t, ω is the smallest infinite ordinal ( represented by the natural numbers n ), and γ is some other ordinal.


in some countries of europe, the european telecommunications standards institute ( etsi ) standards 200 778 - 1 and - 2 – replacing 300 778 - 1 & - 2 – allow 3 physical transport layers ( telcordia technologies ( formerly bellcore ), british telecom ( bt ) and cable communications association ( cca ) ), combined with 2 data formats multiple data message format ( mdmf ) & single data message format ( sdmf ), plus the dual - tone multi - frequency ( dtmf ) system and a no - ring mode for meter - reading and the like. it's more of a recognition that the different types exist than an attempt to define a single " standard ".


nlrp3, for example, recruits asc adaptor protein via pyd - pyd interaction. both pro - caspase - 1 and asc contain a caspase activation and recruitment domain ( card ), and this homotypic card - card interaction enables autocatalytic cleavage and reassembly of procaspase - 1 to form active caspase - 1. alternatively, nlrc4 can directly recruit pro - caspase - 1, as it has a card instead of a pyd.


moreover, if the original cake is rectangular then each piece is a rectangle. several years after this algorithm has been published, it was proved that envy - free partitions with connected pieces cannot be found by finite protocols. hence, an approximation algorithm is the best that we can hope for in finite time.


in medical diagnosis, test sensitivity is the ability of a test to correctly identify those with the disease ( true positive rate ), whereas test specificity is the ability of the test to correctly identify those without the disease ( true negative rate ). if 100 patients known to have a disease were tested, and 43 test positive, then the test has 43 % sensitivity. if 100 with no disease are tested and 96 return a completely negative result, then the test has 96 % specificity.


in some linux desktop environments a letter with double dots can be produced by pressing shift :, then the letter. when the system has a compose key, the same procedure as that described at x - windows ( below ) may be used.


in telecommunication, a variable length buffer or elastic buffer is a buffer into which data may be entered at one rate and removed at another rate without changing the data sequence. most first - in first - out ( fifo ) storage devices are variable - length buffers in that the input rate may be variable while the output rate is constant or the output rate may be variable while the input rate is constant. various clocking and control systems are used to allow control of underflow or overflow conditions.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2568, 12568, 24568, and 124568 are the patterns related to braille pattern dots - 1456, since the two additional dots of kantenji patterns 01456, 14567, and 014567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


many sources define an elliptic curve to be simply a curve given by an equation of this form. ( when the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non - singular cubic curves ; see § elliptic curves over a general field below. ) an elliptic curve is an abelian variety – that is, it has a group law defined algebraically, with respect to which it is an abelian group – and o serves as the identity element.


given any ideal i { \ displaystyle i } it may occur that it is properly contained in some larger ideal j { \ displaystyle j } with coefficients in the base field of i { \ displaystyle i } ; then j { \ displaystyle j } is called a divisor of i { \ displaystyle i }. in general, a divisor in a ring of partial differential operators need not be principal. the greatest common right divisor ( gcrd ) or sum of two ideals i { \ displaystyle i } and j { \ displaystyle j } is the smallest ideal with the property that both i { \ displaystyle i } and j { \ displaystyle j } are contained in it.


noise exposure and its associated disease burden is likely to increase to a level where the disease burden is similar to that of traffic accidents. the rough estimates do not provide a complete picture of the environmental health burden, because data are uncertain, not all environmental - health relationships are known, not all environmental factors have been included, and it was not possible to assess all potential health effects. the effects of a number of these assumptions were evaluated in an uncertainty analysis.


in quantum teleportation, a sender wishes to transmit an arbitrary quantum state of a particle to a possibly distant receiver. consequently, the teleportation process is a quantum channel. the apparatus for the process itself requires a quantum channel for the transmission of one particle of an entangled - state to the receiver. teleportation occurs by a joint measurement of the sent particle and the remaining entangled particle. this measurement results in classical information which must be sent to the receiver to complete the teleportation. importantly, the classical information can be sent after the quantum channel has ceased to exist.


in addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. two different categories may also be considered " equivalent " for purposes of category theory, even if they do not have precisely the same structure.


in mathematics, the arithmetic – geometric mean of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means : begin the sequences with x and y : then define the two interdependent sequences ( an ) and ( gn ) as these two sequences converge to the same number, the arithmetic – geometric mean of x and y ; it is denoted by m ( x, y ), or sometimes by agm ( x, y ) or agm ( x, y ). the arithmetic – geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing π. the arithmetic – geometric mean can be extended to complex numbers and when the branches of the square root are allowed to be taken inconsistently, it is, in general, a multivalued function.


in phylogenetics, a single - access key ( also called dichotomous key, sequential key, analytical key, or pathway key ) is an identification key where the sequence and structure of identification steps is fixed by the author of the key. at each point in the decision process, multiple alternatives are offered, each leading to a result or a further choice. the alternatives are commonly called " leads ", and the set of leads at a given point a " couplet ". single access keys are closely related to decision trees or self - balancing binary search trees.


in the 1970s and 1980s, attempts were made to build database systems with integrated hardware and software. the underlying philosophy was that such integration would provide higher performance at a lower cost. examples were ibm system / 38, the early offering of teradata, and the britton lee, inc. database machine. another approach to hardware support for database management was icl's cafs accelerator, a hardware disk controller with programmable search capabilities.


in the expression named entity, the word named restricts the task to those entities for which one or many strings, such as words or phrases, stands ( fairly ) consistently for some referent. this is closely related to rigid designators, as defined by kripke, although in practice ner deals with many names and referents that are not philosophically " rigid ". for instance, the automotive company created by henry ford in 1903 can be referred to as ford or ford motor company, although " ford " can refer to many other entities as well ( see ford ). rigid designators include proper names as well as terms for certain biological species and substances, but exclude pronouns ( such as " it " ; see coreference resolution ), descriptions that pick out a referent by its properties ( see also de dicto and de re ), and names for kinds of things as opposed to individuals ( for example " bank " ).


from a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. in a mathematical context, random graph refers almost exclusively to the erdos – renyi random graph model. in other contexts, any graph model may be referred to as a random graph.


disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they are related to other entities. when used as a countable noun, the words ontology and ontologies refer not to the science of being but to theories within the science of being. ontological theories can be divided into various types according to their theoretical commitments. monocategorical ontologies hold that there is only one basic category, but polycategorical ontologies rejected this view. hierarchical ontologies assert that some entities exist on a more fundamental level and that other entities depend on them. flat ontologies, on the other hand, deny such a privileged status to any entity.


in practice, the objective value may be noisy or even non - numerical, and hence its gradient information may be unreliable or unavailable. this is particularly true when the problem is multi - objective. at present, many designs and refinements are mainly made through a manual trial - and - error process with the help of a cad simulation package. usually, such a posteriori learning or adjustments need to be repeated many times until a ‘ satisfactory ’ or ‘ optimal ’ design emerges.


quango ( quasi - autonomous - non - governmental organisation ) is a commonly used acronym to refer to a non - departmental public body. the scottish public bodies is used to indicate all quangos and other organisations in scotland. n. b. an entity described by the undefined term public body is not inevitably a statutory corporation.


in statistics, the gauss – markov theorem ( or simply gauss theorem for some authors ) states that the ordinary least squares ( ols ) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. the errors do not need to be normal, nor do they need to be independent and identically distributed ( only uncorrelated with mean zero and homoscedastic with finite variance ). the requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. see, for example, the james – stein estimator ( which also drops linearity ), ridge regression, or simply any degenerate estimator.


the kernel is usually denoted ker f ( or a variation ). in symbols : ker f = { a ∈ a : f ( a ) = e b }.


in multiprocessing, the processors can be used to execute a single sequence of instructions in multiple contexts ( single instruction, multiple data or simd, often used in vector processing ), multiple sequences of instructions in a single context ( multiple instruction, single data or misd, used for redundancy in fail - safe systems and sometimes applied to describe pipelined processors or hyper - threading ), or multiple sequences of instructions in multiple contexts ( multiple instruction, multiple data or mimd ).


it is important to know which notation is being used when working in different software programs. the respective iso standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10. fractional numbers are rarely displayed in other number bases, but, when they are, a radix character may be used for the same purpose. when used with the binary ( base 2 ) representation, it may be called " binary point ".


in terms of instruction set, arm11 builds on the preceding arm9 generation. it incorporates all arm926ej - s features and adds the armv6 instructions for media support ( simd ) and accelerating irq response. microarchitecture improvements in arm11 cores include : simd instructions which can double mpeg - 4 and audio digital signal processing algorithm speed cache is physically addressed, solving many cache aliasing problems and reducing context switch overhead. unaligned and mixed - endian data access is supported.


the leftmost digit'1'of the result is then discarded. discarding the leftmost'1'is especially convenient on calculators or computers that use a fixed number of digits : there is nowhere for it to go so it is simply lost during the calculation. the nines'complement plus one is known as the ten's complement. the method of complements can be extended to other number bases ( radices ) ; in particular, it is used on most digital computers to perform subtraction, represent negative numbers in base 2 or binary arithmetic and test underflow and overflow in calculation.


rather the program's behavior is undefined. to make a fuzzer more sensitive to failures other than crashes, sanitizers can be used to inject assertions that crash the program when a failure is detected. there are different sanitizers for different kinds of bugs : to detect memory related errors, such as buffer overflows and use - after - free ( using memory debuggers such as addresssanitizer ), to detect race conditions and deadlocks ( threadsanitizer ), to detect undefined behavior ( undefinedbehaviorsanitizer ), to detect memory leaks ( leaksanitizer ), or to check control - flow integrity ( cfisanitizer ). fuzzing can also be used to detect " differential " bugs if a reference implementation is available.


in software engineering, blue – green ( also blue / green ) deployment is a method of installing changes to a web, app, or database server by swapping alternating production and staging servers.


the class separation in a direction w → { \ displaystyle { \ vec { w } } } in this case will be given by s = w → t σ b w → w → t σ w → { \ displaystyle s = { \ frac { { \ vec { w } } ^ { \ mathrm { t } } \ sigma _ { b } { \ vec { w } } } { { \ vec { w } } ^ { \ mathrm { t } } \ sigma { \ vec { w } } } } } this means that when w → { \ displaystyle { \ vec { w } } } is an eigenvector of σ − 1 σ b { \ displaystyle \ sigma ^ { - 1 } \ sigma _ { b } } the separation will be equal to the corresponding eigenvalue. if σ − 1 σ b { \ displaystyle \ sigma ^ { - 1 } \ sigma _ { b } } is diagonalizable, the variability between features will be contained in the subspace spanned by the eigenvectors corresponding to the c − 1 largest eigenvalues ( since σ b { \ displaystyle \ sigma _ { b } } is of rank c − 1 at most ). these eigenvectors are primarily used in feature reduction, as in pca.


in several mathematical areas, generalized distributivity laws are considered. this may involve the weakening of the above conditions or the extension to infinitary operations. especially in order theory one finds numerous important variants of distributivity, some of which include infinitary operations, such as the infinite distributive law ; others being defined in the presence of only one binary operation, such as the according definitions and their relations are given in the article distributivity ( order theory ). this also includes the notion of a completely distributive lattice.


a tensor may be expressed as a linear sum of the tensor product of vector and covector basis elements. the resulting tensor components are labelled by indices of the basis. each index has one possible value per dimension of the underlying vector space.


they are specified within the lmf document. on the contrary, languagecoding, language, partofspeech, commonnoun, writtenform, grammaticalnumber, singular, plural are data categories that are taken from the data category registry. these marks adorn the structure.


in statutory interpretation, it refers to the problem of giving meaning to groups of words where one of the words is ambiguous or inherently unclear. for example, in road traffic law, a statute may require consideration of large vehicles separately from other vehicles. the word large is ambiguous per se, but may be considered heavy.


in mathematics, a diffiety ( ) is a geometrical object which plays the same role in the modern theory of partial differential equations that algebraic varieties play for algebraic equations, that is, to encode the space of solutions in a more conceptual way. the term was coined in 1984 by alexandre mikhailovich vinogradov as portmanteau from differential variety.


the javascript ( e4x ) extension explicitly defines two specific objects ( xml and xmllist ), which support xml document nodes and xml node lists as distinct objects and use a dot - notation specifying parent - child relationships. these data structures represent xml documents as a tree structure. an xml tree represented graphically can be as simple as an ascii chart or a more graphically complex hierarchy.


equating the derivative of the lagrangian with respect to the various probabilities to zero yields a functional form for those probabilities which corresponds to those used in logistic regression. as in the above section on multinomial logistic regression, we will consider m + 1 { \ displaystyle m + 1 } explanatory variables denoted x m { \ displaystyle x _ { m } } and which include x 0 = 1 { \ displaystyle x _ { 0 } = 1 }. there will be a total of k data points, indexed by k = { 1, 2, …, k } { \ displaystyle k = \ { 1, 2, \ dots, k \ } }, and the data points are given by x m k { \ displaystyle x _ { mk } } and y k { \ displaystyle y _ { k } }. the xmk will also be represented as an ( m + 1 ) { \ displaystyle ( m + 1 ) } - dimensional vector x k = { x 0 k, x 1 k, …, x m k } { \ displaystyle { \ boldsymbol { x } } _ { k } = \ { x _ { 0k }, x _ { 1k }, \ dots, x _ { mk } \ } }.


{ \ displaystyle x \ times y. } a binary relation is called a homogeneous relation when x = y. a binary relation is also called a heterogeneous relation when it is not necessary that x = y. since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, and satisfying the laws of an algebra of sets.


in mathematical optimization, the proximal operator is an operator associated with a proper, lower semi - continuous convex function f { \ displaystyle f } from a hilbert space x { \ displaystyle { \ mathcal { x } } } to { \ displaystyle }, and is defined by : prox f ( v ) = arg min x ∈ x ( f ( x ) + 1 2 ‖ x − v ‖ x 2 ). { \ displaystyle \ operatorname { prox } _ { f } ( v ) = \ arg \ min _ { x \ in { \ mathcal { x } } } \ left ( f ( x ) + { \ frac { 1 } { 2 } } \ | x - v \ | _ { \ mathcal { x } } ^ { 2 } \ right ). } for any function in this class, the minimizer of the right - hand side above is unique, hence making the proximal operator well - defined. the proximal operator is used in proximal gradient methods, which is frequently used in optimization algorithms associated with non - differentiable optimization problems such as total variation denoising.


in the examples below, bold denotes the primary stress of the measure, and italics denote a secondary stress. syllables such as " and " are frequently used for pulsing in between numbers. simple : 34 is a simple triple meter time signature that represents three quarter notes ( crotchets ), usually perceived as three beats. in this case the subdivision would be the eighth note ( quaver ). it is felt as 34 : one and two and three and... compound : most often, 68 is felt as two beats, each being a dotted quarter note ( crotchet ), and each containing subdivisions of three eighth notes ( quavers ). it is felt as 68 : one two three four five six... ( or, if counting dotted - quarter beats, one and a two and a ) the table below shows the characteristics of the most frequently used time signatures.


in telephony, multi - frequency signaling ( mf ) is a type of signaling that was introduced by the bell system after world war ii. it uses a combination of audible tones for address ( telephone number ) transport and supervision signaling on trunk lines between central offices. the signaling is sent in - band over the same channel as the bearer channel used for voice traffic.


in microeconomics, quasiconcave utility functions imply that consumers have convex preferences. quasiconvex functions are important also in game theory, industrial organization, and general equilibrium theory, particularly for applications of sion's minimax theorem. generalizing a minimax theorem of john von neumann, sion's theorem is also used in the theory of partial differential equations.


rather, the appearance of any given colorant is inherent to its chemical and physical properties, the purity of such a substance being unrelated to whether it conforms to our arbitrary conception of an ideal hue. moreover, the identity of gamut - optimizing primary colors is determined by the physiology underlying human color vision. although no set of three primary paints can be mixed to obtain the complete color gamut perceived by humans, red, yellow, and blue are a poor choice if high - chroma mixtures are desired.


the powerpc model uses a single fence instruction called the sync instruction. it is similar to the mb instruction, but with a little exception that reads can occur out of program order even if a sync is placed between two reads to the same location.


, a n { \ displaystyle a _ { 1 }, a _ { 2 },..., a _ { n } } of sentences in its language, if a 1, a 2,...


in visual sensor networks ( vsn ), sensors are cameras which record images and video sequences. in many applications of vsn, a camera can't give a perfect illustration including all details of the scene. this is because of the limited depth of focus of the optical lens of cameras.


the term implies that the hidden complexity is at least in principle understandable, in contrast to black magic and deep magic ( see variants ), which describe arcane techniques that are deliberately hidden or extremely difficult to understand. however, the term can also be applied endearingly, suggesting a " charm " about the code. the action of such abstractions is described as being done " automagically ", a portmanteau of " automatically " and " magically ".


in programming and information security, a buffer overflow or buffer overrun is an anomaly whereby a program writes data to a buffer beyond the buffer's allocated memory, overwriting adjacent memory locations. buffers are areas of memory set aside to hold data, often while moving it from one section of a program to another, or between programs. buffer overflows can often be triggered by malformed inputs ; if one assumes all inputs will be smaller than a certain size and the buffer is created to be that size, then an anomalous transaction that produces more data could cause it to write past the end of the buffer. if this overwrites adjacent data or executable code, this may result in erratic program behavior, including memory access errors, incorrect results, and crashes.


the descriptors for degree of substitution, primary, secondary, tertiary, and quaternary, are translated as ( bo ), ( zhong ), ( shu ), ( ji ), which refer to the first, second, third, and fourth male siblings in a family. for instance, tert - butyllithium is translated as (,,, ). other commonly used isomeric descriptors normal -, iso -, and neo - are translated as 正 ( zheng,'proper'), ( yi,'different'), and 新 ( xin,'new'), respectively.


in order to fully test that all the requirements of an application are met, there must be at least two test cases for each requirement : one positive test and one negative test. if a requirement has sub - requirements, each sub - requirement must have at least two test cases. keeping track of the link between the requirement and the test is frequently done using a traceability matrix.


the problem is generally attributed to harold davenport in about 1927, though he did not publish it at the time. davenport did not claim to be its discoverer " because he could not believe that it had not been stated earlier ". the first publication of a version of the birthday problem was by richard von mises in 1939.


then for each γ ∈ s, { \ displaystyle \ gamma \ in s, } γ ∈ c β { \ displaystyle \ gamma \ in c _ { \ beta } } for all β < γ. { \ displaystyle \ beta < \ gamma. } since each c β { \ displaystyle c _ { \ beta } } is closed, α ∈ c β { \ displaystyle \ alpha \ in c _ { \ beta } } for all β < α, { \ displaystyle \ beta < \ alpha, } so α ∈ c.


in positional voting, voters complete a ranked ballot by expressing their preferences in rank order. the rank position of each voter preference is allotted a specific fixed weighting. typically, the higher the rank of the preference, the more points it is worth. occasionally, it may share the same weighting as a lower - ranked preference but it is never worth fewer points.


in terms of the relational model of databases, a table can be considered a convenient representation of a relation, but the two are not strictly equivalent. for instance, a sql table can potentially contain duplicate rows, whereas a true relation cannot contain duplicate rows that we call tuples. similarly, representation as a table implies a particular ordering to the rows and columns, whereas a relation is explicitly unordered.


the cumulants of the sum of the grouped variable and the uniform variable are the sums of the cumulants. as odd cumulants of a uniform distribution are zero ; only even moments are affected. the second and fourth cumulants of the uniform distribution on ( −0. 5c, 0. 5c ) are respectively, c2 / 12 and −c4 / 120. the correction to moments can be derived from the relation between cumulants and moments.


project planning resource leveling is the process of resolving these conflicts. it can also be used to balance the workload of primary resources over the course of the project, usually at the expense of one of the traditional triple constraints ( time, cost, scope ). when using specially designed project software, leveling typically means resolving conflicts or over allocations in the project plan by allowing the software to calculate delays and update tasks automatically.


this implies that each element q i ∈ { 0, 1,..


in order to fall within the obligation for disclosure, the matter must meet three conditions : it must be legal authority, it must be directly adverse, and it must be from a controlling jurisdiction. legal authority the matter for which disclosure is compelled must be a matter of decided law, rather than a mere opinion rendered by an academic. for example, where an attorney is arguing that a certain transfer of assets should be permitted in a bankruptcy proceeding, that attorney need not disclose a law review article, casebook, or op - ed piece in which the author argues that exactly such a transfer of assets should never be permitted. such a writing need not be disclosed even if the author of the article is a leading expert on the area of law, and the article contains strong and well - written arguments in support of the position.


in mathematics, a minkowski plane ( named after hermann minkowski ) is one of the benz planes ( the others being mobius plane and laguerre plane ).


in mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. for example, 1234567890 ( one billion two hundred thirty four million five hundred sixty seven thousand eight hundred ninety ) is a pandigital number in base 10. the first few pandigital base 10 numbers are given by ( sequence a171102 in the oeis ) : 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689the smallest pandigital number in a given base b is an integer of the form b b − 1 + d = 2 b − 1 d b b − 1 − d = b b − b ( b − 1 ) 2 + ( b − 1 ) × b b − 2 − 1 { \ displaystyle b ^ { b - 1 } + \ sum _ { d = 2 } ^ { b - 1 } db ^ { b - 1 - d } = { \ frac { b ^ { b } - b } { ( b - 1 ) ^ { 2 } } } + ( b - 1 ) \ times b ^ { b - 2 } - 1 } the following table lists the smallest pandigital numbers of a few selected bases. oeis : a049363 gives the base 10 values for the first 18 bases.


in statistics, bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. it is defined as δ ( p, q ) = arccos bc ( p, q ) { \ displaystyle \ delta ( p, q ) = \ arccos \ operatorname { bc } ( p, q ) } where pi, qi are the probabilities assigned to the point i, for i = 1,..., n, and bc ( p, q ) = i = 1 n p i q i { \ displaystyle \ operatorname { bc } ( p, q ) = \ sum _ { i = 1 } ^ { n } { \ sqrt { p _ { i } q _ { i } } } } is the bhattacharya coefficient. the bhattacharya distance is the geodesic distance in the orthant of the sphere s n − 1 { \ displaystyle s ^ { n - 1 } } obtained by projecting the probability simplex on the sphere by the transformation p i ↦ p i, i = 1, …, n { \ displaystyle p _ { i } \ mapsto { \ sqrt { p _ { i } } }, \ i = 1, \ ldots, n }. this distance is compatible with fisher metric. it is also related to bures distance and fidelity between quantum states as for two diagonal states one has δ ( ρ, σ ) = arccos f ( ρ, σ ). { \ displaystyle \ delta ( \ rho, \ sigma ) = \ arccos { \ sqrt { f ( \ rho, \ sigma ) } }. }


it is a collaborative effort, developed by sandia national laboratories, los alamos national laboratories, and the united states army research laboratory, and funded by the advanced simulation and computing program. it is developed under a bsd license. pyomo is a python - based optimization mathematical programming language which supports most commercial and open - source solver engines.


{ \ displaystyle \ { 1, 2, 3, \ ldots \ }. } finite sets are particularly important in combinatorics, the mathematical study of counting. many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.


providers of nomadic voip service — those who are unable to determine the location of their users — are exempt from state telecommunications regulation. another legal issue that the us congress is debating concerns changes to the foreign intelligence surveillance act. the issue in question is calls between americans and foreigners. the nsa is not authorized to tap americans'conversations without a warrant — but the internet, and specifically voip does not draw as clear a line to the location of a caller or a call's recipient as the traditional phone system does. as voip's low cost and flexibility convinces more and more organizations to adopt the technology, surveillance for law enforcement agencies becomes more difficult. voip technology has also increased federal security concerns because voip and similar technologies have made it more difficult for the government to determine where a target is physically located when communications are being intercepted, and that creates a whole set of new legal challenges.


in mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. they are also known as the recursive numbers, effective numbers or the computable reals or recursive reals. the concept of a computable real number was introduced by emile borel in 1912, using the intuitive notion of computability available at the time. equivalent definitions can be given using μ - recursive functions, turing machines, or λ - calculus as the formal representation of algorithms. the computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.


), and spruces ( picea spp. ). in some areas of this biome, the conifers may be a more important canopy species than the broadleaf species. in the southern hemisphere, endemic genera such as nothofagus and eucalyptus occupy this biome, and most coniferous trees ( members of the araucariaceae and podocarpaceae ) occur in mixtures with broadleaf species, and are classed as broadleaf and mixed forests.


in mathematics, projections onto convex sets ( pocs ), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. it is a very simple algorithm and has been rediscovered many times. the simplest case, when the sets are affine spaces, was analyzed by john von neumann. the case when the sets are affine spaces is special, since the iterates not only converge to a point in the intersection ( assuming the intersection is non - empty ) but to the orthogonal projection of the point onto the intersection.


it is sometimes denoted rsi - value if the si units are used. an r - value can be given for a material ( e. g. for polyethylene foam ), or for an assembly of materials ( e. g. a wall or a window ). in the case of materials, it is often expressed in terms of r - value per metre.


the researchers estimated that a 1024 - bit rsa modulus would take about 500 times as long. not all numbers of a given length are equally hard to factor. the hardest instances of these problems ( for currently known techniques ) are semiprimes, the product of two prime numbers. when they are both large, for instance more than two thousand bits long, randomly chosen, and about the same size ( but not too close, for example, to avoid efficient factorization by fermat's factorization method ), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical ; that is, as the number of digits of the integer being factored increases, the number of operations required to perform the factorization on any computer increases drastically. many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem — for example, the rsa problem. an algorithm that efficiently factors an arbitrary integer would render rsa - based public - key cryptography insecure.


in the analysis of algorithms, several authors have studied the computation of the volume of high - dimensional convex bodies, a problem that can also be used to model many other problems in combinatorial enumeration. often these works use a black box model of computation in which the input is given by a subroutine for testing whether a point is inside or outside of the convex body, rather than by an explicit listing of the vertices or faces of a convex polytope. it is known that, in this model, no deterministic algorithm can achieve an accurate approximation, and even for an explicit listing of faces or vertices the problem is # p - hard. however, a joint work by martin dyer, alan m. frieze and ravindran kannan provided a randomized polynomial time approximation scheme for the problem, providing a sharp contrast between the capabilities of randomized and deterministic algorithms. the main result of the paper is a randomized algorithm for finding an ε { \ displaystyle \ varepsilon } approximation to the volume of a convex body k { \ displaystyle k } in n { \ displaystyle n } - dimensional euclidean space by assuming the existence of a membership oracle.


in network science, preferential attachment means that nodes of a network tend to connect to those nodes which have more links. if the network is growing and new nodes tend to connect to existing ones with linear probability in the degree of the existing nodes then preferential attachment leads to a scale - free network. if this probability is sub - linear then the network ’ s degree distribution is stretched exponential and hubs are much smaller than in a scale - free network. if this probability is super - linear then almost all nodes are connected to a few hubs.


in mathematics, an open set is a generalization of an open interval in the real line. in a metric space ( a set along with a distance defined between any two points ), an open set is a set that, along with every point p, contains all points that are sufficiently near to p ( that is, all points whose distance to p is less than some value depending on p ). more generally, an open set is a member of a given collection of subsets of a given set, a collection that has the property of containing every union of its members, every finite intersection of its members, the empty set, and the whole set itself. a set in which such a collection is given is called a topological space, and the collection is called a topology.


in mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set. this means that for a uniformly random input string of bits, the probability of getting a 1 is 1 / 2. examples of balanced boolean functions are the function that copies the first bit of its input to the output, and the function that produces the exclusive or of the input bits.


in nature, networks rarely appear in isolation. they are typically elements in larger systems and can have non - trivial effects on one another. for example, infrastructure networks exhibit interdependency to a large degree. the power stations which form the nodes of the power grid require fuel delivered via a network of roads or pipes and are also controlled via the nodes of communications network.


brasch et al. 2012 show how a generalized fibonacci sequence also can be connected to the field of economics. in particular, it is shown how a generalized fibonacci sequence enters the control function of finite - horizon dynamic optimisation problems with one state and one control variable. the procedure is illustrated in an example often referred to as the brock – mirman economic growth model.


relations of this kind are treated in more detail in the section " types of spaces ". it is not always clear whether a given mathematical object should be considered as a geometric " space ", or an algebraic " structure ". a general definition of " structure ", proposed by bourbaki, embraces all common types of spaces, provides a general definition of isomorphism, and justifies the transfer of properties between isomorphic structures.


the state set at input position k is called s ( k ). the parser is seeded with s ( 0 ) consisting of only the top - level rule. the parser then repeatedly executes three operations : prediction, scanning, and completion.


normally, they represent information concerning time ( " @ past ", " @ future ", etc. ), reference ( " @ def ", " @ indef ", etc. ), modality ( " @ can ", " @ must ", etc. ), focus ( " @ topic ", " @ focus ", etc. ), and so on. within the unl program, the process of representing natural language sentences in unl graphs is called unlization, and the process of generating natural language sentences out of unl graphs is called nlization. unlization, which involves natural language analysis and understanding, is intended to be carried out semi - automatically ( i. e., by humans with computer aids ) ; and nlization is intended to be carried out fully automatically.


in network management, fault management is the set of functions that detect, isolate, and correct malfunctions in a telecommunications network, compensate for environmental changes, and include maintaining and examining error logs, accepting and acting on error detection notifications, tracing and identifying faults, carrying out sequences of diagnostics tests, correcting faults, reporting error conditions, and localizing and tracing faults by examining and manipulating database information. when a fault or event occurs, a network component will often send a notification to the network operator using a protocol such as snmp. an alarm is a persistent indication of a fault that clears only when the triggering condition has been resolved. a current list of problems occurring on the network component is often kept in the form of an active alarm list such as is defined in rfc 3877, the alarm mib. a list of cleared faults is also maintained by most network management systems. fault management systems may use complex filtering systems to assign alarms to severity levels.


the natural logarithm has the number e ≈ 2. 718 as its base ; its use is widespread in mathematics and physics, because of its very simple derivative. the binary logarithm uses base 2 and is frequently used in computer science.


in operating systems, a task manager is a system monitor program used to provide information about the processes and applications running on a computer, as well as the general status of the computer. some implementations can also be used to terminate processes and applications, as well as change the processes'scheduling priority. in some environments, users can access a task manager with the control - alt - delete keyboard shortcut. task managers can display running services ( processes ) as well as those that were stopped. they can display information about the services, including their process identifier and group identifier.


the maximum among the conductance of clusters provides a bound which can be used, along with inter - cluster edge weight, to define a measure on the quality of clustering. intuitively, the conductance of a cluster ( which can be seen as a set of vertices in a graph ) should be low. apart from this, the conductance of the subgraph induced by a cluster ( called " internal conductance " ) can be used as well.


{ \ displaystyle \ pr \ left \ geq \ pr \ left. } while this intuitive - seeming result is true for gaussian processes, it is not in general true for other random variables — not even those with expectation 0. as a corollary, if ( x t ) t ≥ 0 { \ displaystyle ( x _ { t } ) _ { t \ geq 0 } } is a centered stationary gaussian process such that e ≥ 0 { \ displaystyle \ operatorname { e } \ geq 0 } for all t { \ displaystyle t }, it holds for any real number c { \ displaystyle c } that pr x t ≤ c ] ≥ pr x t ≤ c ] pr x t ≤ c ], t, s > 0. { \ displaystyle \ pr \ left } x _ { t } \ leq c \ right ] \ geq \ pr \ left } x _ { t } \ leq c \ right ] \ pr \ left } x _ { t } \ leq c \ right ], \ quad t, s > 0. }


another term, used to denote call attempts that fail during the call setup procedure, is blocked calls. the call setup success rate in conventional ( so - called land - line ) networks is extremely high and is significantly above 99. 9 %. in mobile communication systems using radio channels the call setup success rate is lower and may range for commercial networks between 90 % and 98 % or higher.


in mathematics, specifically group theory, given a prime number p, a p - group is a group in which the order of every element is a power of p. that is, for each element g of a p - group g, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. the orders of different elements may be different powers of p. abelian p - groups are also called p - primary or simply primary. a finite group is a p - group if and only if its order ( the number of its elements ) is a power of p. given a finite group g, the sylow theorems guarantee the existence of a subgroup of g of order pn for every prime power pn that divides the order of g. every finite p - group is nilpotent. the remainder of this article deals with finite p - groups. for an example of an infinite abelian p - group, see prufer group, and for an example of an infinite simple p - group, see tarski monster group.


in programming and software development, fuzzing or fuzz testing is an automated software testing technique that involves providing invalid, unexpected, or random data as inputs to a computer program. the program is then monitored for exceptions such as crashes, failing built - in code assertions, or potential memory leaks. typically, fuzzers are used to test programs that take structured inputs.


in the context of telephony, a telephone line ( the system ) typically offers a set of features that include call forwarding and call waiting. call waiting allows one call to be suspended while a second call is answered, while call forwarding enables a customer to specify a secondary phone number to which additional calls will be forwarded in the event that the customer is already using the phone. to illustrate the example, we consider a telephone line provided to a customer, and we assume that both call forwarding and call waiting are enabled on the line. when a first call arrives on the line, the phone rings and is answered.


in phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character - state changes ( or minimizes the cost of differentially weighted character - state changes ). under the maximum - parsimony criterion, the optimal tree will minimize the amount of homoplasy ( i. e., convergent evolution, parallel evolution, and evolutionary reversals ). in other words, under this criterion, the shortest possible tree that explains the data is considered best. some of the basic ideas behind maximum parsimony were presented by james s. farris in 1970 and walter m. fitch in 1971. maximum parsimony is an intuitive and simple criterion, and it is popular for this reason.


in pattern recognition and machine learning, a feature vector is an n - dimensional vector of numerical features that represent some object. many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. when representing images, the feature values might correspond to the pixels of an image, while when representing texts the features might be the frequencies of occurrence of textual terms. feature vectors are equivalent to the vectors of explanatory variables used in statistical procedures such as linear regression.


in spoken language yes / no questions will oftentimes differ in their word order from the statement form. for example, in english : english statement : he will buy the shirt. english yes / no q : will he buy the shirt? in asl, yes / no questions are marked by the non - manual grammatical markings ( as discussed in section 4. 4. 1 ). this eyebrow raise, slight tilt of the head and lean forward are what indicate that a yes / no question is being asked, without any change in word order from the statement form. there is speculation amongst linguists that these non - manual grammatical markings that indicate a yes / no questions are similar to the question intonation of spoken languages. yes / no questions differ from wh - questions as they do not differ in word order from the original statement form of the sentence, whereas wh - questions do.


the examples we choose should stress simple dutifulness. the first of these methods, argues kant, is destined to fail because students will not come to understand the unconditional nature of duty. the examples will also not be very inspiring.


both of these examples use multiple sensors to sample signals and form images based on the manipulation of these multiple signals. processing in multi - dimension ( m - d ) requires more complex algorithms, compared to the 1 - d case, to handle calculations such as the fast fourier transform due to more degrees of freedom. in some cases, m - d signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable.


the order of a group g is denoted by ord ( g ) or | g |, and the order of an element a is denoted by ord ( a ) or | a |, instead of ord ( ⟨ a ⟩ ), { \ displaystyle \ operatorname { ord } ( \ langle a \ rangle ), } where the brackets denote the generated group. lagrange's theorem states that for any subgroup h of a finite group g, the order of the subgroup divides the order of the group ; that is, | h | is a divisor of | g |. in particular, the order | a | of any element is a divisor of | g |.


in order to assess the performance of machine learning models, tensorflow gives api access to commonly used metrics. examples include various accuracy metrics ( binary, categorical, sparse categorical ) along with other metrics such as precision, recall, and intersection - over - union ( iou ).


in mathematical programming and polyhedral combinatorics, the hirsch conjecture is the statement that the edge - vertex graph of an n - facet polytope in d - dimensional euclidean space has diameter no more than n − d. that is, any two vertices of the polytope must be connected to each other by a path of length at most n − d. the conjecture was first put forth in a letter by warren m. hirsch to george b. dantzig in 1957 and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. the conjecture is now known to be false in general. the hirsch conjecture was proven for d < 4 and for various special cases, while the best known upper bounds on the diameter are only sub - exponential in n and d. after more than fifty years, a counter - example was announced in may 2010 by francisco santos leal, from the university of cantabria.


the row is then interpreted as a relvar composed of a set of tuples, with each tuple consisting of the two items : the name of the relevant column and the value this row provides for that column. each column expects a data value of a particular type. for example, one column might require a unique identifier, another might require text representing a person's name, another might require an integer representing hourly pay in dollars.


in the catalan language, sentences consist of a collection of noun phrases grouped around a verb. one of these noun phrases has the syntactic function of subject while the others function as complements ( direct, indirect, prepositional or verbal ), or adverbials ( of time, place, manner, etc. ). the sentence can be introduced by a'frame'( for example'as far as x is concerned ', or an adverbial of time or place ). the main features of the sentence are the agreement in person and number between the subject and the verb - which marks the relation between the speaker, on the one hand, and his or her interlocutors and any other people, on the other - and time, which situates the action in relation to the present of the speaker or in relation to the time of the other sentences of the text or discourse.


thus, recipes for the production of hydrochloric acid only appear in the late sixteenth century, the earliest being found in giovanni battista della porta's ( 1535 – 1615 ) magiae naturalis ( " natural magic " ) and in the works of other contemporary chemists like andreas libavius ( c. 1550 – 1616 ), jean beguin ( 1550 – 1620 ), and oswald croll ( c. 1563 – 1609 ). the knowledge of mineral acids such as hydrochloric acid would be of key importance to seventeenth - century chemists like daniel sennert ( 1572 – 1637 ) and robert boyle ( 1627 – 1691 ), who used their capability to rapidly dissolve metals in their demonstrations of the composite nature of bodies.


- four years study ( 4 b. eng. or b. asc. ) names are traditionally prefixed with the ir.


in mathematics, in particular linear algebra, the bunch – nielsen – sorensen formula, named after james r. bunch, christopher p. nielsen and danny c. sorensen, expresses the eigenvectors of the sum of a symmetric matrix a { \ displaystyle a } and the outer product, v v t { \ displaystyle vv ^ { t } }, of vector v { \ displaystyle v } with itself.


in functional programming, property - based testing has allowed the mathematical specification and testing ( if not exhaustive testing ) of the expected behaviour of individual functions. the object constraint language ( and specializations such as java modeling language ) has allowed object - oriented systems to be formally specified, if not necessarily formally verified.


in the united states, the health insurance portability and accountability act and health information technology for economic and clinical health act require companies to report data breaches to affected individuals and the federal government. health information privacy health insurance portability and accountability act of 1996 ( hipaa ). - 45 cfr parts 160 and 164, standards for privacy of individually identifiable health information and security standards for the protection of electronic protected health information. hipaa includes provisions designed to save health care businesses money by encouraging electronic transactions, as well as regulations to protect the security and confidentiality of patient information.


for example, many early email systems were not 8 - bit clean ; they seemed to transfer typical short text messages properly, but converted " unusual " characters ( the control characters, the " high ascii " characters ) in an irreversible way into some other " usual " character. many of these systems also changed user data in other irreversible ways – such as inserting linefeeds to make sure each line is less than some maximum length, and inserting a " > " at the beginning of every line that begins with " from ". until 8bitmime, a variety of binary - to - text encoding techniques have been overlaid on top of such systems to restore transparency – to make sure that any possible file can be transferred so that the final output " user data " is actually identical to the original user data.


for positive odd primes p, q { \ displaystyle p, q } the solubility of n 2 − p ≡ 0 mod q { \ displaystyle n ^ { 2 } - p \ equiv 0 { \ bmod { q } } } for n { \ displaystyle n } determines the solubility of m 2 − q ≡ 0 mod p { \ displaystyle m ^ { 2 } - q \ equiv 0 { \ bmod { p } } } for m { \ displaystyle m } and vice versa by the comparatively simple criterion whether ( − 1 ) p − 1 2 q − 1 2 { \ displaystyle ( - 1 ) ^ { { \ frac { p - 1 } { 2 } } { \ frac { q - 1 } { 2 } } } } is 1 { \ displaystyle 1 } or − 1 { \ displaystyle - 1 }. by the factor theorem and the behavior of degrees in factorizations the solubility of such quadratic congruence equations is equivalent to the splitting of associated quadratic polynomials over a residue ring into linear factors. in this terminology the law of quadratic reciprocity is stated as follows. for positive odd primes p, q { \ displaystyle p, q } the splitting of the polynomial x 2 − p { \ displaystyle x ^ { 2 } - p } in mod q { \ displaystyle { \ bmod { q } } } - residues determines the splitting of the polynomial x 2 − q { \ displaystyle x ^ { 2 } - q } in mod p { \ displaystyle { \ bmod { p } } } - residues and vice versa through the quantity ( − 1 ) p − 1 2 q − 1 2 ∈ { ± 1 } { \ displaystyle ( - 1 ) ^ { { \ frac { p - 1 } { 2 } } { \ frac { q - 1 } { 2 } } } \ in \ { \ pm 1 \ } }. this establishes the bridge from the name giving reciprocating behavior of primes introduced by legendre to the splitting behavior of polynomials used in the generalizations.


in natural language processing and information retrieval, explicit semantic analysis ( esa ) is a vectoral representation of text ( individual words or entire documents ) that uses a document corpus as a knowledge base. specifically, in esa, a word is represented as a column vector in the tf – idf matrix of the text corpus and a document ( string of words ) is represented as the centroid of the vectors representing its words. typically, the text corpus is english wikipedia, though other corpora including the open directory project have been used. esa was designed by evgeniy gabrilovich and shaul markovitch as a means of improving text categorization and has been used by this pair of researchers to compute what they refer to as " semantic relatedness " by means of cosine similarity between the aforementioned vectors, collectively interpreted as a space of " concepts explicitly defined and described by humans ", where wikipedia articles ( or odp entries, or otherwise titles of documents in the knowledge base corpus ) are equated with concepts. the name " explicit semantic analysis " contrasts with latent semantic analysis ( lsa ), because the use of a knowledge base makes it possible to assign human - readable labels to the concepts that make up the vector space.


in propositional calculus and proof complexity a propositional proof system ( pps ), also called a cook – reckhow propositional proof system, is a system for proving classical propositional tautologies.


in probability theory the hypoexponential distribution or the generalized erlang distribution is a continuous distribution, that has found use in the same fields as the erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes. it is called the hypoexponetial distribution as it has a coefficient of variation less than one, compared to the hyper - exponential distribution which has coefficient of variation greater than one and the exponential distribution which has coefficient of variation of one.


for functions of a single real variable whose graphs have a bounded number of intersection points, the complexity of the lower or upper envelope can be bounded using davenport – schinzel sequences, and these envelopes can be computed efficiently by a divide - and - conquer algorithm that computes and then merges the envelopes of subsets of the functions. for convex functions or quasiconvex functions, the upper envelope is again convex or quasiconvex. the lower envelope is not, but can be replaced by the lower convex envelope to obtain an operation analogous to the lower envelope that maintains convexity.


in number theory, the study of diophantine approximation deals with the approximation of real numbers by rational numbers. it is named after diophantus of alexandria. the first problem was to know how well a real number can be approximated by rational numbers. for this problem, a rational number a / b is a " good " approximation of a real number α if the absolute value of the difference between a / b and α may not decrease if a / b is replaced by another rational number with a smaller denominator.


from the 1980s onwards, critics increasingly refused to ask questions about diegetic elements of the text, instead acknowledging that many elements simply cannot be known definitively. focus shifted away from whether the ghosts were real and onto how james generated and then sustained the text's ambiguity. a study into revisions james made to two paragraphs in the novella concluded that james was not striving for clarity, but to create a text which could not be interpreted definitively in either direction. this is still a position held by many critics, such as giovanni bottiroli, who argues that evidence for the intended ambiguity of the text can be found at the beginning of the novella, where douglas tells his fictional audience that the governess had never told anyone but himself about the events that happened at bly, and that they " would easily judge " why. bottiroli believes that this address to douglas'fictional audience is also meant as an address to the reader, telling them that they will " easily judge " whether or not the ghosts are real.


a major result of complexity theory is that np can be characterized as the problems solvable by probabilistically checkable proofs where the verifier uses o ( log n ) random bits and examines only a constant number of bits of the proof string ( the class pcp ( log n, 1 ) ). more informally, this means that the np verifier described above can be replaced with one that just " spot - checks " a few places in the proof string, and using a limited number of coin flips can determine the correct answer with high probability. this allows several results about the hardness of approximation algorithms to be proven.


in radio networks, the n nodes may in every round choose to either transmit or receive a message. if no collision detection is available, then a node cannot distinguish between silence or receiving more than one message at a time. should collision detection be available, then a node may detect more than one incoming message at the same time, even though the messages itself cannot be decoded in that case. in the beeping model, nodes can only distinguish between silence or at least one message via carrier sensing. known runtimes for single - hop networks range from a constant ( expected with collision detection ) to o ( n log n ) rounds ( deterministic and no collision detection ). in multi - hop networks, known runtimes differ from roughly o ( ( d + log n ) ( log2 log n ) ) rounds ( with high probability in the beeping model ), o ( d log n ) ( deterministic in the beeping model ), o ( n ) ( deterministic with collision detection ) to o ( n log3 / 2 n ( log log n ) 0. 5 ) rounds ( deterministic and no collision detection ).


search engines rank web pages by their expected relevance to a user's query using a combination of query - dependent and query - independent methods. query - independent methods attempt to measure the estimated importance of a page, independent of any consideration of how well it matches the specific query. query - independent ranking is usually based on link analysis ; examples include the hits algorithm, pagerank and trustrank.


in microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. it involves determining the best approach to use when looking for a specific item or person in a sizable, uncharted environment. the goal of the theory is to determine the best search strategy, one that maximises the chance of finding the target while minimising search - related expenses. search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction.


in numerical linear algebra, the rayleigh – ritz method is commonly applied to approximate an eigenvalue problem for the matrix a ∈ c n × n { \ displaystyle a \ in \ mathbb { c } ^ { n \ times n } } of size n { \ displaystyle n } using a projected matrix of a smaller size m < n { \ displaystyle m


it may be used in both wired or wireless communications, so that adjacent frequency bands on the same media can avoid interference. the spectrum can also be licensed for low - power devices such as a private mobile phone network. = = references = =


in the branches of mathematical logic known as proof theory and type theory, a pure type system ( pts ), previously known as a generalized type system ( gts ), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. the framework can be seen as a generalisation of barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a pts with just two sorts. in fact, barendregt ( 1991 ) framed his cube in this setting.


if we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition. for the acceptance of the hypothesis, there are, as we have suggested, quite compelling grounds. the church – turing thesis : stephen kleene, in introduction to metamathematics, finally goes on to formally name " church's thesis " and " turing's thesis ", using his theory of recursive realizability.


for each qubit sent, alice chooses one computational basis state and one hadamard basis state such that the state of the qubit is one of these two states. alice then announces those two states. alice will note whether the state is the computational basis state or the hadamard basis state ; that piece of information makes up the secret bit that alice wishes to communicate to bob.


in some languages, the tilde is a diacritic mark placed over a letter to indicate a change in its pronunciation :


in statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of l p { \ displaystyle l ^ { p } } metrics, and measures of central tendency can be characterized as solutions to variational problems. in penalized regression, " l1 penalty " and " l2 penalty " refer to penalizing either the l 1 { \ displaystyle l ^ { 1 } } norm of a solution's vector of parameter values ( i. e. the sum of its absolute values ), or its l 2 { \ displaystyle l ^ { 2 } } norm ( its euclidean length ). techniques which use an l1 penalty, like lasso, encourage solutions where many parameters are zero. techniques which use an l2 penalty, like ridge regression, encourage solutions where most parameter values are small. elastic net regularization uses a penalty term that is a combination of the l 1 { \ displaystyle l ^ { 1 } } norm and the l 2 { \ displaystyle l ^ { 2 } } norm of the parameter vector.


in the field of database design, a multi - model database is a database management system designed to support multiple data models against a single, integrated backend. in contrast, most database management systems are organized around a single data model that determines how data can be organized, stored, and manipulated. document, graph, relational, and key – value models are examples of data models that may be supported by a multi - model database.


in some models, all operations to different locations are relaxed. a read or write may be reordered with respect to a different read or write in a different location. the weak ordering may be classified under this category and two types of release consistency models ( rcsc and rcpc ) also come under this model. three commercial architectures are also proposed under this category of relaxation : the digital alpha, sparc v9 relaxed memory order ( rmo ), and ibm powerpc models.


in the united states, the environmental protection agency ( epa ) sets performance standards for marine sanitation devices, and the u. s. coast guard ( uscg ) issues regulations governing the design, construction, certification, installation and operation of msds. uscg has certified three kinds of marine sanitation devices.


in number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. a weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. outside of number theory, the term " multiplicative function " is often taken to be synonymous with " completely multiplicative function " as defined in this article.


pgp uses key ids to refer to public keys for a variety of purposes. these are not, properly speaking, fingerprints, since their short length prevents them from being able to securely authenticate a public key. 32bit key ids should not be used as current hardware can generate a colliding 32bit key id in just 4 seconds.


just as in the 2 - component cat code, one needs to stabilize the code in order to prevent bit - flips. the same strategies can be used but are challenging to implement experimentally because higher order non - linearities are required. = = references = =


in order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. the first few steps are listed here. a generator can be found here abacaba is a " quickly growing word ", often described as chiastic or " symmetrically organized around a central axis " ( see : chiastic structure and χ ). the number of members in each iteration is a ( n ) = 2n − 1, the mersenne numbers ( oeis : a000225 ).


let a d { \ displaystyle a _ { d } } denote the set of elements of a { \ displaystyle a } divisible by d { \ displaystyle d } when d { \ displaystyle d } is a product of distinct primes from p { \ displaystyle p }. further let a 1 { \ displaystyle a _ { 1 } } denote a { \ displaystyle a } itself. let z { \ displaystyle z } be a positive real number and p ( z ) { \ displaystyle p ( z ) } denote the product of the primes in p { \ displaystyle p } which are ≤ z { \ displaystyle \ leq z }.


the initial object in the category of bounded lattices is a boolean domain. in computer science, a boolean variable is a variable that takes values in some boolean domain. some programming languages feature reserved words or symbols for the elements of the boolean domain, for example false and true. however, many programming languages do not have a boolean datatype in the strict sense. in c or basic, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1, and all variables that can take these values can also take any other numerical values.


here, a conceptual problem arises. the basic reason is that the income of one institutional unit is the expenditure of another, and the input of one institutional unit is the output of another. if therefore we want to measure the total value - added by all institutional units, we need to devise a consistent procedure for grossing and netting the incomes and outlays of all units, within a system of transactors. lacking such a system, we would end up double counting incomes and expenditures of interacting units, exaggerating the quantity of value - added or investments. to estimate the annual net output of a country, for example, the cost of goods and services used up is deducted from gross revenue, all flows are valued uniformly, and flows which fall outside the production boundary are excluded.


in modern mathematical language, the problem posed on the tablet is the following : a rectangle has area a = 0. 75 and diagonal c = 1. 25. what are the lengths a and b of the sides of the rectangle? the solution can be understood as proceeding in two stages : in stage 1, the quantity c 2 − 2 a { \ displaystyle { \ sqrt { c ^ { 2 } - 2a } } } is computed to be 0. 25. in stage 2, the well - attested old babylonian method of completing the square is used to solve what is effectively the system of equations b − a = 0. 25, ab = 0. 75.


in the internet protocol suite ( tcp / ip ), osi's data link layer functionality is contained within its lowest layer, the link layer. the tcp / ip link layer has the operating scope of the link a host is connected to, and only concerns itself with hardware issues to the point of obtaining hardware ( mac ) addresses for locating hosts on the link and transmitting data frames onto the link. the link - layer functionality was described in rfc 1122 and is defined differently than the data link layer of osi, and encompasses all methods that affect the local link. the tcp / ip model is not a top - down comprehensive design reference for networks.


for instance, this is true of the order polytope of any partially ordered set, a polytope defined by pairwise inequalities between coordinates corresponding to comparable elements in the set. another well - known polytope in combinatorial optimization is the matching polytope. clearly, one seeks for finding matchings algorithmically and one technique is linear programming.


for example, in the word 司 ( sushi ), the two characters are respectively read as su and shi, but the character means " one's natural life span " and 司 means " to administer ", neither of which has anything to do with the food – this is ateji. conversely, in the word ( tabako ) for " tobacco ", the individual kanji respectively mean " smoke " and " herb ", which corresponds to the meaning, while none of their possible readings have a phonetic relationship to the word tabako – this is jukujikun. in some cases, however, the kanji were chosen for both their semantic and phonetic values, a form of phono - semantic matching.


in probability theory and computer science, a log probability is simply a logarithm of a probability. the use of log probabilities means representing probabilities on a logarithmic scale ( − inf, 0 ] { \ displaystyle ( - \ inf, 0 ] }, instead of the standard { \ displaystyle } unit interval. since the probabilities of independent events multiply, and logarithms convert multiplication to addition, log probabilities of independent events add. log probabilities are thus practical for computations, and have an intuitive interpretation in terms of information theory : the negative of the average log probability is the information entropy of an event. similarly, likelihoods are often transformed to the log scale, and the corresponding log - likelihood can be interpreted as the degree to which an event supports a statistical model. the log probability is widely used in implementations of computations with probability, and is studied as a concept in its own right in some applications of information theory, such as natural language processing.


the born rule associates a probability with each unit vector in the hilbert space, in such a way that these probabilities sum to 1 for any set of unit vectors comprising an orthonormal basis. moreover, the probability associated with a unit vector is a function of the density operator and the unit vector, and not of additional information like a choice of basis for that vector to be embedded in. gleason's theorem establishes the converse : all assignments of probabilities to unit vectors ( or, equivalently, to the operators that project onto them ) that satisfy these conditions take the form of applying the born rule to some density operator. gleason's theorem holds if the dimension of the hilbert space is 3 or greater ; counterexamples exist for dimension 2.


because of this, it is less affected by the curse of dimensionality than e. g. a p - dimensional smoother. furthermore, the am is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. problems with am, like many other machine learning methods, include model selection, overfitting, and multicollinearity.


in multi - programming or in a multi - user environment, many users may execute the same program, written so that its code and data are in separate pages. to minimize ram use, all users share a single copy of the program. each process's page table is set up so that the pages that address code point to the single shared copy, while the pages that address data point to different physical pages for each process. different programs might also use the same libraries.


in numerical analysis, the kahan summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite - precision floating - point numbers, compared to the obvious approach. this is done by keeping a separate running compensation ( a variable to accumulate small errors ), in effect extending the precision of the sum by the precision of the compensation variable. in particular, simply summing n { \ displaystyle n } numbers in sequence has a worst - case error that grows proportional to n { \ displaystyle n }, and a root mean square error that grows as n { \ displaystyle { \ sqrt { n } } } for random inputs ( the roundoff errors form a random walk ). with compensated summation, using a compensation variable with sufficiently high precision the worst - case error bound is effectively independent of n { \ displaystyle n }, so a large number of values can be summed with an error that only depends on the floating - point precision of the result. the algorithm is attributed to william kahan ; ivo babuska seems to have come up with a similar algorithm independently ( hence kahan – babuska summation ). similar, earlier techniques are, for example, bresenham's line algorithm, keeping track of the accumulated error in integer operations ( although first documented around the same time ) and the delta - sigma modulation.


in the context of network theory, a complex network is a graph ( network ) with non - trivial topological features — features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. the study of complex networks is a young and active area of scientific research ( since 2000 ) inspired largely by empirical findings of real - world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.


in particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm, bottom, or top quark. this form of matter may exist in a stable form within the core of some neutron stars. hyperons are sometimes generically represented by the symbol y.