for example, the original subroutine call instructions bal, branch and link, and its register - register equivalent, balr, branch and link register, store certain status information, the instruction length code, the condition code and the program mask, in the top byte of the return address. a bas, branch and save, instruction was added to allow 31 - bit return addresses. bas, and its register - register equivalent, basr, branch and save register, was part of the instruction set of the 360 / 67, which was the only system / 360 model to allow addresses longer than 24 bits.


in mathematics, the schwartz – zippel lemma ( also called the demillo – lipton – schwartz – zippel lemma ) is a tool commonly used in probabilistic polynomial identity testing, i. e. in the problem of determining whether a given multivariate polynomial is the 0 - polynomial ( or identically equal to 0 ). it was discovered independently by jack schwartz, richard zippel, and richard demillo and richard j. lipton, although demillo and lipton's version was shown a year prior to schwartz and zippel's result. the finite field version of this bound was proved by øystein ore in 1922.


( we use the transitive closure of { x } rather than of x itself to avoid confusing the elements of x with elements of its elements or whatever. ) a code includes that information identifying x and also information about the particular injection from x into ω which was used to create e. the extra information about the injection is non - essential, so there are many codes for the same set which are equally useful. so codes are a way of mapping h 1 { \ displaystyle h _ { \ aleph _ { 1 } } } into the powerset of ω×ω.


{ \ displaystyle \ nabla \ cdot \ mathbf { h } ( x ) = 0. } as h { \ displaystyle \ mathbf { h } } contains similar terms. the expression ∇ × e ( x ) { \ displaystyle \ nabla \ times \ mathbf { e } ( x ) } contains terms of the form p × 1 ( p ) { \ displaystyle \ mathbf { p } \ times \ mathbf { \ epsilon ^ { 1 } } ( \ mathbf { p } ) } while ∂ h ( x ) / ∂ t { \ displaystyle \ partial \ mathbf { h } ( x ) / \ partial t } contains terms of form i p 0 1 ( p ) { \ displaystyle ip _ { 0 } \ mathbf { \ epsilon ^ { 1 } } ( \ mathbf { p } ) }.


in quantum error correction, css codes, named after their inventors, robert calderbank, peter shor and andrew steane, are a special type of stabilizer code constructed from classical codes with some special properties. an example of a css code is the steane code.


this is exactly analogous to guntsch's system, designed as a means to improve performance, rather than to solve the problems involved in multi - programming. the first true virtual memory system was that implemented at the university of manchester to create a one - level storage system as part of the atlas computer. it used a paging mechanism to map the virtual addresses available to the programmer onto the real memory that consisted of 16, 384 words of primary core memory with an additional 98, 304 words of secondary drum memory.


the codeword for that symbol is the string of " 0 " s and " 1 " s that records which half of the divides it fell on. this method was proposed in a later ( in print ) technical report by fano ( 1949 ). shannon – fano codes are suboptimal in the sense that they do not always achieve the lowest possible expected codeword length, as huffman coding does. however, shannon – fano codes have an expected codeword length within 1 bit of optimal.


in order to interpret the credible sets as confidence sets, a bernstein – von mises theorem is needed. in case of the dirichlet process we compare the posterior distribution with the empirical process p n = 1 n i = 1 n δ x i { \ displaystyle \ mathbb { p } _ { n } = { \ frac { 1 } { n } } \ sum _ { i = 1 } ^ { n } \ delta _ { x _ { i } } }. suppose f { \ displaystyle { \ mathcal { f } } } is a p 0 { \ displaystyle p _ { 0 } } - donsker class, i. e. ( n ) ( p n − p 0 ) g p 0 { \ displaystyle { \ begin { aligned } { \ sqrt { ( } } n ) \ left ( \ mathbb { p } _ { n } - p _ { 0 } \ right ) \ rightsquigarrow g _ { p _ { 0 } } \ end { aligned } } } for some brownian bridge g p 0 { \ displaystyle g _ { p _ { 0 } } }. suppose also that there exists a function f { \ displaystyle f } such that f ( x ) ≥ sup f ∈ f f ( x ) { \ displaystyle f ( x ) \ geq \ sup _ { f \ in { \ mathcal { f } } } f ( x ) } such that f 2 d h < ∞ { \ displaystyle \ int f ^ { 2 } \ mathrm { d } h < \ infty }, then, p 0 { \ displaystyle p _ { 0 } } almost surely n ( p − p n ) | x 1,, x n g p 0. { \ displaystyle { \ sqrt { n } } \ left ( p - \ mathbb { p } _ { n } \ right ) | x _ { 1 }, \ cdots, x _ { n } \ rightsquigarrow g _ { p _ { 0 } }. } this implies that credible sets you construct are asymptotic confidence sets, and the bayesian inference based on the dirichlet process is asymptotically also valid frequentist inference.


in scholarly and academic publishing, scientific and non - fiction books that are released serially ( in successive parts ) once a year, or less often, are also called a series. ( publications that are released more often than once a year are known as periodicals. ) the connection among books belonging to such a series can be by discipline, focus, approach, type of work, or geographic location. examples of such series include the " antwerp working papers in linguistics ", " early english manuscripts in facsimile ", " garland reference library ", " canterbury tales project ", " early english text society ", and " cambridge companions to music ".


if this is done, the data can be shuffled for each pass to prevent cycles. typical implementations may use an adaptive learning rate so that the algorithm converges. in pseudocode, stochastic gradient descent can be presented as : a compromise between computing the true gradient and the gradient at a single sample is to compute the gradient against more than one training sample ( called a " mini - batch " ) at each step. this can perform significantly better than " true " stochastic gradient descent described, because the code can make use of vectorization libraries rather than computing each step separately as was first shown in where it was called " the bunch - mode back - propagation algorithm ".


in mathematical logic, proof compression by recycleunits is a method for compressing propositional logic resolution proofs. its main idea is to make use of intermediate ( e. g. non input ) proof results being unit clauses, i. e. clauses containing only one literal. certain proof nodes can be replaced with the nodes representing these unit clauses. after this operation the obtained graph is transformed into a valid proof. the output proof is shorter than the original while being equivalent or stronger.


in plant anatomy, tissues are categorized broadly into three tissue systems : the epidermis, the ground tissue, and the vascular tissue. epidermis – cells forming the outer surface of the leaves and of the young plant body. vascular tissue – the primary components of vascular tissue are the xylem and phloem.


in mathematics, the hardy – ramanujan theorem, proved by ramanujan and checked by hardy states that the normal order of the number ω ( n ) of distinct prime factors of a number n is log ( log ( n ) ). roughly speaking, this means that most numbers have about this number of distinct prime factors.


{ \ displaystyle ( n, m ) \ in \ times \,. } this defines a permutation on the numbers a = 0, …, m n − 1 { \ displaystyle a = 0, \ ldots, mn - 1 }.


addresses in the process vas are mapped to bytes in the exe file. the os manages the mapping : 0 4 gib vas | - - - vvv - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | mapping | | | file bytes app the v's are values from bytes in the mapped file. then, required dll files are mapped ( this includes custom libraries as well as system ones such as kernel32. dll and user32. dll ) : 0 4 gib vas | - - - vvv - - - - - - - - vvvvvv - - - vvvv - - - - - - - - - - - - - - - - - - - | mapping | | | | | | | | | | | | | file bytes app kernel user the process then starts executing bytes in the exe file.


there are similar arguments for a sanskrit substrate, a greek one, and a substrate underlying the sami languages. relatively clear examples are the finno - ugric languages of the chude and the " volga finns " ( merya, muromian, and meshcheran ) : while unattested, their existence has been noted in medieval chronicles, and one or more of them have left substantial influence in the northern russian dialects. by contrast more contentious cases are the vasconic substratum theory and old european hydronymy, which hypothesize large families of substrate languages across western europe.


early batch systems gave the currently running job the entire computer ; program decks and tapes had to include what we would now think of as operating system code to talk to i / o devices and do whatever other housekeeping was needed. midway through the batch period, after 1957, various groups began to experiment with so - called " load - and - go " systems. these used a monitor program which was always resident on the computer.


in probability theory, the markov – krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known. the result is named after andrey markov and mark krein. the theorem can be used to bound average response times in the m / g / k queueing system. = = references = =


in some languages — particularly, those without garbage collection — the treiber stack can be at risk for the aba problem. when a process is about to remove an element from the stack ( just before the compare and set in the pop routine below ) another process can change the stack such that the head is the same, but the second element is different. the compare and swap will set the head of the stack to the old second element in the stack mixing up the complete data structure. however, the java version on this page is not subject to this problem, because of the stronger guarantees offered by the java runtime ( it is impossible for a newly created, unaliased object reference to be reference - equal to any other reachable object. )


in an 8 - bit code, this allowed the entire range from 0xa0 to 0xff to be used for graphical characters. use of 96 - code sets also meant that the meaning of the bytes 0x20 and 0x7f in the corresponding 7 - bit code could differ from " space " and " delete ", unless the code was in the shift in state. using 96 - code sets for the g0 ( shift in ) set was not made possible. in accordance with this revised 8 - bit iso 2022 code structure, iso 8859 defines sets of characters to be encoded over 0xa0 – ff, in combination with the ascii graphical characters over 0x20 – 7e, and reserves the bytes outside of these ranges for use as non - graphical codes by other specifications such as iso / iec 6429. unicode inherits its first 256 code points from iso 8859 - 1, hence also incorporating a range reserved for a c1 control code set, although it mostly leaves their function to be defined by higher level protocols, with iso / iec 6429 suggested as a default.


if p ~ { \ displaystyle { \ tilde { p } } } is never lucky, then v will reject at phase k + 1. since we have now shown that both ip ⊆ pspace and pspace ⊆ ip, we can conclude that ip = pspace as desired. moreover, we have shown that any ip algorithm may be taken to be public - coin, since the reduction from pspace to ip has this property.


in mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. there are different definitions used in group theory and ring theory.


in mathematics, and more particularly in number theory, primorial, denoted by " # ", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers. the name " primorial ", coined by harvey dubner, draws an analogy to primes similar to the way the name " factorial " relates to factors.


the integers 7 and 10 are coprime, and φ ( 10 ) = 4 { \ displaystyle \ varphi ( 10 ) = 4 }. so euler's theorem yields 7 4 ≡ 1 ( mod 10 ) { \ displaystyle 7 ^ { 4 } \ equiv 1 { \ pmod { 10 } } }, and we get 7 222 ≡ 7 4 × 55 + 2 ≡ ( 7 4 ) 55 × 7 2 ≡ 1 55 × 7 2 ≡ 49 ≡ 9 ( mod 10 ) { \ displaystyle 7 ^ { 222 } \ equiv 7 ^ { 4 \ times 55 + 2 } \ equiv ( 7 ^ { 4 } ) ^ { 55 } \ times 7 ^ { 2 } \ equiv 1 ^ { 55 } \ times 7 ^ { 2 } \ equiv 49 \ equiv 9 { \ pmod { 10 } } }. in general, when reducing a power of a { \ displaystyle a } modulo n { \ displaystyle n } ( where a { \ displaystyle a } and n { \ displaystyle n } are coprime ), one needs to work modulo φ ( n ) { \ displaystyle \ varphi ( n ) } in the exponent of a { \ displaystyle a } : if x ≡ y ( mod φ ( n ) ) { \ displaystyle x \ equiv y { \ pmod { \ varphi ( n ) } } }, then a x ≡ a y ( mod n ) { \ displaystyle a ^ { x } \ equiv a ^ { y } { \ pmod { n } } }. euler's theorem underlies the rsa cryptosystem, which is widely used in internet communications. in this cryptosystem, euler's theorem is used with n being a product of two large prime numbers, and the security of the system is based on the difficulty of factoring such an integer.


in modern computers, binary data refers to any data represented in binary form rather than interpreted on a higher level or converted into some other form. at the lowest level, bits are stored in a bistable device such as a flip - flop. while most binary data has symbolic meaning ( except for don't cares ) not all binary data is numeric.


before system / 360, each computer model often had its own specific devices and programs that could not be used with other systems. buying a bigger cpu also meant buying new printers, card readers, tape drives, etc. in addition, customers would have to rewrite their programs to run on the new cpu, something customers often balked at. with the s / 360, ibm wanted to offer a huge range of computer systems, all sharing a single processor architecture, instruction set, i / o interface, and operating system.


5 of the 9 symbols got erased by the channel. the decoder is still able to reconstruct the message, i. e. the whole puzzle. note that the symbols sent over the channel are not binary.


it starts with a peripheral node and then generates levels r i { \ displaystyle r _ { i } } for i = 1, 2,.. { \ displaystyle i = 1, 2,.. } until all nodes are exhausted. the set r i + 1 { \ displaystyle r _ { i + 1 } } is created from set r i { \ displaystyle r _ { i } } by listing all vertices adjacent to all nodes in r i { \ displaystyle r _ { i } }. these nodes are ordered according to predecessors and degree.


since the 1970s, the subject has been shaped decisively by saharon shelah's stability theory. compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. this has prompted the comment that " if proof theory is about the sacred, then model theory is about the profane ".


in some applications, such as the evaporation of spherical liquid droplets in air, the following correlation is used : n u d = 2 + 0. 4 r e d 1 / 2 p r 1 / 3 { \ displaystyle \ mathrm { nu } _ { d } \ = { 2 } + 0. 4 \, \ mathrm { re } _ { d } ^ { 1 / 2 } \, \ mathrm { pr } ^ { 1 / 3 } \, }


this had been solved earlier by monroe donsker and srinivasa varadhan using a probabilistic path integral method. in another work with herm brascamp in 1976, lieb extended the prekopa - leindler inequality to other types of convex combinations of two positive functions. he strengthened the inequality and the brunn - minkowski inequality by introducing the notion of essential addition.


in model theory, a branch of mathematical logic, the łos – vaught test is a criterion for a theory to be complete, unable to be augmented without becoming inconsistent. for theories in classical logic, this means that for every sentence, the theory contains either the sentence or its negation but not both.


according to music week the song sold a total of 30, 830 equivalent units, placing it at number four on the uk singles downloads chart, and number 28 on the official audio streaming chart. it had sharp drops down the chart and was present in the top 100 for just six weeks. in france, the track debuted at number one on the french singles chart.


diplomatic sources include charters and other legal documents which usually follow a set format. social documents are records created by organizations, such as registers of births and tax records. in historiography, when the study of history is subject to historical scrutiny, a secondary source becomes a primary source. for a biography of a historian, that historian's publications would be primary sources.


in the final analytical step the team discusses its results with management to confirm ( or refute ) assumptions, provide missing information, reveal deficiencies in the organization and establish future priorities.


in some games, extra limitations are added ; for instance : the associations between words must be strictly obvious, rather than the usual " first word that comes to mind ", which can often require explaining to see how it is connected with the previous word. if played in - person, a time limit of two or three seconds can be placed to make a very fast - paced game, often combined with the previous rule of an'explicit'connection, and extra emphasis on the idea that a previously used word cannot be repeated. word disassociation ( sometimes called dissociation ) is sometimes played. in this game, the aim is to say a word that is as unrelated as possible to the previous one.


a client may then receive a " level 2 oplock " from the server. a level 2 oplock allows the caching of read requests but excludes write caching. filter oplocks added in windows nt 4. 0, filter oplocks are similar to level 2 oplocks but prevent sharing - mode violations between file open and lock reception.


in statistics, the gradient of the least - squares regression best - fitting line for a given sample of data may be written as : m = r s y s x { \ displaystyle m = { \ frac { rs _ { y } } { s _ { x } } } }, this quantity m is called as the regression slope for the line y = m x + c { \ displaystyle y = mx + c }. the quantity r { \ displaystyle r } is pearson's correlation coefficient, s y { \ displaystyle s _ { y } } is the standard deviation of the y - values and s x { \ displaystyle s _ { x } } is the standard deviation of the x - values. this may also be written as a ratio of covariances : m = cov ( y, x ) cov ( x, x ) { \ displaystyle m = { \ frac { \ operatorname { cov } ( y, x ) } { \ operatorname { cov } ( x, x ) } } }


in contrast to quantum key distribution where unconditional security can be achieved based only on the laws of quantum physics, in the case of various tasks in mistrustful cryptography there are no - go theorems showing that it is impossible to achieve unconditionally secure protocols based only on the laws of quantum physics. however, some of these tasks can be implemented with unconditional security if the protocols not only exploit quantum mechanics but also special relativity. for example, unconditionally secure quantum bit commitment was shown impossible by mayers and by lo and chau.


the stack must be depth shallow enough for the cpu's available copy instructions. hand - written stack code often uses this approach, and achieves speeds like general - purpose register machines. unfortunately, algorithms for optimal " stack scheduling " are not in wide use by programming languages.


in mathematics, a preradical is a subfunctor of the identity functor in the category of left modules over a ring with identity. the class of all preradicals over r - mod is denoted by r - pr. there is a natural order in r - pr given by, for any two preradicals σ { \ displaystyle \ sigma } and τ { \ displaystyle \ tau }, σ ≤ τ { \ displaystyle \ sigma \ leq \ tau }, if for any left r - module m, σ m ≤ τ m { \ displaystyle \ sigma m \ leq \ tau m }. with this order r - pr becomes a big lattice.


in order to access a record with key c { \ displaystyle c }, a family of hash functions, called collectively a dynamic hash function is applied to the key c { \ displaystyle c }. at any time, at most two hash functions h i { \ displaystyle h _ { i } } and h i + 1 { \ displaystyle h _ { i + 1 } } are used. a typical example uses the division modulo x operation. if the original number of buckets is n { \ displaystyle n }, then the family of hash functions is h i ( c ) ↦ c ( mod n ⋅ 2 i ) { \ displaystyle h _ { i } ( c ) \ mapsto c { \ pmod { n \ cdot 2 ^ { i } } } }


one attempt by germain to prove fermat ’ s last theorem was to let p be a prime number of the form 8k + 7 and to let n = p – 1. in this case, x n + y n = z n { \ displaystyle x ^ { n } + y ^ { n } = z ^ { n } } is unsolvable. germain ’ s proof, however, remained unfinished.


furthermore, insofar as it would be featureless, it could neither be encountered by the senses, nor could its supposition lend additional explanatory power. hero of alexandria challenged the theory in the first century ad, but his attempts to create an artificial vacuum failed. the theory was debated in the context of 17th - century fluid mechanics, by thomas hobbes and robert boyle, among others, and through the early 18th century by sir isaac newton and gottfried leibniz.


( x x ) { \ displaystyle \ lambda x. \! ( x \ ; x ) } can be assigned the type ( ( α → β ) ∩ α ) → β { \ displaystyle ( ( \ alpha \ to \ beta ) \ cap \ alpha ) \ to \ beta } in most intersection type systems, assuming for the term variable x { \ displaystyle x } both the function type α → β { \ displaystyle \ alpha \ to \ beta } and the corresponding argument type α { \ displaystyle \ alpha }.


in mathematics, and more particularly in set theory, a cover ( or covering ) of a set x { \ displaystyle x } is a family of subsets of x { \ displaystyle x } whose union is all of x { \ displaystyle x }. more formally, if c = { u α : α ∈ a } { \ displaystyle c = \ lbrace u _ { \ alpha } : \ alpha \ in a \ rbrace } is an indexed family of subsets u α ⊂ x { \ displaystyle u _ { \ alpha } \ subset x } ( indexed by the set a { \ displaystyle a } ), then c { \ displaystyle c } is a cover of x { \ displaystyle x } if α ∈ a u α = x { \ displaystyle \ bigcup _ { \ alpha \ in a } u _ { \ alpha } = x }. thus the collection { u α : α ∈ a } { \ displaystyle \ lbrace u _ { \ alpha } : \ alpha \ in a \ rbrace } is a cover of x { \ displaystyle x } if each element of x { \ displaystyle x } belongs to at least one of the subsets u α { \ displaystyle u _ { \ alpha } }. a subcover of a cover of a set is a subset of the cover that also covers the set. a cover is called an open cover if each of its elements is an open set.


the conditions of additivity and homogeneity are often combined in the superposition principle f ( α x + β y ) = α f ( x ) + β f ( y ) { \ displaystyle f ( \ alpha x + \ beta y ) = \ alpha f ( x ) + \ beta f ( y ) } an equation written as f ( x ) = c { \ displaystyle f ( x ) = c } is called linear if f ( x ) { \ displaystyle f ( x ) } is a linear map ( as defined above ) and nonlinear otherwise. the equation is called homogeneous if c = 0 { \ displaystyle c = 0 } and f ( x ) { \ displaystyle f ( x ) } is a homogeneous function. the definition f ( x ) = c { \ displaystyle f ( x ) = c } is very general in that x { \ displaystyle x } can be any sensible mathematical object ( number, vector, function, etc. ), and the function f ( x ) { \ displaystyle f ( x ) } can literally be any mapping, including integration or differentiation with associated constraints ( such as boundary values ). if f ( x ) { \ displaystyle f ( x ) } contains differentiation with respect to x { \ displaystyle x }, the result will be a differential equation.


there are guidelines for notification depending on type ; these types include : mail, phone, facsimile, e - mail, media. instructions and mechanics are information provided to the consumer regarding appropriate action for the recall. the instructions include if the product is to be returned, and if so, where and how they should return the product. it is important to consider the recalled drug ’ s place in the market, should the recall lead to market shortages.


resource productivity of the eu is expressed by the amount of gross domestic product ( gdp ) generated per unit of material consumed ( domestic material consumption, see below ), in other words gdp / dmc in euro per kg. this means that less material was consumed in order to produce the same amount of products in the eu. however, breaking down the components of the index it is seen that both gdp and dmc are increasing, only not equally fast.


typically, multidimensional signal processing is directly associated with digital signal processing because its complexity warrants the use of computer modelling and computation. a multidimensional signal is similar to a single dimensional signal as far as manipulations that can be performed, such as sampling, fourier analysis, and filtering. the actual computations of these manipulations grow with the number of dimensions.


thus, from 64 bits in the page table entry, 12 low - order and 12 high - order bits have other uses, leaving 40 bits ( bits 12 though 51 ) for the physical page number. combined with 12 bits of " offset within page " from the linear address, a maximum of 52 bits are available to address physical memory. this allows a maximum ram configuration of 252 bytes, or 4 petabytes ( about 4. 5×1015 bytes ).


in the case where two objects are traveling in parallel directions, the relativistic formula for relative velocity is similar in form to the formula for addition of relativistic velocities. v → b | a = v → b − v → a 1 − v → a v → b c 2 { \ displaystyle { \ vec { v } } _ { \ mathrm { b | a } } = { \ frac { { \ vec { v } } _ { \ mathrm { b } } - { \ vec { v } } _ { \ mathrm { a } } } { 1 - { \ frac { { \ vec { v } } _ { \ mathrm { a } } { \ vec { v } } _ { \ mathrm { b } } } { c ^ { 2 } } } } } } the relative speed is given by the formula : v b | a = | v → b − v → a | 1 − v → a v → b c 2 { \ displaystyle v _ { \ mathrm { b | a } } = { \ frac { \ left | { \ vec { v } } _ { \ mathrm { b } } - { \ vec { v } } _ { \ mathrm { a } } \ right | } { 1 - { \ frac { { \ vec { v } } _ { \ mathrm { a } } { \ vec { v } } _ { \ mathrm { b } } } { c ^ { 2 } } } } } }


even though the units are initially chosen with known probabilities, the nonresponse mechanisms are unknown. for surveys with substantial nonresponse, statisticians have proposed statistical models with which the data sets are analyzed. issues related to survey sampling are discussed in several sources, including salant and dillman ( 1994 ).


it is possible to use segmentation in 32 - bit protected mode as well ( resulting in 48 - bit pointers ) and there exist c language compilers which support that. however segmentation in 32 - bit mode does not allow to access a larger address space than what a single segment would cover, unless some segments are not always present in memory and the linear address space is just used as a cache over a larger segmented virtual space. it allows better protection for access to various objects ( areas up to 1 mb long can benefit from a one - byte access protection granularity, versus the coarse 4 kib granularity offered by sole paging ), and is therefore only used in specialized applications, like telecommunications software. technically, the " flat " 32 - bit address space is a " tiny " memory model for the segmented address space. under both reigns all four segment registers contain one and the same value.


prototypical examples of cancellative semigroups are the positive integers under addition or multiplication. cancellative semigroups are considered to be very close to being groups because cancellability is one of the necessary conditions for a semigroup to be embeddable in a group. moreover, every finite cancellative semigroup is a group. one of the main problems associated with the study of cancellative semigroups is to determine the necessary and sufficient conditions for embedding a cancellative semigroup in a group. the origins of the study of cancellative semigroups can be traced to the first substantial paper on semigroups, ( suschkewitsch 1928 ).


in mathematical group theory, the hall – higman theorem, due to philip hall and graham higman ( 1956, theorem b ), describes the possibilities for the minimal polynomial of an element of prime power order for a representation of a p - solvable group.


in mobile cellular telephony networks like gsm and umts the ss7 application map is used. voice connections are circuit switched ( cs ) and data connections are packet switched ( ps ) applications. some of the gsm / umts circuit switched interfaces in the mobile switching center ( msc ) transported over ss7 include the following : b - > vlr ( uses map / b ). most mscs are associated with a visitor location register ( vlr ), making the b interface " internal ". c - > hlr ( uses map / c ) messages between msc to hlr handled by c interface d - > hlr ( uses map / d ) for attaching to the cs network and location update e - > msc ( uses map / e ) for inter - msc handover f - > eir ( uses map / f ) for equipment identity check h - > sms - g ( uses map / h ) for short message service ( sms ) over cs i - > me ( uses map / i ) messages between msc to me handled by i interface j - > scf ( uses map / j ) messages between hlr to gsmscf handled by j interface there are also several gsm / umts ps interfaces in the serving gprs support node ( sgsn ) transported over ss7 : gr - > hlr for attaching to the ps network and location update gd - > sms - c for sms over ps gs - > msc for combined cs + ps signaling over ps ge - > charging for customised applications for mobile networks enhanced logic ( camel ) prepaid charging gf - > eir for equipment identity check = = references = =


in mathematics, the cake number, denoted by cn, is the maximum of the number of regions into which a 3 - dimensional cube can be partitioned by exactly n planes. the cake number is so - called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube - shaped cake. it is the 3d analogue of the lazy caterer's sequence. the values of cn for n = 0, 1, 2,... are given by 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232,... ( sequence a000125 in the oeis ).


in the following simple stack implementation in java, each element popped from the stack becomes semantic garbage once there are no outside references to it : this is because elements still contains a reference to the object, but the object will never be accessed again through this reference, because elements is private to the class and the pop method only returns references to elements it has not already popped. ( after it decrements size, this class will never access that element again. ) however, knowing this requires analysis of the code of the class, which is undecidable in general. if a later push call re - grows the stack to the previous size, overwriting this last reference, then the object will become syntactic garbage, because it can never be accessed again, and will be eligible for garbage collection.


in order to acquire the world's demand for wood, it is suggested that high yielding forest plantations are suitable according to forest writers botkins and sedjo. plantations that yield 10 cubic meters per hectare a year would supply enough wood for trading of 5 % of the world's existing forestland. by contrast, natural forests produce about 1 – 2 cubic meters per hectare ; therefore, 5 – 10 times more forestland would be required to meet demand.


in mathematics, a permutation group is a group g whose elements are permutations of a given set m and whose group operation is the composition of permutations in g ( which are thought of as bijective functions from the set m to itself ). the group of all permutations of a set m is the symmetric group of m, often written as sym ( m ). the term permutation group thus means a subgroup of the symmetric group. if m = { 1, 2,..., n } then sym ( m ) is usually denoted by sn, and may be called the symmetric group on n letters.


coset enumeration is usually considered to be one of the fundamental problems in computational group theory. the original algorithm for coset enumeration was invented by john arthur todd and h. s. m. coxeter. various improvements to the original todd – coxeter algorithm have been suggested, notably the classical strategies of v. felsch and hlt ( haselgrove, leech and trotter ).


in proof by contradiction, also known by the latin phrase reductio ad absurdum ( by reduction to the absurd ), it is shown that if some statement is assumed true, a logical contradiction occurs, hence the statement must be false. a famous example involves the proof that 2 { \ displaystyle { \ sqrt { 2 } } } is an irrational number : suppose that 2 { \ displaystyle { \ sqrt { 2 } } } were a rational number. then it could be written in lowest terms as 2 = a b { \ displaystyle { \ sqrt { 2 } } = { a \ over b } } where a and b are non - zero integers with no common factor. thus, b 2 = a { \ displaystyle b { \ sqrt { 2 } } = a }.


in order to address the issues presented by memorization and security many businesses and internet sites have turned to accepting different types of authentication. this authentication could be a single use password, non - text based, biometric, a 2d key, multi - factor authentication, or cognitive passwords that are question based. many of these options are more expensive, time consuming or still require some form of memorization. thus, most businesses and individuals still use the common format of single word and text - based passwords as security protection.


in specifying a regular expression, alternate delimiters may also be used to simplify the syntax for match and substitution operations in perl. for example, a simple match operation may be specified in perl with the following syntax : the syntax is flexible enough to specify match operations with alternate delimiters, making it easy to avoid delimiter collision :


in number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. consequently, any prime number that divides a does not divide b, and vice versa. this is equivalent to their greatest common divisor ( gcd ) being 1.


cello, another early browser, also had bookmarking features. with the advent of social bookmarking, shared bookmarks have become a means for users sharing similar interests to pool web resources, or to store their bookmarks in such a way that they are not tied to one specific computer or browser. web - based bookmarking services let users save bookmarks on a remote web server, accessible from anywhere.


in fact, turing's machine does this — it prints on alternate squares, leaving blanks between figures so it can print locator symbols. turing always left alternate squares blank so his machine could place a symbol to the left of a figure ( or a letter if the machine is the universal machine and the scanned square is actually in the “ program ” ). in our little example we will forego this and just put symbols ( ) around the scanned symbol, as follows : let us write a simple program : start : p1, r, p1, r, p1, h remember that we always start with blank tape.


itself. this check can be restricted to seeds involved by s, i. e. this drawback can be avoided by requiring that the distribution of { z 1, …, z m | s = s } { \ displaystyle \ { z _ { 1 }, \ ldots, z _ { m } | s = s \ } } is independent of?. an easy way to check this property is by mapping seed specifications into x i { \ displaystyle x _ { i } } s specifications. the mapping of course depends on?, but the distribution of { x 1, …, x m | s = s } { \ displaystyle \ { x _ { 1 }, \ ldots, x _ { m } | s = s \ } } will not depend on?, if the above seed independence holds – a condition that looks like a local sufficiency of the statistic s. the remainder of the present article is mainly concerned with the context of data mining procedures applied to statistical inference and, in particular, to the group of computationally intensive procedure that have been called algorithmic inference.


for example, r ( x ) { \ displaystyle r ( { \ textbf { x } } ) } may be one or more linear combinations of x { \ displaystyle { \ textbf { x } } }. a dimension reduction r ( x ) { \ displaystyle r ( { \ textbf { x } } ) } is said to be sufficient if the distribution of y r ( x ) { \ displaystyle y \ mid r ( { \ textbf { x } } ) } is the same as that of y x { \ displaystyle y \ mid { \ textbf { x } } }. in other words, no information about the regression is lost in reducing the dimension of x { \ displaystyle { \ textbf { x } } } if the reduction is sufficient.


in probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non - zero skewness.


in one dimension, generalized balanced ternary is equivalent to standard balanced ternary, with three digits ( 0, 1, and - 1 ). b { \ displaystyle b } is a 1 × 1 { \ displaystyle 1 \ times 1 } matrix, and the digits d i { \ displaystyle d _ { i } } are length - 1 vectors, so they appear here without the extra brackets.


in statistics, ordinary least squares ( ols ) is a type of linear least squares method for choosing the unknown parameters in a linear regression model ( with fixed level - one effects of a linear function of a set of explanatory variables ) by the principle of least squares : minimizing the sum of the squares of the differences between the observed dependent variable ( values of the variable being observed ) in the input dataset and the output of the ( linear ) function of the independent variable. geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface — the smaller the differences, the better the model fits the data. the resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation.


at this point, the above equation looks like this : ln ( k ∈ k ⊂ z 0 + 1 + 2 − k ) = k ∈ k ⊂ z 0 + ln ( 1 + 2 − k ) { \ displaystyle \ ln \ left ( \ prod _ { k \ in k \ subset \ mathbb { z } _ { 0 } ^ { + } } 1 + 2 ^ { - k } \ right ) = \ sum _ { k \ in k \ subset \ mathbb { z } _ { 0 } ^ { + } } \ ln ( 1 + 2 ^ { - k } ) } this choice of a k { \ displaystyle a _ { k } } reduces the computational complexity of the product from repeated multiplication to simple addition and bit - shifting depending on the implementation. finally, by storing the values ln ( 1 + 2 − k ) { \ displaystyle \ ln ( 1 + 2 ^ { - k } ) } in a table, calculating the solution is also a simple matter of addition. iteratively, this gives us two separate sequences.


in mathematics, an information source is a sequence of random variables ranging over a finite alphabet γ, having a stationary distribution. the uncertainty, or entropy rate, of an information source is defined as h { x } = lim n → ∞ h ( x n | x 0, x 1, …, x n − 1 ) { \ displaystyle h \ { \ mathbf { x } \ } = \ lim _ { n \ to \ infty } h ( x _ { n } | x _ { 0 }, x _ { 1 }, \ dots, x _ { n - 1 } ) } where x 0, x 1, …, x n { \ displaystyle x _ { 0 }, x _ { 1 }, \ dots, x _ { n } } is the sequence of random variables defining the information source, and h ( x n | x 0, x 1, …, x n − 1 ) { \ displaystyle h ( x _ { n } | x _ { 0 }, x _ { 1 }, \ dots, x _ { n - 1 } ) } is the conditional information entropy of the sequence of random variables. equivalently, one has h { x } = lim n → ∞ h ( x 0, x 1, …, x n − 1, x n ) n + 1. { \ displaystyle h \ { \ mathbf { x } \ } = \ lim _ { n \ to \ infty } { \ frac { h ( x _ { 0 }, x _ { 1 }, \ dots, x _ { n - 1 }, x _ { n } ) } { n + 1 } }. }


for a hyperedge e ∈ e { \ displaystyle e \ in { \ mathcal { e } } }, set χ ( e ) : = v ∈ e χ ( v ). { \ displaystyle \ chi ( e ) : = \ sum _ { v \ in e } \ chi ( v ). } the discrepancy of h { \ displaystyle { \ mathcal { h } } } with respect to χ { \ displaystyle \ chi } and the discrepancy of h { \ displaystyle { \ mathcal { h } } } are defined by disc ( h, χ ) : = max e ∈ e | χ ( e ) |, { \ displaystyle \ operatorname { disc } ( { \ mathcal { h } }, \ chi ) : = \ ; \ max _ { e \ in { \ mathcal { e } } } | \ chi ( e ) |, } disc ( h ) : = min χ : v → { − 1, + 1 } disc ( h, χ ).


with this strategy, if a ranks ahead of b and c ( which compare equal ) which are both ranked ahead of d, then a gets ranking number 1 ( " first " ) and d gets ranking number 4 ( " fourth " ), and either b gets ranking number 2 ( " second " ) and c gets ranking number 3 ( " third " ) or c gets ranking number 2 ( " second " ) and b gets ranking number 3 ( " third " ). in computer data processing, ordinal ranking is also referred to as " row numbering ". this method corresponds to the " first ", " last ", and " random " methods in the r programming language to handle ties.


mips cores can be found in newer cisco, linksys and mikrotik's routerboard routers, cable modems and asymmetric digital subscriber line ( adsl ) modems, smartcards, laser printer engines, set - top boxes, robots, and hand - held computers. in cellphones and pdas, mips has been largely unable to displace the incumbent, competing arm architecture. mips architecture processors include : idt rc32438 ; ati / amd xilleon ; alchemy au1000, 1100, 1200 ; broadcom sentry5 ; rmi xlr7xx, cavium octeon cn30xx, cn31xx, cn36xx, cn38xx and cn5xxx ; infineon technologies easyport, amazon, danube, adm5120, wildpass, inca - ip, inca - ip2 ; microchip technology pic32 ; nec emma and emma2, nec vr4181a, vr4121, vr4122, vr4181a, vr4300, vr5432, vr5500 ; oak technologies generation ; pmc - sierra rm11200 ; quicklogic quickmips esp ; toshiba donau, toshiba tmpr492x, tx4925, tx9956, tx7901 ; komdiv - 32, komdiv - 64, elvees multicore from russia.


in telecommunication, a paired disparity code is a line code in which at least one of the data characters is represented by two codewords of opposite disparity that are used in sequence so as to minimize the total disparity of a longer sequence of digits. a particular codeword of any line code can either have no disparity ( the average weight of the codeword is zero ), negative disparity ( the average weight of the codeword is negative ), or positive disparity ( the average weight of the codeword is positive ). in a paired disparity code, every codeword that averages to a negative level ( negative disparity ) is paired with some other codeword that averages to a positive level ( positive disparity ). in a system that uses a paired disparity code, the transmitter must keep track of the running dc buildup – the running disparity – and always pick the codeword that pushes the dc level back towards zero.


in mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. combinatorial explosion is sometimes used to justify the intractability of certain problems. examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the ackermann function.


in modern computing practice, unicode is the standard and default method for character encoding. however, unicode itself and many legacy applications have echoes of earlier practices. furthermore, the limited character set provided by computer keyboards has also required practical and pragmatic adjustments. these issues are detailed below.


also p ( r n w ) { \ displaystyle p ( r _ { n } \ mid w ) } is the probability that player 1 experiences gambler's ruin having started with n + 1 { \ displaystyle n + 1 } amount of money : p ( r n + 1 ) { \ displaystyle p ( r _ { n + 1 } ) } ; and p ( r n w ) { \ displaystyle p ( r _ { n } \ mid { \ bar { w } } ) } is the probability that player 1 experiences gambler's ruin having started with n − 1 { \ displaystyle n - 1 } amount of money : p ( r n − 1 ) { \ displaystyle p ( r _ { n - 1 } ) }. denoting q n = p ( r n ) { \ displaystyle q _ { n } = p ( r _ { n } ) }, we get the linear homogeneous recurrence relation q n = q n + 1 p + q n − 1 q, { \ displaystyle q _ { n } = q _ { n + 1 } p + q _ { n - 1 } q, } which we can solve using the fact that q 0 = 1 { \ displaystyle q _ { 0 } = 1 } ( i. e. the probability of gambler's ruin given that player 1 starts with no money is 1 ), and q n 1 + n 2 = 0 { \ displaystyle q _ { n _ { 1 } + n _ { 2 } } = 0 } ( i. e. the probability of gambler's ruin given that player 1 starts with all the money is 0. ) for a more detailed description of the method see e. g. feller ( 1970 ), an introduction to probability theory and its applications, 3rd ed.


in the case of the lf logical framework, the meta - language is the λπ - calculus. this is a system of first - order dependent function types which are related by the propositions as types principle to first - order minimal logic. the key features of the λπ - calculus are that it consists of entities of three levels : objects, types and kinds ( or type classes, or families of types ). it is predicative, all well - typed terms are strongly normalizing and church - rosser and the property of being well - typed is decidable.


in mathematics, gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. it consists of a sequence of operations performed on the corresponding matrix of coefficients. this method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. the method is named after carl friedrich gauss ( 1777 – 1855 ).


a move defines endpoints for a data transport taking place in a transport bus. for instance, a move can state that a data transport from function unit f, port 1, to register file r, register index 2, should take place in bus b1. in case there are multiple buses in the target processor, each bus can be utilized in parallel in the same clock cycle.


in technical terms, palatalization refers to the secondary articulation of consonants by which the body of the tongue is raised toward the hard palate and the alveolar ridge during the articulation of the consonant. such consonants are phonetically palatalized. " pure " palatalization is a modification to the articulation of a consonant, where the middle of the tongue is raised, and nothing else. it may produce a laminal articulation of otherwise apical consonants such as / t / and / s /.


in most applications of protocol spoofing, a communications device such as a modem or router simulates ( " spoofs " ) the remote endpoint of a connection to a locally attached host, while using a more appropriate protocol to communicate with a compatible remote device that performs the equivalent spoof at the other end of the communications link.


this specification is long, however 2 key points relating to the tree structure of an xml document are : the begin, end, and empty - element tags that delimit the elements are correctly nested, with none missing and none overlapping a single " root " element contains all the other elementsthese features resemble those of trees, in that there is a single root node, and an order to the elements. xml has appeared as a first - class data type in other languages.


when thus organized, residuated lattices form an equational class or variety, whose homomorphisms respect the residuals as well as the lattice and monoid operations. note that distributivity x • ( y ∨ z ) = ( x • y ) ∨ ( x • z ) and x • 0 = 0 are consequences of these axioms and so do not need to be made part of the definition.


in sequence modeling, the graph of interest is usually a chain graph. an input sequence of observed variables x { \ displaystyle x } represents a sequence of observations and y { \ displaystyle y } represents a hidden ( or unknown ) state variable that needs to be inferred given the observations. the y i { \ displaystyle y _ { i } } are structured to form a chain, with an edge between each y i − 1 { \ displaystyle y _ { i - 1 } } and y i { \ displaystyle y _ { i } }. as well as having a simple interpretation of the y i { \ displaystyle y _ { i } } as " labels " for each element in the input sequence, this layout admits efficient algorithms for : model training, learning the conditional distributions between the y i { \ displaystyle y _ { i } } and feature functions from some corpus of training data.


in the united states, bridge weight limits for trucks and other heavy vehicles may be expressed in terms of gross vehicle weight or empty weight.


{ \ displaystyle \ mu _ { r _ { 0 } } ^ { \ text { g } } ( \ mathbf { x } - { \ hat { \ mathbf { x } } } _ { j } ) = { \ frac { 1 } { ( 2 \ pi r _ { 0 } ^ { 2 } ) ^ { 3 / 2 } } } \, \ exp \ left ( - { \ frac { ( \ mathbf { x } - { \ hat { \ mathbf { x } } } _ { j } ) ^ { 2 } } { 2r _ { 0 } ^ { 2 } } } \ right ). } choosing one or another distribution μ r 0 ( x − x ^ j ) { \ displaystyle \ mu _ { r _ { 0 } } ( \ mathbf { x } - { \ hat { \ mathbf { x } } } _ { j } ) } does not affect significantly the predictions of the model, as long as the same value for r 0 { \ displaystyle r _ { 0 } } is considered.


the loss function could include terms from several levels of the hierarchy. in statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. the concept, as old as laplace, was reintroduced in statistics by abraham wald in the middle of the 20th century.


in some cases the iterates converge but do not converge as quickly as promised. in these cases simpler methods converge just as quickly as newton's method.


in the calculus of variations and classical mechanics, the euler – lagrange equations are a system of second - order ordinary differential equations whose solutions are stationary points of the given action functional. the equations were discovered in the 1750s by swiss mathematician leonhard euler and italian mathematician joseph - louis lagrange. because a differentiable functional is stationary at its local extrema, the euler – lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. this is analogous to fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero.


in quantum information, the diamond norm, also known as completely bounded trace norm, is a norm on the space of quantum operations, or more generally on any linear map that acts on complex matrices. its main application is to measure the " single use distinguishability " of two quantum channels. if an agent is randomly given one of two quantum channels, permitted to pass one state through the unknown channel, and then measures the state in an attempt to determine which operation they were given, then their maximal probability of success is determined by the diamond norm of the difference of the two channels. although the diamond norm can be efficiently computed via semidefinite programming, it is in general difficult to obtain analytical expressions and those are known only for a few particular cases.


the base code rate is typically given as n / k { \ displaystyle n / k }, where n is the raw input data rate and k is the data rate of output channel encoded stream. n is less than k because channel coding inserts redundancy in the input bits. the memory is often called the " constraint length " k, where the output is a function of the current input as well as the previous k − 1 { \ displaystyle k - 1 } inputs.


first, it takes up the idea of considering the event giving rise to the right to compensation, starting from the nature of the interest affected. moreover, there is an astonishing resemblance between the respective formulations : § 823 paragraph 1 bgb is supposed to protect the integrity of property and persons by granting protection " to life, body, health, freedom, to property ". starck, for his part, claims " a right to life, to bodily integrity and to the material integrity of the objects belonging to us ". finally, on both sides, it is with the same arguments, such as the need to protect the freedom to act, that a less intense protection of purely economic and moral interests is justified. nevertheless, boris starck departs from the german model by raising the protection of physical integrity by a notch, believing that the only breach here generates a right to compensation.


the predicate added to each new test class is the precondition of one of the terms in the operation's predicate. standard partitions ( sp ).


in the final step, the linguist checks to see how the proto - phonemes fit the known typological constraints. for example, a hypothetical system, has only one voiced stop, * b, and although it has an alveolar and a velar nasal, * n and * ŋ, there is no corresponding labial nasal. however, languages generally maintain symmetry in their phonemic inventories. in this case, a linguist might attempt to investigate the possibilities that either what was earlier reconstructed as * b is in fact * m or that the * n and * ŋ are in fact * d and * g. even a symmetrical system can be typologically suspicious.


in number theory, znam's problem asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. znam's problem is named after the slovak mathematician stefan znam, who suggested it in 1972, although other mathematicians had considered similar problems around the same time. the initial terms of sylvester's sequence almost solve this problem, except that the last chosen term equals one plus the product of the others, rather than being a proper divisor. sun ( 1983 ) showed that there is at least one solution to the ( proper ) znam problem for each k ≥ 5 { \ displaystyle k \ geq 5 }.


in mathematics, the dimension of a vector space v is the cardinality ( i. e., the number of vectors ) of a basis of v over its base field. it is sometimes called hamel dimension ( after georg hamel ) or algebraic dimension to distinguish it from other types of dimension. for every vector space there exists a basis, and all bases of a vector space have equal cardinality ; as a result, the dimension of a vector space is uniquely defined.


in statistical physics, phase transitions can only appear in many particle systems. though phase transitions are well known in network science, in single networks they are second order only. with the introduction of internetwork dependency, first order transitions emerge. this is a new phenomenon and one with profound implications for systems engineering. where system dissolution takes place after steady ( if steep ) degradation for second order transitions, the existence of a first order transition implies that the system can go from a relatively healthy state to complete collapse with no advanced warning.


other variations on the concept include being able to listen to the past but not view it. one reason authors may choose to write about time viewers rather than time machines is to circumvent the issue of temporal paradoxes. recurring applications include studying history, solving crimes, and entertainment in the form of displaying historic events to an audience.


in numerical linear algebra, an incomplete lu factorization ( abbreviated as ilu ) of a matrix is a sparse approximation of the lu factorization often used as a preconditioner.


consequently, apart from the provisions of this convention, the extent of protection, as well as the means of redress afforded to the author to protect his rights, shall be governed exclusively by the laws of the country where protection is claimed. — berne convention, article 5 ( 2 ). this specifies national treatment, and also makes the existence of copyright on a work in one country independent from the existence of copyright on the work in other countries ( lex loci protectionis ). a wipo study in 2011 recommended that « the difficulty of the rule of the comparison of terms applicable to the duration for protection, as provided by article 7 ( 8 ) of the berne convention, should at least be assessed ».


beyond the cardinalities given by each of the natural numbers, there is an infinite hierarchy of infinite cardinalities, although only very few such cardinalities occur in ordinary mathematics ( that is, outside set theory that explicitly studies possible cardinalities ). counting, mostly of finite sets, has various applications in mathematics.


in representation theory, a branch of mathematics, the kostant partition function, introduced by bertram kostant ( 1958, 1959 ), of a root system δ { \ displaystyle \ delta } is the number of ways one can represent a vector ( weight ) as a non - negative integer linear combination of the positive roots δ + ⊂ δ { \ displaystyle \ delta ^ { + } \ subset \ delta }. kostant used it to rewrite the weyl character formula as a formula ( the kostant multiplicity formula ) for the multiplicity of a weight of an irreducible representation of a semisimple lie algebra. an alternative formula, that is more computationally efficient in some cases, is freudenthal's formula. the kostant partition function can also be defined for kac – moody algebras and has similar properties.


0 3 8 1 6 11 4 9 2 7 0 4 8 | 0 4 8 0 4 8 0 4 8 0 4 8 0 3 9 | 0 3 6 9 0 3 6 9 0 3 6 9 0 2 10 | 0 2 4 6 8 10 0 2 4 6 8 10 0 1 11 | 0 1 2 3 4 5 6 7 8 9 10 11 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 source :


in most popular programming languages, source code is delivered and deployed in granules of functionality which we will here call packages ; actual terminology for this concept varies between language. each package may contain multiple type, value, and function definitions, packages are often compiled separately in languages with a compilation step, and a non - cyclical dependency relationship may exist. a complete program is a set of packages, with a main package which may depend on several other packages, and the whole program consisting of the transitive closure of the dependency relationship. the so - called expression problem relates to the ability for code in a depending package to extend behaviors ( functions or datatypes ) defined in a base package from within an including package, without modifying the source to the base package.


information on virulence factors can be obtained from the usage of the provided browser tool. once the browser tool is used, the results are returned as a readable table that is organized by ascending e - values, each of which are hyperlinked to their related page. mvirdb is implemented in an oracle 10g relational database.


uws are intended to represent universal concepts, but are expressed in english words or in any other natural language in order to be humanly readable. they consist of a " headword " ( the uw root ) and a " constraint list " ( the uw suffix between parentheses ), where the constraints are used to disambiguate the general concept conveyed by the headword. the set of uws is organized in the unl ontology, in which high - level concepts are related to lower - level ones through the relations " icl " ( = is a kind of ), " iof " ( = is an instance of ) and " equ " ( = is equal to ).


in practice, optimization ( and searching, and learning ) problems are often np - hard, complex, and time - consuming. two major approaches are traditionally used to tackle these problems : exact methods and metaheuristics. exact methods allow to find exact solutions but are often impractical as they are extremely time - consuming for real - world problems ( large dimension, hardly constrained, multimodal, time - varying, epistatic problems ). conversely, metaheuristics provide sub - optimal ( sometimes optimal ) solutions in a reasonable time.


forester chad oliver has suggested a forest mosaic with high - yield forest lands interspersed with conservation land. plantation forests cover about 131 million ha, which is 3 percent of the global forest area and 45 percent of the total area of planted forests. globally, planted forests increased from 4. 1 % to 7. 0 % of the total forest area between 1990 and 2015. plantation forests made up 280 million ha in 2015, an increase of about 40 million ha in the last ten years. globally, planted forests consist of about 18 % exotic or introduced species while the rest are species native to the country where they are planted.


a logical system l { \ displaystyle { \ mathcal { l } } } is represented by its signature which assigns kinds and types to a finite set of constants that represents its syntax, its judgements and its rule schemes. an object - logic's rules and proofs are seen as primitive proofs of hypothetico - general judgements λ x ∈ c.


however this theoretical approach was widely considered unattainable, since the taniyama – shimura conjecture was itself widely seen as completely inaccessible to proof with current knowledge. for example, wiles'ex - supervisor john coates states that it seemed " impossible to actually prove ", and ken ribet considered himself " one of the vast majority of people who believed was completely inaccessible ". hearing of the 1986 proof of the epsilon conjecture, wiles decided to begin researching exclusively towards a proof of the taniyama – shimura conjecture. ribet later commented that " andrew wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove. "


in the united states, local carriers have been responsible for distributing telephone numbers to individuals and businesses since at & t split up into local and long - distance carriers as a result of demonopolization. orders to change long - distance carriers would be submitted to them, and the local carrier would make the change. in the most common scenario regarding slamming, an employee of a telephone company ( usually a telemarketer making outbound calls to prospective clients ) would submit an order to change carriers to the local exchange carrier without the approval of the customer. in the united kingdom, landline telecommunications services were provided exclusively by bt until 1984 when the industry was demonopolized, and the number of independent operators providing fixed - line domestic telephone services increased.


older operating systems forced upon the programmer a record structure and frequently non - orthogonal data semantics and device control. unix eliminated this complexity with the concept of a data stream : an ordered sequence of data bytes which can be read until the end of file. a program may also write bytes as desired and need not, and cannot easily declare their count or grouping.


in some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. for example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up. one example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin.


in metadata, a data element definition is a human readable phrase or sentence associated with a data element within a data dictionary that describes the meaning or semantics of a data element. data element definitions are critical for external users of any data system. good definitions can dramatically ease the process of mapping one set of data into another set of data. this is a core feature of distributed computing and intelligent agent development. there are several guidelines that should be followed when creating high - quality data element definitions.


c + + is an example of a language that supports both inner classes and inner types ( via typedef declarations ). another type is a local class, which is a class defined within a procedure or function. this limits references to the class name to within the scope where the class is declared. depending on the semantic rules of the language, there may be additional restrictions on local classes compared to non - local ones. one common restriction is to disallow local class methods to access local variables of the enclosing function. for example, in c + +, a local class may refer to static variables declared within its enclosing function, but may not access the function's automatic variables.


in mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. factorization systems are a generalization of this situation in category theory.


in the announcement for shindig's first code commit, four primary features of shindig were cited : gadget container javascript — core javascript foundation for general gadget functionality. this javascript manages security, communication, ui layout, and feature extensions, such as the opensocial api. gadget server — an open source version of gmodules. com, which is used to render the gadget xml into javascript and html for the container to expose via the container javascript.


in most logical systems, one proves a statement of the form " p iff q " by proving either " if p, then q " and " if q, then p ", or " if p, then q " and " if not - p, then not - q ". proving these pairs of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. an alternative is to prove the disjunction " ( p and q ) or ( not - p and not - q ) ", which itself can be inferred directly from either of its disjuncts — that is, because " iff " is truth - functional, " p iff q " follows if p and q have been shown to be both true, or both false.


in mathematics, an extreme point of a convex set s { \ displaystyle s } in a real or complex vector space is a point in s { \ displaystyle s } which does not lie in any open line segment joining two points of s. { \ displaystyle s. } in linear programming problems, an extreme point is also called vertex or corner point of s. { \ displaystyle s. }


in the design of experiments, consecutive sampling, also known as total enumerative sampling, is a sampling technique in which every subject meeting the criteria of inclusion is selected until the required sample size is achieved. along with convenience sampling and snowball sampling, consecutive sampling is one of the most commonly used kinds of nonprobability sampling. consecutive sampling is typically better than convenience sampling in controlling sampling bias.


this process of converting a raw score into a standard score is called standardizing or normalizing ( however, " normalizing " can refer to many types of ratios ; see normalization for more ). standard scores are most commonly called z - scores ; the two terms may be used interchangeably, as they are in this article. other equivalent terms in use include z - value, z - statistic, normal score, standardized variable and pull in high energy physics. computing a z - score requires knowledge of the mean and standard deviation of the complete population to which a data point belongs ; if one only has a sample of observations from the population, then the analogous computation using the sample mean and sample standard deviation yields the t - statistic.


while the probability of " netshop " is extremely low, since " netshop " isn't currently a compound or phrase in english, and " sweatshop " also seems contextually improbable, " pet shop " is a good fit because it is a common phrase and is also related to the word " dog ". moreover, an utterance can have different meanings depending on how it is split into words. a popular example, often quoted in the field, is the phrase " how to wreck a nice beach ", which sounds very similar to " how to recognize speech ". as this example shows, proper lexical segmentation depends on context and semantics which draws on the whole of human knowledge and experience, and would thus require advanced pattern recognition and artificial intelligence technologies to be implemented on a computer.


on calculators, it is printed as " log ", but mathematicians usually mean natural logarithm ( logarithm with base e ≈ 2. 71828 ) rather than common logarithm when they write " log ". to mitigate this ambiguity, the iso 80000 specification recommends that log10 ( x ) should be written lg ( x ), and loge ( x ) should be ln ( x ). before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not widely available.


for a simple hypothesis, α = p ( test rejects h 0 h 0 ). { \ displaystyle \ alpha = p ( { \ text { test rejects } } h _ { 0 } \ mid h _ { 0 } ). } in the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.


in number theory, euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. it is written using the greek letter phi as φ ( n ) { \ displaystyle \ varphi ( n ) } or ( n ) { \ displaystyle \ phi ( n ) }, and may also be called euler's phi function. in other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd ( n, k ) is equal to 1. the integers k of this form are sometimes referred to as totatives of n. for example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8. they are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since gcd ( 9, 3 ) = gcd ( 9, 6 ) = 3 and gcd ( 9, 9 ) = 9.


in non - broadcast multiple - access network ( nbma ), neighbor adjacency is formed with unicast packets to remote host. a network may have more than two routers, but is no broadcast support. ip 192. 0. 2. 1 > 192. 0. 2. 2 : ospfv2, hello ip 192. 0. 2. 2 > 192. 0. 2. 1 : ospfv2, hello ip 192. 0. 2. 1 > 192. 0. 2. 2 : ospfv2, database description ip 192. 0. 2. 2 > 192. 0. 2. 1 : ospfv2, database description types of non - broadcast networks : x. 25 public data network wireguard serial interface requires all routers to be able to communicate directly, on the same network. designated router is elected for the network. lsa is generated for the network.


in most cases, java support is unnecessary in web browsers, and security experts recommend that it not be run in a browser unless absolutely necessary. it was suggested that, if java is required by a few web sites, users should have a separate browser installation specifically for those sites.


in proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. the first sequent calculi systems, lk and lj, were introduced in 1934 / 1935 by gerhard gentzen as a tool for studying natural deduction in first - order logic ( in classical and intuitionistic versions, respectively ). gentzen's so - called " main theorem " ( hauptsatz ) about lk and lj was the cut - elimination theorem, a result with far - reaching meta - theoretic consequences, including consistency. gentzen further demonstrated the power and flexibility of this technique a few years later, applying a cut - elimination argument to give a ( transfinite ) proof of the consistency of peano arithmetic, in surprising response to godel's incompleteness theorems. since this early work, sequent calculi, also called gentzen systems, and the general concepts relating to them, have been widely applied in the fields of proof theory, mathematical logic, and automated deduction.


they argue that unrestricted use of digital resources can cause an overproduction of redundant data which causes noise and corrupts communication channels within the digital environment. others argue that the pollution caused by the overuse of digital resources also causes pollution in the physical environment. they argue that unrestricted use of digital resources causes misinformation, fake news, crime, and terrorism, as well as problems of a different nature such as confusion, manipulation, insecurity, and loss of confidence.


under the integrability condition that e ‖ x ‖ l 2 2 { \ displaystyle \ mathbb { e } \ | x \ | _ { l ^ { 2 } } ^ { 2 } } is finite, the covariance operator of x { \ displaystyle x } is a linear operator c : h → h { \ displaystyle { \ mathcal { c } } : h \ to h } that is uniquely defined by the relation c h = e, h ∈ h, { \ displaystyle { \ mathcal { c } } h = \ mathbb { e }, \ qquad h \ in h, } or, in tensor form, c = e { \ displaystyle { \ mathcal { c } } = \ mathbb { e } }. the spectral theorem allows to decompose x { \ displaystyle x } as the karhunen - loeve decomposition x = μ + i = 1 ∞ ⟨ x, φ i ⟩ φ i, { \ displaystyle x = \ mu + \ sum _ { i = 1 } ^ { \ infty } \ langle x, \ varphi _ { i } \ rangle \ varphi _ { i }, } where φ i { \ displaystyle \ varphi _ { i } } are eigenvectors of c { \ displaystyle { \ mathcal { c } } }, corresponding to the nonnegative eigenvalues of c { \ displaystyle { \ mathcal { c } } }, in a non - increasing order. truncating this infinite series to a finite order underpins functional principal component analysis.


in probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable x is given by f x ( x ) = i = 1 n f y i ( x ) p i, { \ displaystyle f _ { x } ( x ) = \ sum _ { i = 1 } ^ { n } f _ { y _ { i } } ( x ) \ ; p _ { i }, } where each yi is an exponentially distributed random variable with rate parameter λi, and pi is the probability that x will take on the form of the exponential distribution with rate λi. it is named the hyperexponential distribution since its coefficient of variation is greater than that of the exponential distribution, whose coefficient of variation is 1, and the hypoexponential distribution, which has a coefficient of variation smaller than one. while the exponential distribution is the continuous analogue of the geometric distribution, the hyperexponential distribution is not analogous to the hypergeometric distribution. the hyperexponential distribution is an example of a mixture density. an example of a hyperexponential random variable can be seen in the context of telephony, where, if someone has a modem and a phone, their phone line usage could be modeled as a hyperexponential distribution where there is probability p of them talking on the phone with rate λ1 and probability q of them using their internet connection with rate λ2.


the feti - dp method is hybrid between a dual and a primal method. non - overlapping domain decomposition methods are also called iterative substructuring methods. mortar methods are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains.


in mathematics, kronecker's congruence, introduced by kronecker, states that φ p ( x, y ) ≡ ( x − y p ) ( x p − y ) mod p, { \ displaystyle \ phi _ { p } ( x, y ) \ equiv ( x - y ^ { p } ) ( x ^ { p } - y ) { \ bmod { p } }, } where p is a prime and φp ( x, y ) is the modular polynomial of order p, given by φ n ( x, j ) = τ ( x − j ( τ ) ) { \ displaystyle \ phi _ { n } ( x, j ) = \ prod _ { \ tau } ( x - j ( \ tau ) ) } for j the elliptic modular function and τ running through classes of imaginary quadratic integers of discriminant n.


clearly, we don't want to integrate a mixed loss when the less is significantly larger than the gain. this is often referred to as a " silver lining ", a reference to the folk maxim " every cloud has a silver lining ". when the loss is just barely larger than the gain, integration may be preferred.


coastal flood hazards have been mapped by a similar approach that includes the relevant physical processes. most areas where serious floods can occur in the united states have been mapped consistently in this manner.


in physics, an overline sometimes indicates a vector, although boldface and arrows are also commonly used : x = | x | x ^ { \ displaystyle { \ overline { x } } = | x | { \ hat { x } } }


the opposite of embarrassingly parallel problems are inherently serial problems, which cannot be parallelized at all. a common example of an embarrassingly parallel problem is 3d video rendering handled by a graphics processing unit, where each frame ( forward method ) or pixel ( ray tracing method ) can be handled with no interdependency. some forms of password cracking are another embarrassingly parallel task that is easily distributed on central processing units, cpu cores, or clusters.


in the following case, one proposer achieves acceptance of value v1 of two acceptors before failing. a new proposer may start another round, but it is now impossible for that proposer to prepare a majority that doesn't include at least one acceptor that has accepted v1. as such, even though the proposer doesn't see the existing consensus, the proposer's only option is to propose the value already agreed upon. new proposers can continually increase the identifier to restart the process, but the consensus can never be changed.


in recent years, a variety of machine learning techniques have been used in record linkage. it has been recognized that the classic fellegi - sunter algorithm for probabilistic record linkage outlined above is equivalent to the naive bayes algorithm in the field of machine learning, and suffers from the same assumption of the independence of its features ( an assumption that is typically not true ). higher accuracy can often be achieved by using various other machine learning techniques, including a single - layer perceptron, random forest, and svm. in conjunction with distributed technologies, accuracy and scale for record linkage can be improved further.


abstract object theory is a discipline that studies the nature and role of abstract objects. it holds that properties can be related to objects in two ways : through exemplification and through encoding. concrete objects exemplify their properties while abstract objects merely encode them. this approach is also known as the dual copula strategy.


without an online connection to a licensing server to verify the licensing status every two weeks ( four weeks since version 9. 0. 0 ), the software would fall back to the functionality of the freeware version. this caused an uproar in the user community, in particular among those who work in secure or remote environments without direct internet access and users for whom it is mandatory to be able to gain full access to their designs even after extended periods of time ( several years up to decades ) without depending on third - parties such as autodesk to allow reactivation ( who may no longer be around or support the product by then ). many users have indicated they would refuse to upgrade under a subscription model and rather migrate to other electronic design applications such as kicad.


in recent years more advanced strategies have been proposed, they all rely on machine learning and attempt to merge the content and collaborative information in a single model. one example of this approaches is called attribute to feature mapping which is tailored to matrix factorization algorithms. the basic idea is the following. a matrix factorization model represents the user - item interactions as the product of two rectangular matrices whose content is learned using the known interactions via machine learning.


in the x window system, every individual, physical key is associated a number in the range 8 – 255, called its keycode. a keycode only identifies a key, not a particular character or term ( e. g., " page up " ) among the ones that may be printed on the key. each one of these characters or terms is instead identified by a keysym. while a keycode only depends on the actual key that is pressed, a keysym may depend, for example, on whether the shift key or another modifier was also pressed.


the rest of the numbers are counted half - step - wise such that : b = 0, c = 1, c♯ / d♭ = 2, d = 3, d♯ / e♭ = 4, e = 5, f = 6, f♯ / g♭ = 7, g = 8, g♯ / a♭ = 9, a = 10, and a♯ / b♭ = 11. prime zero is retrieved entirely by choice of the composer. to receive the retrograde of any given prime, the numbers are simply rewritten backwards.


in this case, the metacharacter character ( $ ) ( not to be confused with the sigil in the variable assignment statement ) is interpreted to indicate variable interpolation, and requires some escaping if it needs to be outputted literally. this should be contrasted with the printf function, which produces the same output using notation such as : but does not perform interpolation : the % s is a placeholder in a printf format string, but the variables themselves are outside the string. this is contrasted with " raw " strings : which produce output like : $ name said $ greeting to the crowd of people. here the $ characters are not metacharacters, and are not interpreted to have any meaning other than plain text.


in probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. let e 1 { \ displaystyle e _ { 1 } } and e 2 { \ displaystyle e _ { 2 } } denote two mutually exclusive events which might occur on a given trial. then the probability that e 1 { \ displaystyle e _ { 1 } } occurs before e 2 { \ displaystyle e _ { 2 } } equals the conditional probability that e 1 { \ displaystyle e _ { 1 } } occurs given that e 1 { \ displaystyle e _ { 1 } } or e 2 { \ displaystyle e _ { 2 } } occur on the next trial, which is p = p = p p + p { \ displaystyle \ operatorname { p } = \ operatorname { p } \ left = { \ frac { \ operatorname { p } } { \ operatorname { p } + \ operatorname { p } } } } the events e 1 { \ displaystyle e _ { 1 } } and e 2 { \ displaystyle e _ { 2 } } need not be collectively exhaustive ( if they are, the result is trivial ).


this recursive process ends when the entropy is zero so that either all pixels in that subset are corners or non - corners. this generated decision tree can then be converted into programming code, such as c and c + +, which is just a bunch of nested if - else statements. for optimization purpose, profile - guided optimization is used to compile the code.


max pooling layers are located after the second, the forth and the fifth convolution layer. a global average pooling is also applied before the output. all convolution layers use leaky relu nonlinearity activation function.


in the uk, the spoofed number is called the " presentation number ". this must be either allocated to the caller, or if allocated to a third party, it is only to be used with the third party's explicit permission. starting 2016, direct marketing companies are obliged to display their phone numbers. any offending companies can be fined up to £2 million by ofcom. in 2021, huw saunders, a director at ofcom, the uk regulator, said the current uk phone network ( public switched telephone network ) is being updated to a new system ( voice over internet protocol ), which should be in place by 2025. saunders said, " it's only when the vast majority of people are on the new technology ( voip ) that we can implement a new patch to address this problem. "


in the context of population genetics, lda was proposed by j. k. pritchard, m. stephens and p. donnelly in 2000. lda was applied in machine learning by david blei, andrew ng and michael i. jordan in 2003.


once all missing values have been imputed, the data set can then be analysed using standard techniques for complete data. there have been many theories embraced by scientists to account for missing data but the majority of them introduce bias. a few of the well known attempts to deal with missing data include : hot deck and cold deck imputation ; listwise and pairwise deletion ; mean imputation ; non - negative matrix factorization ; regression imputation ; last observation carried forward ; stochastic imputation ; and multiple imputation.


the english verb is to krige and the most common noun is kriging ; both are often pronounced with a hard " g ", following the pronunciation of the name " krige ". advantages very good in local and global estimates. geological knowledge is captured in variogram.


the data protection legislation requires that the collection and processing of personal data be fair, lawful and transparent. this means that the collection and processing of data as defined by data protection legislation must always have a valid lawful basis and must also meet the requirements of the cldc. in the china, article 18 of the " national health care big data standards, security and services management measures ( for trial implementation ) " ( national health planning and development ( 2018 ) no. 23 ) promulgated by the national health care commission in 2018 states, " the responsible unit shall adopt measures such as data classification, important data backup, and encryption authentication to guarantee the security of health care big data. " however, the scope and definition of important data are not covered. although the " information security technology - healthcare data security guide " ( the " guide " ) issued by the national standardization committee also proposes that important data should be evaluated and approved in accordance with the regulations, there is likewise no definition of the connotation and definition of important data.


initially, this proof was not accepted by all mathematicians because the computer - assisted proof was infeasible for a human to check by hand. the proof has gained wide acceptance since then, although some doubters remain. the four color theorem was proved in 1976 by kenneth appel and wolfgang haken after many false proofs and counterexamples ( unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map ). to dispel any remaining doubts about the appel – haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by robertson, sanders, seymour, and thomas. in 2005, the theorem was also proved by georges gonthier with general - purpose theorem - proving software.


in statistics, a kaniadakis distribution ( also known as κ - distribution ) is a statistical distribution that emerges from the kaniadakis statistics. there are several families of kaniadakis distributions related to different constraints used in the maximization of the kaniadakis entropy, such as the κ - exponential distribution, κ - gaussian distribution, kaniadakis κ - gamma distribution and κ - weibull distribution. the κ - distributions have been applied for modeling a vast phenomenology of experimental statistical distributions in natural or artificial complex systems, such as, in epidemiology, quantum statistics, in astrophysics and cosmology, in geophysics, in economy, in machine learning. the κ - distributions are written as function of the κ - deformed exponential, taking the form f i = exp κ ( − β e i + β μ ) { \ displaystyle f _ { i } = \ exp _ { \ kappa } ( - \ beta e _ { i } + \ beta \ mu ) } enables the power - law description of complex systems following the consistent κ - generalized statistical theory., where exp κ ( x ) = ( 1 + κ 2 x 2 + κ x ) 1 / κ { \ displaystyle \ exp _ { \ kappa } ( x ) = ( { \ sqrt { 1 + \ kappa ^ { 2 } x ^ { 2 } } } + \ kappa x ) ^ { 1 / \ kappa } } is the kaniadakis κ - exponential function. the κ - distribution becomes the common boltzmann distribution at low energies, while it has a power - law tail at high energies, the feature of high interest of many researchers.


the error terms, which are not directly observed in data and are often denoted using the scalar e i { \ displaystyle e _ { i } }. in various fields of application, different terminologies are used in place of dependent and independent variables. most regression models propose that y i { \ displaystyle y _ { i } } is a function ( regression function ) of x i { \ displaystyle x _ { i } } and β { \ displaystyle \ beta }, with e i { \ displaystyle e _ { i } } representing an additive error term that may stand in for un - modeled determinants of y i { \ displaystyle y _ { i } } or random statistical noise : y i = f ( x i, β ) + e i { \ displaystyle y _ { i } = f ( x _ { i }, \ beta ) + e _ { i } } the researchers'goal is to estimate the function f ( x i, β ) { \ displaystyle f ( x _ { i }, \ beta ) } that most closely fits the data. to carry out regression analysis, the form of the function f { \ displaystyle f } must be specified.


quoting shaler, " we have two opinions in this case. that, in essence, is a 50 percent error rate. "


in certain types of programmable logic arrays and read - only memory, a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. in optical discs, a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. in one - dimensional bar codes, bits are encoded as the thickness of alternating black and white lines.


there will be n + 1 { \ displaystyle n + 1 } possible values of the categorical variable y ranging from 0 to n. let pn ( x ) be the probability, given explanatory variable vector x, that the outcome will be y = n { \ displaystyle y = n }. define p n k = p n ( x k ) { \ displaystyle p _ { nk } = p _ { n } ( { \ boldsymbol { x } } _ { k } ) } which is the probability that for the k - th measurement, the categorical outcome is n. the lagrangian will be expressed as a function of the probabilities pnk and will minimized by equating the derivatives of the lagrangian with respect to these probabilities to zero. an important point is that the probabilities are treated equally and the fact that they sum to unity is part of the lagrangian formulation, rather than being assumed from the beginning.


in mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a " normal form " that can be computed by a finite transducer : multiplication in such a monoid is " easy ", in the sense that it can be described by a rational function.


that is, truth is reducible to this process of verification. according to perspectivism and relativism, a proposition is only true relative to a particular perspective. roughly, a proposition is true relative to a perspective if and only if it is accepted, endorsed, or legitimated by that perspective.


logarithms were introduced by john napier in 1614 as a means of simplifying calculations. they were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high - accuracy computations more easily. using logarithm tables, tedious multi - digit multiplication steps can be replaced by table look - ups and simpler addition.


in statistical data analysis the total sum of squares ( tss or sst ) is a quantity that appears as part of a standard way of presenting results of such analyses. for a set of observations, y i, i ≤ n { \ displaystyle y _ { i }, i \ leq n }, it is defined as the sum over all squared differences between the observations and their overall mean y { \ displaystyle { \ bar { y } } }. : t s s = i = 1 n ( y i − y ) 2 { \ displaystyle \ mathrm { tss } = \ sum _ { i = 1 } ^ { n } \ left ( y _ { i } - { \ bar { y } } \ right ) ^ { 2 } } for wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. for proof of this in the multivariate ols case, see partitioning in the general ols model.


in matroid theory, a binary matroid is a matroid that can be represented over the finite field gf ( 2 ). that is, up to isomorphism, they are the matroids whose elements are the columns of a ( 0, 1 ) - matrix and whose sets of elements are independent if and only if the corresponding columns are linearly independent in gf ( 2 ).


in some verbs, the past tense, past participle, or both are identical in form to the basic ( infinitive ) form of the verb. this is the case with certain strong verbs, where historical sound changes have led to a leveling of the vowel modifications : for example, let has both past tense and past participle identical to the infinitive, while come has the past participle identical ( but a different past tense, came ). the same is true of the verbs listed above under § weak verbs as having undergone coalescence of final consonants ( and without other irregularities such as vowel shortening or devoicing of the ending ) : bet, bid, etc. ( these verbs have infinitive, past tense and past participle all identical, although some of them also have alternative regular forms in - ed ).


in measurements, the measurement obtained can suffer from two types of uncertainties. the first is the random uncertainty which is due to the noise in the process and the measurement. the second contribution is due to the systematic uncertainty which may be present in the measuring instrument. systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed.


for example, international standard book number ( isbn ) uses modulo 11 ( for 10 digit isbn ) or modulo 10 ( for 13 digit isbn ) arithmetic for error detection. likewise, international bank account numbers ( ibans ), for example, make use of modulo 97 arithmetic to spot user input errors in bank account numbers. in chemistry, the last digit of the cas registry number ( a unique identifying number for each chemical compound ) is a check digit, which is calculated by taking the last digit of the first two parts of the cas registry number times 1, the previous digit times 2, the previous digit times 3 etc., adding all these up and computing the sum modulo 10.


this report consolidated many ideas circulating at the time and featured three key language innovations : nested block structure : code sequences and associated declarations could be grouped into blocks without having to be turned into separate, explicitly named procedures ; lexical scoping : a block could have its own private variables, procedures and functions, invisible to code outside that block, that is, information hiding. another innovation, related to this, was in how the language was described : a mathematically exact notation, backus – naur form ( bnf ), was used to describe the language's syntax. nearly all subsequent programming languages have used a variant of bnf to describe the context - free portion of their syntax. algol 60 was particularly influential in the design of later languages, some of which soon became more popular. the burroughs large systems were designed to be programmed in an extended subset of algol.


in mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. it was introduced by mcnulty and shallon, and has seen many uses in the field of universal algebra since then.


parameters on which items are characterized include their difficulty ( known as " location " for their location on the difficulty range ) ; discrimination ( slope or correlation ), representing how steeply the rate of success of individuals varies with their ability ; and a pseudoguessing parameter, characterising the ( lower ) asymptote at which even the least able persons will score due to guessing ( for instance, 25 % for a pure chance on a multiple choice item with four possible responses ). in the same manner, irt can be used to measure human behavior in online social networks. the views expressed by different people can be aggregated to be studied using irt. its use in classifying information as misinformation or true information has also been evaluated.


the conversion of letter case in a string is common practice in computer applications, for instance to make case - insensitive comparisons. many high - level programming languages provide simple methods for case conversion, at least for the ascii character set. whether or not the case variants are treated as equivalent to each other varies depending on the computer system and context. for example, user passwords are generally case sensitive in order to allow more diversity and make them more difficult to break. in contrast, case is often ignored in keyword searches in order to ignore insignificant variations in keyword capitalisation both in queries and queried material.


here, z / pz denotes the cyclic group of order p ( or equivalently the integers mod p ), and the superscript notation means the n - fold direct product of groups. in general, a ( possibly infinite ) elementary abelian p - group is a direct sum of cyclic groups of order p. ( note that in the finite case the direct product and direct sum coincide, but this is not so in the infinite case. ) in the rest of this article, all groups are assumed finite.


" multiple combinations of centralized and decentralized systems exist. another classification of sensor configuration refers to the coordination of information flow between sensors. these mechanisms provide a way to resolve conflicts or disagreements and to allow the development of dynamic sensing strategies.


in order to illustrate generalized paxos, the example below shows a message flow between two concurrently executing clients and a replicated state machine implementing read / write operations over two distinct registers a and b. note that in this table indicates operations which are non - commutative. a possible sequence of operations : < 1 : read ( a ), 2 : read ( b ), 3 : write ( b ), 4 : read ( b ), 5 : read ( a ), 6 : write ( a ) > since 5 : read ( a ) commutes with both 3 : write ( b ) and 4 : read ( b ), one possible permutation equivalent to the previous order is the following : < 1 : read ( a ), 2 : read ( b ), 5 : read ( a ), 3 : write ( b ), 4 : read ( b ), 6 : write ( a ) > in practice, a commute occurs only when operations are proposed concurrently.


in mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. it is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation. a very closely related topic is geometric group theory, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides. it also comprises a number of algorithmically insoluble problems, most notably the word problem for groups ; and the classical burnside problem.