in numerical analysis, the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the cholesky decomposition, to reduce the number of non - zeros in the cholesky factor. this results in reduced storage requirements and means that the cholesky factor can be applied with fewer arithmetic operations. ( sometimes it may also pertain to an incomplete cholesky factor used as a preconditioner — for example, in the preconditioned conjugate gradient algorithm. ) minimum degree algorithms are often used in the finite element method where the reordering of nodes can be carried out depending only on the topology of the mesh, rather than on the coefficients in the partial differential equation, resulting in efficiency savings when the same mesh is used for a variety of coefficient values.


in simple conditions, f can be easily computed in terms of population size or of genealogical information. f is often denoted using lowercase ( f ), but should not be confused with the coancestry coefficient. however, the above prediction for the fitness decline rarely applies, since it was derived assuming no selection, and fitness is precisely the target trait of natural selection.


in mathematics, the levy – prokhorov metric ( sometimes known just as the prokhorov metric ) is a metric ( i. e., a definition of distance ) on the collection of probability measures on a given metric space. it is named after the french mathematician paul levy and the soviet mathematician yuri vasilyevich prokhorov ; prokhorov introduced it in 1956 as a generalization of the earlier levy metric.


in the calculation of low energy states the term proportional to n 2 u { \ displaystyle n ^ { 2 } u } means that large occupation of a single site is improbable, allowing for truncation of local hilbert space to states containing at most d < ∞ { \ displaystyle d < \ infty } particles. then the local hilbert space dimension is d + 1. { \ displaystyle d + 1. }


in mathematical logic, the de bruijn notation is a syntax for terms in the λ calculus invented by the dutch mathematician nicolaas govert de bruijn. it can be seen as a reversal of the usual syntax for the λ calculus where the argument in an application is placed next to its corresponding binder in the function instead of after the latter's body.


in 1970, electronic parts were introduced, and the current black - coloured plates were changed to blue. the range of sets was reduced by one with the deletion of the old no. 9 set and the renumbering of the old no. 0 to 8 sets to no. 1 to 9. the no. 10 set remained unchanged.


however, not every total recursive function is a primitive recursive function — the most famous example is the ackermann function. other equivalent classes of functions are the functions of lambda calculus and the functions that can be computed by markov algorithms. the subset of all total recursive functions with values in { 0, 1 } is known in computational complexity theory as the complexity class r.


so how does a state machine move an arbitrarily large constant directly into a register, e. g. move ( k, r ) ( move constant k to register r )? if huge constants are necessary they must either start out in the registers themselves or be created by the state machine using a finite number of instructions e. g. multiply and add subroutines using inc and dec ( but not a quasi - infinite number of these! ). sometimes the constant k will be created by use of clr ( r ) followed by inc ( r ) repeated k times – e. g. to put the constant k = 3 into register r, i. e. 3 → r, so at the end of the instruction = 3 : clr ( r ), inc ( r ), inc ( r ), inc ( r ).


in the united states, the 100 - year flood provides the risk basis for flood insurance rates. complete information on the national flood insurance program ( nfip ) is available here. a regulatory flood or base flood is routinely established for river reaches through a science - based rule - making process targeted to a 100 - year flood at the historical average recurrence interval. in addition to historical flood data, the process accounts for previously established regulatory values, the effects of flood - control reservoirs, and changes in land use in the watershed.


the difference of two moser – de bruijn numbers, multiplied by two, is never square. every natural number can be formed in a unique way as the sum of a moser – de bruijn number and twice a moser – de bruijn number. this representation as a sum defines a one - to - one correspondence between integers and pairs of integers, listed in order of their positions on a z - order curve. the moser – de bruijn sequence can be used to construct pairs of transcendental numbers that are multiplicative inverses of each other and both have simple decimal representations. a simple recurrence relation allows values of the moser – de bruijn sequence to be calculated from earlier values, and can be used to prove that the moser – de bruijn sequence is a 2 - regular sequence.


the set of k - almost primes is usually denoted by pk. the smallest k - almost prime is 2k. the first few k - almost primes are : the number πk ( n ) of positive integers less than or equal to n with exactly k prime divisors ( not necessarily distinct ) is asymptotic to : π k ( n ) ( n log n ) ( log log n ) k − 1 ( k − 1 )!


let kp be a boolean variable which indicates whether p is a corner, then the entropy of kp is used to measure the information of p being a corner. for a set of pixels q, the total entropy of kq ( not normalized ) is : h ( q ) = ( c + n ) log2 ( c + n ) - clog2c - nlog2n where c = | { i ∈ q : ki is true } | ( number of corners ) where n = | { i ∈ q : ki is false } | ( number of non - corners ) the information gain can then be represented as : hg = h ( p ) - h ( pb ) - h ( ps ) - h ( pd ) a recursive process is applied to each subsets in order to select each x that could maximize the information gain. for example, at first an x is selected to partition p into pd, ps, pb with the most information ; then for each subset pd, ps, pb, another y is selected to yield the most information gain ( notice that the y could be the same as x ).


in number theory, a prime number p is a sophie germain prime if 2p + 1 is also prime. the number 2p + 1 associated with a sophie germain prime is called a safe prime. for example, 11 is a sophie germain prime and 2 × 11 + 1 = 23 is its associated safe prime. sophie germain primes are named after french mathematician sophie germain, who used them in her investigations of fermat's last theorem.


the frame received on port b is then forwarded to ports a and c, the frame received on port c to ports a and b. so, the node on port a receives two copies of its own broadcast frame while the other two copies produced by the loop continue to cycle. likewise, each broadcast frame entering the system continues to cycle through the loop in both directions, rebroadcasting back to the network in each loop, and broadcasts accumulate. eventually, the accumulated broadcasts exhaust the egress capacity of the links, the switch begins dropping frames, and communication across the switch becomes unreliable or even impossible.


in number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below ( in other words, it's closer to the following than to the preceding prime ). or to put it algebraically, writing the sequence of prime numbers as ( p1, p2, p3,... ) = ( 2, 3, 5,... ), pn is a strong prime if pn > pn − 1 + pn + 1 / 2. for example, 17 is the seventh prime : the sixth and eighth primes, 13 and 19, add up to 32, and half that is 16 ; 17 is greater than 16, so 17 is a strong prime. the first few strong primes are 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499 ( sequence a051634 in the oeis ). in a twin prime pair ( p, p + 2 ) with p > 5, p is always a strong prime, since 3 must divide p − 2, which cannot be prime.


in mathematics, specifically in control theory, subspace identification ( sid ) aims at identifying linear time invariant ( lti ) state space models from input - output data. sid does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, sid methods do not suffer from problems related to local minima that often lead to unsatisfactory identification results.


in the r5rs standard and also in later reports, the syntax of scheme can easily be extended via the macro system. the r5rs standard introduced a powerful hygienic macro system that allows the programmer to add new syntactic constructs to the language using a simple pattern matching sublanguage ( r5rs sec 4. 3 ). prior to this, the hygienic macro system had been relegated to an appendix of the r4rs standard, as a " high level " system alongside a " low level " macro system, both of which were treated as extensions to scheme rather than an essential part of the language. implementations of the hygienic macro system, also called syntax - rules, are required to respect the lexical scoping of the rest of the language. this is assured by special naming and scoping rules for macro expansion and avoids common programming errors that can occur in the macro systems of other programming languages.


in the context of computer science, semantics refers to the meaning behind programming language constructs, distinguishing it from their mere syntax, which is the arrangement of symbols and keywords. this concept is crucial for ensuring that code is not only correctly written in terms of syntax but also logically meaningful and functional. according to euzenat, semantics " provides the rules for interpreting the syntax which do not provide the meaning directly but constrains the possible interpretations of what is declared ".


in server / client architectures, the program at the other side may not be an authorised client and the client's server may not be an authorised server. even when they are, a man - in - the - middle attack could compromise communications. often the easiest way to break the security of a client / server system is not to go head on to the security mechanisms, but instead to go around them. a man in the middle attack is a simple example of this, because you can use it to collect details to impersonate a user.


in the context of information science, an ontology is a formal representation of knowledge within a domain, using hierarchies of terms including their definitions, attributes, and relations. ontologies provide a common terminology in a machine - readable framework that facilitates sharing and discovery of data. having an established ontology for nanoparticles is important for cancer nanomedicine due to the need of researchers to search, access, and analyze large amounts of data. the nanoparticle ontology is an ontology for the preparation, chemical composition, and characterization of nanomaterials involved in cancer research.


in public - key cryptography and computer security, a root key ceremony is a procedure during which a unique pair of public and private root keys gets generated. depending on the certificate policy, the generation of the root keys may require notarization, legal representation, witnesses, and " key holders " to be present, as the information on the system is the responsibility of the parties. a commonly recognized practice is to follow the sas 70 standard for root key ceremonies. at the heart of every certificate authority ( ca ) is at least one root key or root certificate and usually at least one intermediate root certificate. " root key " is the term for a unique passcode that must be generated for secure server interaction with a protective network, usually called the root zone.


in the 1967 black power, stokely carmichael introduces black nationalism. he illustrates the prosperity of the black race in the united states as being dependent on the implementation of black sovereignty. under his theory, black nationalism in the united states would allow blacks to socially, economically and politically be empowered in a manner that has never been plausible in american history. a black nation would work to reverse the exploitation of the black race in america, as blacks would intrinsically work to benefit their own state of affairs.


this is the class of functions from a { \ displaystyle a } to c { \ displaystyle c } in a pure set theory. below the notation x → y { \ displaystyle x \ to y } is also used for y x { \ displaystyle y ^ { x } }, for the sake of distinguishing it from ordinal exponentiation. when functions are understood as just function graphs as above, the membership proposition f ∈ c a { \ displaystyle f \ in c ^ { a } } is also written f : a → c { \ displaystyle f \ colon a \ to c }. the boolean - valued χ b : a → { 0, 1 } { \ displaystyle \ chi _ { b } \ colon a \ to \ { 0, 1 \ } } are among the classes discussed next.


the trace 1 condition means j a j ∗ a j = 1. { \ displaystyle \ sum _ { j } a _ { j } ^ { * } a _ { j } = 1. } let p i = a i ∗ a i, { \ displaystyle p _ { i } = a _ { i } ^ { * } a _ { i }, } and vi be the normalized ai. we see that { p i, v i } { \ displaystyle \ left \ { p _ { i }, v _ { i } \ right \ } } gives the mixed state ρ.


in mathematics, a proof by infinite descent, also known as fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. it is a method which relies on the well - ordering principle, and is often used to show that a given equation, such as a diophantine equation, has no solutions. typically, one shows that if a solution to a problem existed, which in some sense was related to one or more natural numbers, it would necessarily imply that a second solution existed, which was related to one or more'smaller'natural numbers. this in turn would imply a third solution related to smaller natural numbers, implying a fourth solution, therefore a fifth solution, and so on. however, there cannot be an infinity of ever - smaller natural numbers, and therefore by mathematical induction, the original premise — that any solution exists — is incorrect : its correctness produces a contradiction.


in telecommunication networks, the transmission time is the amount of time from the beginning until the end of a message transmission. in the case of a digital message, it is the time from the first bit until the last bit of a message has left the transmitting node. the packet transmission time in seconds can be obtained from the packet size in bit and the bit rate in bit / s as : packet transmission time = packet size / bit rateexample : assuming 100 mbit / s ethernet, and the maximum packet size of 1526 bytes, results in maximum packet transmission time = 1526×8 bit / ( 100 × 106 bit / s ) ≈ 122 μs


in single - ended signalling, the transmitter generates a single voltage that the receiver compares with a fixed reference voltage, both relative to a common ground connection shared by both ends. in many instances, single - ended designs are not feasible. another difficulty is the electromagnetic interference that can be generated by a single - ended signalling system that attempts to operate at high speed.


in object - oriented programming, there is also the concept of a static member variable, which is a " class variable " of a statically defined class, i. e., a member variable of a given class which is shared across all instances ( objects ), and is accessible as a member variable of these objects. a class variable of a dynamically defined class, in languages where classes can be defined at run time, is allocated when the class is defined and is not static. object constants known at compile - time, such as string literals, are usually allocated statically. in object - oriented programming, the virtual method tables of classes are usually allocated statically. a statically defined value can also be global in its scope ensuring the same immutable value is used throughout a run for consistency.


in mathematical logic, a proof calculus or a proof system is built to prove statements.


in the third quarter of 2006, at least 12 billion text messages were sent on at & t's network, up almost 15 % from the preceding quarter. in the u. s., while texting is mainly popular among people from 13 – 22 years old, it is also increasing among adults and business users. the age that a child receives his / her first cell phone has also decreased, making text messaging a popular way of communicating.


the largest component has logarithmic size. the graph is a pseudoforest. most of its components are trees : the number of vertices in components that have cycles grows more slowly than any unbounded function of the number of vertices.


traversing this eulerian trail generates an orientation d of g such that every point has indegree and outdegree = k. next, replace every vertex v v ( d ) by two vertices v ’ and v ”, and replace every directed edge uv of the oriented graph by an undirected edge from u ’ to v ”. since d has in - and outdegrees equal to k the resulting bipartite graph g ’ is k - regular. the edges of g ’ can be partitioned into k perfect matchings by a theorem of konig. now merging v ’ with v ” for every v recovers the graph g, and maps the k perfect matchings of g ’ onto k 2 - factors of g which partition its edges.


in mathematics and electronics engineering, a binary golay code is a type of linear error - correcting code used in digital communications. the binary golay code, along with the ternary golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. these codes are named in honor of marcel j. e. golay whose 1949 paper introducing them has been called, by e. r. berlekamp, the " best single published page " in coding theory. there are two closely related binary golay codes. the extended binary golay code, g24 ( sometimes just called the " golay code " in finite group theory ) encodes 12 bits of data in a 24 - bit word in such a way that any 3 - bit errors can be corrected or any 7 - bit errors can be detected. the other, the perfect binary golay code, g23, has codewords of length 23 and is obtained from the extended binary golay code by deleting one coordinate position ( conversely, the extended binary golay code is obtained from the perfect binary golay code by adding a parity bit ). in standard coding notation, the codes have parameters and, corresponding to the length of the codewords, the dimension of the code, and the minimum hamming distance between two codewords, respectively.


the model makes the assumption that customers have some idea of what they want and what the standard of the good or service should be. models of sequential search have been used in many disciplines, including finance and labour economics. sequential search models are used in labour economics to examine how employees look for work and how employers hire new employees.


the symbol ( n k ) { \ displaystyle { \ tbinom { n } { k } } } is usually read as " n choose k " because there are ( n k ) { \ displaystyle { \ tbinom { n } { k } } } ways to choose an ( unordered ) subset of k elements from a fixed set of n elements. for example, there are ( 4 2 ) = 6 { \ displaystyle { \ tbinom { 4 } { 2 } } = 6 } ways to choose 2 elements from { 1, 2, 3, 4 }, { \ displaystyle \ { 1, 2, 3, 4 \ }, } namely { 1, 2 }, { 1, 3 }, { 1, 4 }, { 2, 3 }, { 2, 4 }, { \ displaystyle \ { 1, 2 \ }, \, \ { 1, 3 \ }, \, \ { 1, 4 \ }, \, \ { 2, 3 \ }, \, \ { 2, 4 \ }, } and { 3, 4 }. { \ displaystyle \ { 3, 4 \ }. } the binomial coefficients can be generalized to ( z k ) { \ displaystyle { \ tbinom { z } { k } } } for any complex number z and integer k ≥ 0, and many of their properties continue to hold in this more general form.


flat addressing is possible by applying multiple instructions, which however leads to slower programs. the memory model concept derives from the setup of the segment registers. for example, in the tiny model cs = ds = ss, that is the program's code, data, and stack are all contained within a single 64 kb segment. in the small memory model ds = ss, so both data and stack reside in the same segment ; cs points to a different code segment of up to 64 kb.


it will also not be perfectly aligned with the directions of the document, causing aliasing. features smaller than the resolution will also not be reproduced. in addition, human vision is sensitive to luminance contrast ratio.


... point is that one or two degrees is about the experience that we have had in the last 10, 000 years, the era of human civilization. there haven't been — globally averaged, we're talking — fluctuations of more than a degree or so. so we're actually getting into uncharted territory from the point of view of the relatively benign climate of the last 10, 000 years, if we warm up more than a degree or two.


in simple electromagnetic analysis ( sema ) attacks, the attacker deduces the key directly by observing the trace. it is very effective against asymmetric cryptography implementations. typically, only a few traces are needed, though the attacker needs to have a strong understanding of the cryptographic device and of the implementation of the cryptographic algorithm.


then for any function f : a → b { \ displaystyle f : a \ to b }, the restriction f | s : s → b { \ displaystyle f | _ { s } : s \ to b } of a function f { \ displaystyle f } onto s { \ displaystyle s } can be defined as the composition f | s = f ∘ i s { \ displaystyle f | _ { s } = f \ circ i _ { s } }. analogously, for an inclusion i t : t b { \ displaystyle i _ { t } : t \ hookrightarrow b } the corestriction f | t : a → t { \ displaystyle f | ^ { t } : a \ to t } of f { \ displaystyle f } onto t { \ displaystyle t } is the unique function f | t { \ displaystyle f | ^ { t } } such that there is a decomposition f = i t ∘ f | t { \ displaystyle f = i _ { t } \ circ f | ^ { t } }. the corestriction exists if and only if t { \ displaystyle t } contains the image of f { \ displaystyle f }.


in order to apply control theory tools to the analysis of behavior trees, they can be defined as three - tuple. t i = { f i, r i, δ t }, { \ displaystyle t _ { i } = \ { f _ { i }, r _ { i }, \ delta t \ }, } where i ∈ n { \ displaystyle i \ in \ mathbb { n } } is the index of the tree, f i : r n → r n { \ displaystyle f _ { i } : \ mathbb { r } ^ { n } \ rightarrow \ mathbb { r } ^ { n } } is a vector field representing the right hand side of an ordinary difference equation, δ t { \ displaystyle \ delta t } is a time step and r i : r n → { r i, s i, f i } { \ displaystyle r _ { i } : \ mathbb { r } ^ { n } \ rightarrow \ { r _ { i }, s _ { i }, f _ { i } \ } } is the return status, that can be equal to either running r i { \ displaystyle r _ { i } }, success s i { \ displaystyle s _ { i } }, or failure f i { \ displaystyle f _ { i } }. note : a task is a degenerate behavior tree with no parent and no child.


variants of the functional predicate definition using apartness relations on setoids have been defined as well. it is a metatheorem for theories containing b c s t { \ displaystyle { \ mathsf { bcst } } } that adding a function symbol for a provenly total class function is a conservative extension, despite this changing the scope of bounded separation. some notational conveniences involving function application will only work when a set has indeed been established to be a function.


in mathematics, economics, and computer science, the stable matching polytope or stable marriage polytope is a convex polytope derived from the solutions to an instance of the stable matching problem.


in mathematics, a divisor of an integer n { \ displaystyle n }, also called a factor of n { \ displaystyle n }, is an integer m { \ displaystyle m } that may be multiplied by some integer to produce n { \ displaystyle n }. in this case, one also says that n { \ displaystyle n } is a multiple of m. { \ displaystyle m. } an integer n { \ displaystyle n } is divisible or evenly divisible by another integer m { \ displaystyle m } if m { \ displaystyle m } is a divisor of n { \ displaystyle n } ; this implies dividing n { \ displaystyle n } by m { \ displaystyle m } leaves no remainder.


we can further define a programming language in which we can ensure that even more sophisticated functions always halt. for example, the ackermann function, which is not primitive recursive, nevertheless is a total computable function computable by a term rewriting system with a reduction ordering on its arguments ( ohlebusch, 2002, pp. 67 ). despite the above examples of programming languages which guarantee termination of the programs, there exists no programming language which captures exactly the total recursive functions, i. e. the functions which can be computed by a turing machine that always halts. this is because existence of such a programming language would be a contradiction to the non - semi - decidability of the problem whether a turing machine halts on every input.


} { \ prod _ { j = 0 } ^ { k } n _ { j }! } } } if any q i = 0 { \ displaystyle q _ { i } = 0 }, then the vector q → { \ displaystyle { \ vec { q } } } is shared in common between orthants. because of this, the multiplying factor on the permutation must be adjusted from 2 n { \ displaystyle 2 ^ { n } } to be 2 n − n 0 { \ displaystyle 2 ^ { n - n _ { 0 } } } multiplying the number of amount of permutations by the adjusted amount of orthants yields, e = n!


n 2! ⋅ ( n − n 1 − n 2 )! ( n − n 1 − n 2 − n 3 )!


if a = b, then b = a ( symmetric ). if a = b and b = c, then a = c ( transitive ). each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.


the original highway network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart ( on the mnist dataset, figure 1 in ). no improvement on test accuracy was reported with networks deeper than 19 layers ( on the cifar - 10 dataset ; table 1 in ).


in the context of his theory of numberings, ershov showed that kleene's recursion theorem holds for any precomplete numbering. a godel numbering is a precomplete numbering on the set of computable functions so the generalized theorem yields the kleene recursion theorem as a special case. given a precomplete numbering ν { \ displaystyle \ nu }, then for any partial computable function f { \ displaystyle f } with two parameters there exists a total computable function t { \ displaystyle t } with one parameter such that n ∈ n : ν ∘ f ( n, t ( n ) ) = ν ∘ t ( n ). { \ displaystyle \ forall n \ in \ mathbb { n } : \ nu \ circ f ( n, t ( n ) ) = \ nu \ circ t ( n ). }


apple's garage band even purveys digital music lessons using the very same itunes account as used for the ios app store, they are all part of the same app store. electronic bookstores such as kindle, barnes and noble or kobo are further examples of successful electronic distribution using the app store concept. for the electronic appwrapper distribution, encryption and the digital rights of the software were universally managed for all participating developers much like stores participating in a shopping mall.


in order for consistency in data to be maintained and to attain scalable processor systems where every processor has its own memory, the processor consistency model was derived. all processors need to be consistent in the order in which they see writes done by one processor and in the way they see writes by different processors to the same location ( coherence is maintained ). however, they do not need to be consistent when the writes are by different processors to different locations. every write operation can be divided into several sub - writes to all memories.


under the assumption of stationary statistics, at a given position, the normalized correlation function is g ( 2 ) = ⟨ e ^ − ( 0 ) e ^ − ( τ ) e ^ + ( τ ) e ^ + ( 0 ) ⟩ ⟨ e ^ − ( 0 ) e ^ + ( 0 ) ⟩ ⟨ e ^ − ( τ ) e ^ + ( τ ) ⟩ { \ displaystyle g ^ { ( 2 ) } = { \ frac { \ langle { \ hat { e } } ^ { - } ( 0 ) { \ hat { e } } ^ { - } ( \ tau ) { \ hat { e } } ^ { + } ( \ tau ) { \ hat { e } } ^ { + } ( 0 ) \ rangle } { \ langle { \ hat { e } } ^ { - } ( 0 ) { \ hat { e } } ^ { + } ( 0 ) \ rangle \ langle { \ hat { e } } ^ { - } ( \ tau ) { \ hat { e } } ^ { + } ( \ tau ) \ rangle } } } g ( 2 ) { \ displaystyle g ^ { ( 2 ) } } here measures the probability of coincidence of two photons being detected with a time difference τ { \ displaystyle \ tau }. for all varieties of chaotic light, the following relationship between the first order and second - order coherences holds : g ( 2 ) ( τ ) = 1 + | g ( 1 ) ( τ ) | 2 { \ displaystyle g ^ { ( 2 ) } ( \ tau ) = 1 + | g ^ { ( 1 ) } ( \ tau ) | ^ { 2 } }. this relationship is true for both the classical and quantum correlation functions.


332, 149 s. e. 541 ( 1929 ). " in assessing statutory language, unless words have acquired a peculiar meaning, by virtue of statutory definition or judicial construction, they are to be construed in accordance with their common usage. "


, { \ displaystyle i ( r, \ lambda ) = \ sum _ { y = r } ^ { \ infty } { \ frac { e ^ { - \ lambda } \ lambda ^ { y } } { y! } }, } where s is the integral part of r. the motivation given by staff is that the ratio of successive probabilities in the poisson distribution ( that is p ( x = n ) / p ( x = n − 1 ) { \ displaystyle p ( x = n ) / p ( x = n - 1 ) } ) is given by λ / n { \ displaystyle \ lambda / n } for n > 0 { \ displaystyle n > 0 } and the displaced poisson generalizes this ratio to λ / ( n + r ) { \ displaystyle \ lambda / \ left ( n + r \ right ) }. = = references = =


this evolution has resulted in more complex and more flexible ics being created. the newer circuits are programmable and thus allow a single hardware ic design to undertake a number of different functions, where the appropriate software is installed. network processors are used in the manufacture of many different types of network equipment such as : routers, software routers and switches ( inter - network processors ) firewalls session border controllers intrusion detection devices intrusion prevention devices network monitoring systems network security ( secure cryptoprocessors )


note that the mask constraint relates to the effects and not the causes like the other constraints. the graph's direction is as follows : causes - - > intermediate nodes - - > effects the graph can always be rearranged so there is only one node between any input and any output. see conjunctive normal form and disjunctive normal form. a cause – effect graph is useful for generating a reduced decision table.


in mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. david eisenbud proved that every multivariate real - valued polynomial p without linear terms can be written as a ab = pi, where a and b are square matrices and i is the identity matrix. given the polynomial p, the matrices a and b can be found by elementary methods. example : the polynomial x2 + y2 is irreducible over r, but can be written as = ( x 2 + y 2 ) { \ displaystyle \ left \ left = ( x ^ { 2 } + y ^ { 2 } ) \ left }


in regression, mean response ( or expected response ) and predicted response, also known as mean outcome ( or expected outcome ) and predicted outcome, are values of the dependent variable calculated from the regression parameters and a given value of the independent variable. the values of these two responses are the same, but their calculated variances are different. the concept is a generalization of the distinction between the standard error of the mean and the sample standard deviation.


in mathematical logic and computer science, a general recursive function, partial recursive function, or μ - recursive function is a partial function from natural numbers to natural numbers that is " computable " in an intuitive sense – as well as in a formal one. if the function is total, it is also called a total recursive function ( sometimes shortened to recursive function ). in computability theory, it is shown that the μ - recursive functions are precisely the functions that can be computed by turing machines ( this is one of the theorems that supports the church – turing thesis ). the μ - recursive functions are closely related to primitive recursive functions, and their inductive definition ( below ) builds upon that of the primitive recursive functions.


in mathematics, a nowhere commutative semigroup is a semigroup s such that, for all a and b in s, if ab = ba then a = b. a semigroup s is nowhere commutative if and only if any two elements of s are inverses of each other.


some writers on probability call this the " conditional covariance formula " or use other names. note : the conditional expected values e ( x | z ) and e ( y | z ) are random variables whose values depend on the value of z. note that the conditional expected value of x given the event z = z is a function of z. if we write e ( x | z = z ) = g ( z ) then the random variable e ( x | z ) is g ( z ). similar comments apply to the conditional covariance.


in mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real - valued convex function with a non - empty domain, that never takes on the value − ∞ { \ displaystyle - \ infty } and also is not identically equal to + ∞. { \ displaystyle + \ infty. } in convex analysis and variational analysis, a point ( in the domain ) at which some given function f { \ displaystyle f } is minimized is typically sought, where f { \ displaystyle f } is valued in the extended real number line = r ∪ { ± ∞ }. { \ displaystyle = \ mathbb { r } \ cup \ { \ pm \ infty \ }. }


in mathematics, a subset r of the integers is called a reduced residue system modulo n if : gcd ( r, n ) = 1 for each r in r, r contains φ ( n ) elements, no two elements of r are congruent modulo n. here φ denotes euler's totient function. a reduced residue system modulo n can be formed from a complete residue system modulo n by removing all integers not relatively prime to n. for example, a complete residue system modulo 12 is { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }. the so - called totatives 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is { 1, 5, 7, 11 }. the cardinality of this set can be calculated with the totient function : φ ( 12 ) = 4. some other reduced residue systems modulo 12 are : { 13, 17, 19, 23 } { −11, −7, −5, −1 } { −7, −13, 13, 31 } { 35, 43, 53, 61 }


however, when the code is inserted into a compiler, the compiler may ignore the bidi char and process the characters in a different order than visually displayed. when the compiler is finished, it could potentially execute code that visually appeared to be non - executable. formatting marks can be combined multiple times to create complex attacks.


the ordinal series are based on ordinal numbers such as the english first, second, third ( for numbers higher than 2, the ordinal forms are also used for fractions ; only the fraction 1⁄2 has special forms ). for the hundreds, there are competing forms : those in - gent -, from the original latin, and those in - cent -, derived from centi -, etc. plus the prefixes for 1 – 9. many of the items in the following tables are not in general use, but may rather be regarded as coinages by individuals. in scientific contexts, either scientific notation or si prefixes are used to express very large or very small numbers, and not unwieldy prefixes. the same suffix may be used with more than one series : examples


in memory errors, the faulting program accesses memory that it should not access. examples include : attempting to write to a read - only portion of memory attempting to execute bytes in memory which are not designated as instructions attempting to read as data bytes in memory which are designated as instructions other miscellaneous conflicts between the designation of a part of memory and its usehowever, many modern operating systems implement their memory access - control schemes via paging instead of segmentation, so it is often the case that invalid memory references in operating systems such as windows are reported via page faults instead of general protection faults. operating systems typically provide an abstraction layer ( such as exception handling or signals ) that hides whatever internal processor mechanism was used to raise a memory access error from a program, for the purposes of providing a standard interface for handling many different types of processor - generated error conditions. in terms of the x86 architecture, general protection faults are specific to segmentation - based protection when it comes to memory accesses. however, general protection faults are still used to report other protection violations ( aside from memory access violations ) when paging is used, such as the use of instructions not accessible from the current privilege level ( cpl ). while it is theoretically possible for an operating system to utilize both paging and segmentation, for the most part, common operating systems typically rely on paging for the bulk of their memory access control needs.


in packed bcd ( or simply packed decimal ), each nibble represent a decimal digit. packed bcd has been in use since at least the 1960s and is implemented in all ibm mainframe hardware since then. most implementations are big endian, i. e. with the more significant digit in the upper half of each byte, and with the leftmost byte ( residing at the lowest memory address ) containing the most significant digits of the packed decimal value. the lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag.


in physics, the no - deleting theorem of quantum information theory is a no - go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. it is a time - reversed dual to the no - cloning theorem, which states that arbitrary states cannot be copied. this theorem seems remarkable, because, in many senses, quantum states are fragile ; the theorem asserts that, in a particular case, they are also robust.


the idea originated with the scottish physicist alexander crichton mitchell, who was helped by the royal navy at hms tarlair. he had shown that the passage of a submarine past a cable formed an induction loop which induced a voltage of approximately a millivolt, detectable by a sensitive galvanometer. voltages were also induced in the cable by random fluctuations in the earth's magnetic field and electrical noise from the glasgow tram lines.


for example, while the word representation properly designates a group homomorphism from a group g to gl ( v ), where v is a vector space, it is common to call v " a representation of g ". another common abuse of language consists in identifying two mathematical objects that are different, but canonically isomorphic. other examples include identifying a constant function with its value, identifying a group with a binary operation with the name of its underlying set, or identifying to r 3 { \ displaystyle \ mathbb { r } ^ { 3 } } the euclidean space of dimension three equipped with a cartesian coordinate system.


they are the with - carry analog of m - sequences or maximum length sequences. there are efficient algorithms for fcsr synthesis. this is the problem : given a prefix of a sequence, construct a minimal length fcsr that outputs the sequence.


in mathematics, the littlewood – richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two schur functions as a linear combination of other schur functions. these coefficients are natural numbers, which the littlewood – richardson rule describes as counting certain skew tableaux. they occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of finite - dimensional representations of general linear groups, or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with young tableaux and symmetric polynomials. littlewood – richardson coefficients depend on three partitions, say λ, μ, ν { \ displaystyle \ lambda, \ mu, \ nu }, of which λ { \ displaystyle \ lambda } and μ { \ displaystyle \ mu } describe the schur functions being multiplied, and ν { \ displaystyle \ nu } gives the schur function of which this is the coefficient in the linear combination ; in other words they are the coefficients c λ, μ ν { \ displaystyle c _ { \ lambda, \ mu } ^ { \ nu } } such that s λ s μ = ν c λ, μ ν s ν. { \ displaystyle s _ { \ lambda } s _ { \ mu } = \ sum _ { \ nu } c _ { \ lambda, \ mu } ^ { \ nu } s _ { \ nu }. } the littlewood – richardson rule states that c λ, μ ν { \ displaystyle c _ { \ lambda, \ mu } ^ { \ nu } } is equal to the number of littlewood – richardson tableaux of skew shape ν / λ { \ displaystyle \ nu / \ lambda } and of weight μ { \ displaystyle \ mu }.


in probability theory, dudley's theorem is a result relating the expected upper bound and regularity properties of a gaussian process to its entropy and covariance structure.


in some languages, including a number of chinese varieties, many of the words that serve as prepositions can also be used as verbs. for instance, in standard chinese, dao can be used in either a prepositional or a verbal sense : 我 北 京 wo dao beijing qu ( " i go to beijing " ; qu, meaning " to go ", is the main verb, dao is prepositional meaning " to " ) 我 wo dao le ( " i have arrived " ; dao is the main verb, meaning " to arrive " ) because of this overlap, and the fact that a sequence of prepositional phrases and verb phrases often resembles a serial verb construction, chinese prepositions ( and those of other languages with similar grammatical structures ) are often referred to as coverbs. as noted in previous sections, chinese can also be said to have postpositions, although these can be analyzed as nominal ( noun ) elements. for more information, see the article on chinese grammar, particularly the sections on coverbs and locative phrases.


although the general principles underlying binomial nomenclature are common to these two codes, there are some differences in the terminology they use and their particular rules. in modern usage, the first letter of the generic name is always capitalized in writing, while that of the specific epithet is not, even when derived from a proper noun such as the name of a person or place. similarly, both parts are italicized in normal text ( or underlined in handwriting ).


these kinds of contemporary features help gain citizen a new level of technology. majority of space in the chip has been made available for the private sector to use for their products and services. it might appear expensive for the private sector to use this card initially but once the number of citizens having critical mass is reached, it will be more profitable for the private sector to use this secure and universal platform.


in multitasking computing an operating system can handle several programs, both native applications or emulated software, that are running independent, parallel, together in the same time in the same device, using separated or shared resources and / or data, executing their tasks separately or together, while a user can switch on the fly between them or groups of them to use obtained effects or supervise purposes, without waste of time or waste of performance. in operating systems using gui very often it is done by switching from an active window ( or an object playing similar role ) of a particular software piece to another one but of another software. a computer can compute results on the fly, or retrieve a previously stored result.


when the value of a large quantity of items has a zipf's law distribution, the total value of the n most - valuable items is proportional to the n - th harmonic number. this leads to a variety of surprising conclusions regarding the long tail and the theory of network value. the bertrand - chebyshev theorem implies that, except for the case n = 1, the harmonic numbers are never integers.


in mathematics, the frechet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. it is named after maurice frechet.


in number theory, integer factorization is the decomposition, of a positive integer into a product of integers. if the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime ( in this case, one has a " product " of a single factor ). when the numbers are sufficiently large, no efficient non - quantum integer factorization algorithm is known. however, it has not been proven that such an algorithm does not exist.


the newly created package provided a standard collection of common numerical operations on top of the numeric array data structure. shortly thereafter, fernando perez released ipython, an enhanced interactive shell widely used in the technical computing community, and john hunter released the first version of matplotlib, the 2d plotting library for technical computing. since then the scipy environment has continued to grow with more packages and tools for technical computing.


in sociology a social rule refers to any social convention commonly adhered to in a society. these rules are not written in law or otherwise formalized. in social constructionism there is a great focus on social rules. it is argued that these rules are socially constructed, that these rules act upon every member of a society, but at the same time, are re - produced by the individuals.


in mathematics, modular arithmetic is a system of arithmetic for integers, where numbers " wrap around " when reaching a certain value, called the modulus. the modern approach to modular arithmetic was developed by carl friedrich gauss in his book disquisitiones arithmeticae, published in 1801. a familiar use of modular arithmetic is in the 12 - hour clock, in which the day is divided into two 12 - hour periods.


the coefficient field is called the base field. if constructive and algorithmic methods are the main issue it is q ( x, y ) { \ displaystyle \ mathbb { q } ( x, y ) }. the respective ring of differential operators is denoted by d = q ( x, y ) { \ displaystyle { \ mathcal { d } } = \ mathbb { q } ( x, y ) } or d = f { \ displaystyle { \ mathcal { d } } = { \ mathcal { f } } }.


the conditioning event is interpreted as evidence for the conditioned event. that is, p ( a ) is the probability of a before accounting for evidence e, and p ( a | e ) is the probability of a after having accounted for evidence e or after having updated p ( a ). this is consistent with the frequentist interpretation, which is the first definition given above.


such strings may be translated into english by using " and ", " while ", " ( in order ) to " or other connectives, but some may have a more compact translation, as in the following example ( from hayao miyazaki's mononoke hime ) in which the actions of " following " and " coming " are simultaneous : the following sentence from mandarin chinese can be considered to contain four verb phrases in sequence : in chinese, however, there is often no clear distinction between serial verb phrases and prepositional phrases. the first three " verbs " in the above sentence may alternatively be regarded as prepositions ( this applies particularly to words like cong which do not normally appear as independent verbs ). words used in that way in chinese and in some other languages are commonly referred to as coverbs.


in the category of algebraic varieties, the product is given by the segre embedding. in the category of semi - abelian monoids, the product is given by the history monoid.


in mathematical logic, the hilbert – bernays provability conditions, named after david hilbert and paul bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic ( smith 2007 : 224 ). these conditions are used in many proofs of kurt godel's second incompleteness theorem. they are also closely related to axioms of provability logic.


in several interesting cases, the functor g { \ displaystyle g } is an inclusion of a full subcategory not admitting a left adjoint. for example, the codensity monad of the inclusion of finset into set is the ultrafilter monad associating to any set m { \ displaystyle m } the set of ultrafilters on m. { \ displaystyle m. } this was proven by kennison and gildenhuys, though without using the term " codensity ".


anagrams of words whose letters are different are also permutations : the letters are already ordered in the original word, and the anagram is a reordering of the letters. the study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. permutations are used in almost every branch of mathematics and in many other fields of science.


the solution of eq. 108 has the form where la, ma, ρ, are arbitrary functions of coordinates x, y bound by condition eq. 110 derived from eq. 107. to find higher terms of this decomposition, it is convenient to write the matrix of required quantities γab in the form where the symbol ~ means matrix transposition. matrix h is symmetric and its trace is zero.


in most major handicapping systems, a golfer does not use their exact handicap ( or handicap index ) directly, but use it to produce their playing or course handicap. for some systems, this means simply rounding the exact handicap to the nearest whole number ; however, systems that use slope ratings require a more complex calculation to produce a course handicap with some also factoring in the course rating : course handicap = ( handicap index × slope rating ) 113 { \ displaystyle { \ mbox { course handicap } } = { \ frac { ( { \ mbox { handicap index } } \ times { \ mbox { slope rating } } ) } { \ mbox { 113 } } } } or course handicap = ( handicap index × slope rating ) 113 + ( course rating − par ) { \ displaystyle { \ mbox { course handicap } } = { \ frac { ( { \ mbox { handicap index } } \ times { \ mbox { slope rating } } ) } { \ mbox { 113 } } } + ( { \ mbox { course rating } } - { \ mbox { par } } ) } the usga and golf australia systems use the first calculation ; the whs, ega, and golf rsa systems use the second. under congu's unified handicapping system the exact handicap is rounded to the nearest whole number to produce the playing handicap, and in the argentinian system the exact handicap is used directly. a playing handicap may also refer to the stroke allowance for a given competition dependent on playing format, and is generally calculated as a percentage of the course handicap.


if tests are developed without an understanding of what the business considers to be an acceptable level of risk, it is possible to have a release candidate that passes all the available tests, but which the business leaders would not consider to be ready for release. for the test results to accurately indicate whether each release candidate meets business expectations, the approach to designing tests must be based on the business's tolerance for risks related to security, performance, reliability, and compliance. in addition to having unit tests that check code at a very granular bottom - up level, there is a need for a broader suite of tests to provide a top - down assessment of the release candidate's business risk.


in the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. the purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. for example, in the more common vector framework, tikhonov regularization optimizes over min x ‖ a x − y ‖ 2 + λ ‖ x ‖ 2 { \ displaystyle \ min _ { x } \ | ax - y \ | ^ { 2 } + \ lambda \ | x \ | ^ { 2 } } to find a vector x { \ displaystyle x } that is a stable solution to the regression problem.


in the nfs games underground 2 to carbon, the network ( as cingular ) was shown as the mobile internet provider in the ingame voice / text message.


in matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. the cogirth of a matroid is the girth of its dual matroid. matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, hall sets in bipartite graphs, even sets in families of sets, and general position of point sets. it is hard to compute, but fixed - parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation.


most mobile phone operators had charged for such calls previously, with orange being the final major network to introduce such charges during december 2005. certain helplines, such as those in the 0808 80x xxxx series had remained free from most networks on a voluntary basis and some niche operators, such as giffgaff always offered freephone calls at no charge. the uk mobile operators offer an alternative product to organisations who wish to provide toll - free services - 5 - digit voice short codes which are sold through mobile aggregators. 0500 numbers, introduced by mercury communications ( later known as cable & wireless, now vodafone ) in 1982, were also freephone numbers ( known as " freecall " ), but were officially withdrawn by ofcom on 3 june 2017.


in mechanical typewriters, the shift key functions by mechanically shifting some component so an alternate row of characters on typebars hits the paper. in an electronic system, by contrast, there is no necessary connection between the code points of unshifted and shifted values, though implementation is simpler if the code points of unshifted and shifted keys are related, most simply by a single bit differing. in electromechanical systems, this makes a significant difference in ease of implementation, as shifting must be accomplished by some physical linkage. for this reason, among others ( such as ease of collation ), the ascii standard strove to organize the code points so that shifting could be implemented by simply toggling a bit.


in practice, implementations of optimality theory often make use of many concepts of phonological theories of representations, such as the syllable, the mora, or feature geometry. completely distinct from these, there are sub - theories which have been proposed entirely within optimality theory, such as positional faithfulness theory, correspondence theory ( mccarthy & prince 1995 ), sympathy theory, stratal ot, and a number of theories of learnability, most notably by bruce tesar. other theories within optimality theory are concerned with issues like the need for derivational levels within the phonological domain, the possible formulations of constraints, and constraint interactions other than strict domination.


if the tactic is applied to the second case, then the resulting partition can be considered as the standard partition for that operator. stocks and carrington in ( stocks & carrington 1996 ) illustrate this situation with r ⊕ g = ( dom g r ) ∪ g { \ displaystyle r \ oplus g = ( { \ text { dom } } g \ ntriangleleft r ) \ cup g }, where { \ displaystyle \ ntriangleleft } means domain anti - restriction, by giving standard partitions for { \ displaystyle \ ntriangleleft } and ∪ { \ displaystyle \ cup } and propagating them to calculate a partition for ⊕ { \ displaystyle \ oplus }. specification mutation ( sm ).


for example, a common weighting scheme consists in giving each neighbor a weight of 1 / d, where d is the distance to the neighbor. the neighbors are taken from a set of objects for which the class ( for k - nn classification ) or the object property value ( for k - nn regression ) is known. this can be thought of as the training set for the algorithm, though no explicit training step is required. a peculiarity of the k - nn algorithm is that it is sensitive to the local structure of the data.


in probability and statistics, the dirichlet distribution ( after peter gustav lejeune dirichlet ), often denoted dir ( α ) { \ displaystyle \ operatorname { dir } ( { \ boldsymbol { \ alpha } } ) }, is a family of continuous multivariate probability distributions parameterized by a vector α { \ displaystyle { \ boldsymbol { \ alpha } } } of positive reals. it is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution ( mbd ). dirichlet distributions are commonly used as prior distributions in bayesian statistics, and in fact, the dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. the infinite - dimensional generalization of the dirichlet distribution is the dirichlet process.


its powers have poles of order 4, 6 { \ displaystyle 4, 6 } and so on. therefore, such a p { \ displaystyle p } has the gap sequence 1, 3, 5, …, 2 g − 1. { \ displaystyle 1, 3, 5, \ dots, 2g - 1. }


in project management, risk assessment is an integral part of the risk management plan, studying the probability, the impact, and the effect of every known risk on the project, as well as the corrective action to take should an incident be implied by a risk occur. of special consideration in this area are the relevant codes of practice that are enforced in the specific jurisdiction. understanding the regime of regulations that risk management must abide by is integral to formulating safe and compliant risk assessment practices.


in mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative ; however, the usual representative is the least positive residue, the smallest non - negative integer that belongs to that class ( i. e., the remainder of the euclidean division ). however, other conventions are possible. computers and calculators have various ways of storing and representing numbers ; thus their definition of the modulo operation depends on the programming language or the underlying hardware. in nearly all computing systems, the quotient q and the remainder r of a divided by n satisfy the following conditions : this still leaves a sign ambiguity if the remainder is non - zero : two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur.


in the context of fast fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete fourier transforms ( dfts ) into a larger dft, or vice versa ( breaking a larger dft up into subtransforms ). the name " butterfly " comes from the shape of the data - flow diagram in the radix - 2 case, as described below. the same structure can also be found in the viterbi algorithm, used for finding the most likely sequence of hidden states. the butterfly diagram show a data - flow diagram connecting the inputs x ( left ) to the outputs y that depend on them ( right ) for a " butterfly " step of a radix - 2 cooley – tukey fft algorithm. this diagram resembles a butterfly as in the morpho butterfly shown for comparison, hence the name.


if the univariate polynomial ψ ℓ ( x, j ( e ) ) { \ displaystyle \ psi _ { \ ell } ( x, j ( e ) ) } has a root in f q { \ displaystyle \ mathbb { f } _ { q } }, where j ( e ) { \ displaystyle j ( e ) } denotes the j - invariant of e { \ displaystyle e }, then ℓ { \ displaystyle \ ell } is an elkies prime, and otherwise it is an atkin prime. in the elkies case, further computations involving modular polynomials are used to obtain a proper factor of the division polynomial ψ ℓ { \ displaystyle \ psi _ { \ ell } }. the degree of this factor is o ( ℓ ) { \ displaystyle o ( \ ell ) }, whereas ψ ℓ { \ displaystyle \ psi _ { \ ell } } has degree o ( ℓ 2 ) { \ displaystyle o ( \ ell ^ { 2 } ) }.


in the definition of np - complete given above, the term reduction was used in the technical meaning of a polynomial - time many - one reduction. another type of reduction is polynomial - time turing reduction. a problem x { \ displaystyle \ scriptstyle x } is polynomial - time turing - reducible to a problem y { \ displaystyle \ scriptstyle y } if, given a subroutine that solves y { \ displaystyle \ scriptstyle y } in polynomial time, one could write a program that calls this subroutine and solves x { \ displaystyle \ scriptstyle x } in polynomial time. this contrasts with many - one reducibility, which has the restriction that the program can only call the subroutine once, and the return value of the subroutine must be the return value of the program.


in particular, gxl was developed to enable interoperability between software reengineering tools and components, such as code extractors ( parsers ), analyzers and visualizers. gxl allows software reengineers to combine single - purpose tools especially for parsing, source code extraction, architecture recovery, data flow analysis, pointer analysis, program slicing, query techniques, source code visualization, object recovery, restructuring, refactoring, remodularization, etc., into a single powerful reengineering workbench. there are two innovative features in gxl that make it well - suited to an exchange format for software data. the conceptual data model is a typed, attributed, directed graph.


the purpose of the test theory is to allow a ( v ) and b ( v ) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. ( notice that newtonian physics, which has been conclusively excluded by experiment, results from a ( v ) = b ( v ) = d ( v ) = 1, and e ( v ) = 0. { \ displaystyle a ( v ) = b ( v ) = d ( v ) = 1, { \ text { and } } e ( v ) = 0 \,. }


in some economic models, the role of social networks in job searching often use exogenous job networks. using this framework, calvo - armegnol and jackson were able to point out some network related labor market issues.


in the early seventies stephen wiesner introduced a primitive called multiplexing in his seminal paper " conjugate coding ", which was the starting point of quantum cryptography. unfortunately it took more than ten years to be published. even though this primitive was equivalent to what was later called 1 – 2 oblivious transfer, wiesner did not see its application to cryptography.


these evolutionary lineages can thereby be portrayed through a phylogenetic tree, or cladogram, where varying relatedness amongst species is evidently depicted. through this tree, organisms can be categorized by divergence from the common ancestor, and primitive characters, to clades of organisms with shared derived character states. furthermore, cladograms allow researchers to view the changes and evolutionary alterations occurring in a species over time as they move from primitive characters to varying derived character states. cladograms are important for scientists as they allow them to classify and hypothesize the origin and future of organisms. cladograms allow scientists to propose their evolutionary scenarios about the lineage from a primitive trait to a derived one. by understanding how the trait came to be, scientists can hypothesize the environment that specific organism was in and how that affected the evolutionary adaptations of the trait that came to be. other, more technical, terms for these two conditions — for example, " plesiomorphic " and " synapomorphic " — are frequently encountered ; see the table below.


in number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. no such formula which is efficiently computable is known. a number of constraints are known, showing what such a " formula " can and cannot be.


two moves in : at this point, the requirement that the graph be proper comes into effect, as a red area must be made which does not touch the existing one : once the third region is coloured : note that areas only count as touching if they share edges, not if they only share vertices, so this move is legal. the game continues, players moving alternately, until one player cannot make a move. this player loses. a possible continuation of the game is as follows ( with each move numbered for clarity ) : game over : in this outcome, the blue player has lost.


scheme theory also unifies algebraic geometry with much of number theory, which eventually led to wiles's proof of fermat's last theorem. formally, a scheme is a topological space together with commutative rings for all of its open sets, which arises from gluing together spectra ( spaces of prime ideals ) of commutative rings along their open subsets. in other words, it is a ringed space which is locally a spectrum of a commutative ring.


in recent years, several students of jean - paul benzecri have refined mca and incorporated it into a more general framework of data analysis known as geometric data analysis. this involves the development of direct connections between simple correspondence analysis, principal component analysis and mca with a form of cluster analysis known as euclidean classification. two extensions have great practical use. it is possible to include, as active elements in the mca, several quantitative variables.


if an industry uses little of a factor of production, a small increase in the output of that industry will not bid the price of that factor up. to a first - order approximation, firms in the industry will experience constant costs, and the industry supply curves will not slope up. if an industry uses an appreciable amount of that factor of production, an increase in the output of that industry will exhibit increasing costs.


the sql standard defines the following properties : language - defines the programming language in which the user - defined function is implemented ; examples include sql, c, c # and java. parameter style - defines the conventions that are used to pass the function parameters and results between the implementation of the function and the database system ( only applicable if language is not sql ). specific name - a name for the function that is unique within the database.


links not in the mcf are paid nothing. this routing problem is one of the cases for which vcg is strategyproof and minimum. in 2004, it was shown that the expected vcg overpayment of an erdos – renyi random graph with n nodes and edge probability p, g ∈ g ( n, p ) { \ displaystyle \ scriptstyle g \ in g ( n, p ) } approaches p 2 − p { \ displaystyle { \ frac { p } { 2 - p } } } as n, approaches ∞ { \ displaystyle \ scriptstyle \ infty }, for n p = ω ( n log n ) { \ displaystyle np = \ omega ( { \ sqrt { n \ log n } } ) }. prior to this result, it was known that vcg overpayment in g ( n, p ) is ω ( 1 n p ) { \ displaystyle \ omega \ left ( { \ frac { 1 } { np } } \ right ) } and o ( 1 ) { \ displaystyle o ( 1 ) \, } with high probability given n p = ω ( log n ). { \ displaystyle np = \ omega ( \ log n ). \, }


in order to effectively aid marketers in fully understanding customers and subsequently developing a strategic marketing plan, marketing automation platforms ( maps ) are designed to perform eight key tasks : development and analysis of marketing campaigns and customers management of marketing campaigns appropriate customer data organization and storage moving contacts from leads ( marketing prospects ) to customers lead scoring to qualify leads by measuring their engagement level integration of multiple touch - points such as email and social media lead management campaign performance analytics ( i. e. open rate or click - through rates on emails, conversion rates on landing pages )


in mathematics, mathematical optimization ( or optimization or mathematical programming ) refers to the selection of a best element from some set of available alternatives. in the simplest case, an optimization problem involves maximizing or minimizing a real function by selecting input values of the function and computing the corresponding values of the function. the solution process includes satisfying general necessary and sufficient conditions for optimality. for optimization problems, specialized notation may be used as to the function and its input ( s ).


the negation of an event in probability theory : pr ( a ′ ) = 1 − pr ( a ) ( other notation also exists ). the result of a transformation : tx = x ′ the transpose of a matrix ( other notation also exists ) the dual of a vector spacethe prime is said to " decorate " the letter to which it applies.


in physics, the impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of a potential field u ( r ) created by an object that the projectile is approaching ( see diagram ). it is often referred to in nuclear physics ( see rutherford scattering ) and in classical mechanics. the impact parameter is related to the scattering angle θ by θ = π − 2 b r min ∞ d r r 2 1 − ( b / r ) 2 − 2 u / ( m v ∞ 2 ), { \ displaystyle \ theta = \ pi - 2b \ int _ { r _ { \ text { min } } } ^ { \ infty } { \ frac { dr } { r ^ { 2 } { \ sqrt { 1 - ( b / r ) ^ { 2 } - 2u / ( mv _ { \ infty } ^ { 2 } ) } } } }, } where v∞ is the velocity of the projectile when it is far from the center, and rmin is its closest distance from the center.


in mathematics and abstract algebra, a boolean domain is a set consisting of exactly two elements whose interpretations include false and true. in logic, mathematics and theoretical computer science, a boolean domain is usually written as { 0, 1 }, or b. { \ displaystyle \ mathbb { b }. } the algebraic structure that naturally builds on a boolean domain is the boolean algebra with two elements.


" the text also states that, "... over most of the area affected by the emp the electric field strength on the ground would exceed 0. 5emax. for yields of less than a few hundred kilotons, this would not necessarily be true because the field strength at the earth's tangent could be substantially less than 0. 5emax.


supposing that the kempe chain is connecting the green and yellow neighbors, red and blue must then necessarily not have a kempe chain between them. so, when placing the original vertex v back into the graph, we can simply reverse the colors of the red vertex and its neighbors ( including the red vertex, making it blue ) and color vertex v as red. this results in a four - colored graph.


such a formula can be made either true or false based on the values assigned to its propositional variables. the double turnstile notation s { \ displaystyle \ vdash s } is used to indicate that s is a tautology. tautology is sometimes symbolized by " vpq ", and contradiction by " opq ".


in mathematics, ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. in this sense it is a necessary condition for representability of a matroid over a finite field. let m be a matroid and let ρ be its rank function, ingleton's inequality states that for any subsets x1, x2, x3 and x4 in the support of m, the inequality ρ ( x1 ) + ρ ( x2 ) + ρ ( x1∪x2∪x3 ) + ρ ( x1∪x2∪x4 ) + ρ ( x3∪x4 ) ≤ ρ ( x1∪x2 ) + ρ ( x1∪x3 ) + ρ ( x1∪x4 ) + ρ ( x2∪x3 ) + ρ ( x2∪x4 ) is satisfied. aubrey william ingleton, an english mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. although the article is mainly expository, in this paper ingleton stated and proved ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.


in some states, grand theft of a vehicle may be charged as " grand theft auto " ( see motor vehicle theft for more information ). repeat offenders who continue to steal may become subject to life imprisonment in certain states. sometimes the federal anti - theft - of - government - property law 18 u. s. c. § 640 is used to prosecute cases where the espionage act would otherwise be involved ; the theory being that by retaining sensitive information, the defendant has taken a'thing of value'from the government. for examples, see the amerasia case and united states v. manning.


areas most at risk for flooding could be put to valuable uses that could be abandoned temporarily as people retreat to safer areas when a flood is imminent. planning for flood safety involves many aspects of analysis and engineering, including : observation of previous and present flood heights and inundated areas, statistical, hydrologic, and hydraulic model analyses, mapping inundated areas and flood heights for future flood scenarios, long - term land use planning and regulation, engineering design and construction of structures to control or withstand flooding, intermediate - term monitoring, forecasting, and emergency - response planning, and short - term monitoring, warning, and response operations. each topic presents distinct yet related questions with varying scope and scale in time, space, and the people involved. attempts to understand and manage the mechanisms at work in floodplains have been made for at least six millennia. in the united states, the association of state floodplain managers works to promote education, policies, and activities that mitigate current and future losses, costs, and human suffering caused by flooding and to protect the natural and beneficial functions of floodplains – all without causing adverse impacts. a portfolio of best practice examples for disaster mitigation in the united states is available from the federal emergency management agency.


in simple type theory objects are elements of various disjoint " types ". types are implicitly built up as follows. if τ1,..., τm are types then there is a type ( τ1,..., τm ) that can be thought of as the class of propositional functions of τ1,..., τm ( which in set theory is essentially the set of subsets of τ1×... ×τm ). in particular there is a type ( ) of propositions, and there may be a type ι ( iota ) of " individuals " from which other types are built.


if it is consistent with either state, bob announces that the bit is invalid, since he cannot distinguish which state was transmitted based on the measurement. if on the other hand, one of the two candidate states was inconsistent with the observed measurement, bob announces that the bit is valid since he can deduce the state ( and therefore the secret bit ). consider for example the scenario that alice transmits | ψ 00 ⟩ { \ displaystyle | \ psi _ { 00 } \ rangle } and announces the two states | ψ 00 ⟩ { \ displaystyle | \ psi _ { 00 } \ rangle } and | ψ 01 ⟩ { \ displaystyle | \ psi _ { 01 } \ rangle }.


in probability theory and statistics, the log - laplace distribution is the probability distribution of a random variable whose logarithm has a laplace distribution. if x has a laplace distribution with parameters μ and b, then y = ex has a log - laplace distribution. the distributional properties can be derived from the laplace distribution.


the linear form ⟨ | { \ displaystyle \ langle \ phi | } is a covector to | ⟩ { \ displaystyle | \ phi \ rangle }, and the set of all covectors form a subspace of the dual vector space v ∨ { \ displaystyle v ^ { \ vee } }, to the initial vector space v { \ displaystyle v }. the purpose of this linear form ⟨ | { \ displaystyle \ langle \ phi | } can now be understood in terms of making projections on the state { \ displaystyle { \ boldsymbol { \ phi } } }, to find how linearly dependent two states are, etc. for the vector space c n { \ displaystyle \ mathbb { c } ^ { n } }, kets can be identified with column vectors, and bras with row vectors. combinations of bras, kets, and linear operators are interpreted using matrix multiplication.


since you and your opponent are each infinitely wealthy, there is no limit to how long the game can last. this means the sample space ω must consist of all possible infinite sequences of h { \ displaystyle h } or t : { \ displaystyle t : } however, after n { \ displaystyle n } flips of the coin, you may want to determine or revise your betting strategy in advance of the next flip. the observed information at that point can be described in terms of the 2n possibilities for the first n { \ displaystyle n } flips. formally, since you need to use subsets of ω, this is codified as the σ - algebra observe that then where g ∞ { \ displaystyle { \ mathcal { g } } _ { \ infty } } is the smallest σ - algebra containing all the others.


now we are taking balls randomly in such a way that the probability of taking a particular ball is proportional to its weight, but independent of what happens to the other balls. the number of balls taken of a particular color follows the binomial distribution. if the total number n of balls taken is known then the conditional distribution of the number of taken red balls for given n is fisher's noncentral hypergeometric distribution.


in some types of computer video displays, the related technique of double buffering may be used to improve video performance. in this case, while the processor is updating the contents of one set of physical memory locations, the video generation hardware is accessing and displaying the contents of a second set. when the processor has completed its update, it can signal to the video display hardware to swap active banks, so that the transition visible on screen is free of artifacts or distortion. in this case, the processor may have access to all the memory at once, but the video display hardware is bank - switched between parts of the video memory. if the two ( or more ) banks of video memory contain slightly different images, rapidly cycling ( page - flipping ) between them can create animation or other visual effects that the processor might otherwise be too slow to carry out directly.


this always includes the content of general - purpose cpu registers, the cpu process status word, stack and frame pointers, etc. during context switch, the running process is stopped and another process runs. the kernel must stop the execution of the running process, copy out the values in hardware registers to its pcb, and update the hardware registers with the values from the pcb of the new process. process control information is used by the os to manage the process itself. this includes : process scheduling state – the state of the process in terms of " ready ", " suspended ", etc., and other scheduling information as well, such as priority value, the amount of time elapsed since the process gained control of the cpu or since it was suspended. also, in case of a suspended process, event identification data must be recorded for the event the process is waiting for ; process structuring information – the process's children id's, or the id's of other processes related to the current one in some functional way, which may be represented as a queue, a ring or other data structures ; interprocess communication information – flags, signals and messages associated with the communication among independent processes ; process privileges – allowed / disallowed access to system resources ; process state – new, ready, running, waiting, dead ; process number ( pid ) – unique identification number for each process ( also known as process id ) ; program counter ( pc ) – a pointer to the address of the next instruction to be executed for this process ; cpu registers – register set where process needs to be stored for execution for running state ; cpu scheduling information – information scheduling cpu time ; memory management information – page table, memory limits, segment table ; accounting information – amount of cpu used for process execution, time limits, execution id etc. ; i / o status information – list of i / o devices allocated to the process.


in mathematics, in particular number theory, an odd composite number n is a somer – lucas d - pseudoprime ( with given d ≥ 1 ) if there exists a nondegenerate lucas sequence u ( p, q ) { \ displaystyle u ( p, q ) } with the discriminant d = p 2 − 4 q, { \ displaystyle d = p ^ { 2 } - 4q, } such that gcd ( n, d ) = 1 { \ displaystyle \ gcd ( n, d ) = 1 } and the rank appearance of n in the sequence u ( p, q ) is 1 d ( n − ( d n ) ), { \ displaystyle { \ frac { 1 } { d } } \ left ( n - \ left ( { \ frac { d } { n } } \ right ) \ right ), } where ( d n ) { \ displaystyle \ left ( { \ frac { d } { n } } \ right ) } is the jacobi symbol.


however, there are many different writings on mathematics and mathematics methodology that date back to 1800 bce. these were mostly located in mesopotamia, where the sumerians were practicing multiplication and division. there are also artifacts demonstrating their methodology for solving equations like the quadratic equation.


sql query is tightly coupled and rigidly constrained by datatype within the specific database and can join tables and extract data from tables, and the result is generally a table, and a query can join tables by any columns which match by datatype. sparql query is the standard query language and protocol for linked open data on the web and loosely coupled with the database so that it facilitates the reusability and can extract data through the relations free from the datatype, and not only extract but also generate additional knowledge graph with more sophisticated operations ( logic : transitive / symmetric / inverseof / functional ). the inference based query ( query on the existing asserted facts without the generation of new facts by logic ) can be fast comparing to the reasoning based query ( query on the existing plus the generated / discovered facts based on logic ).


( tcp's sister protocol, udp, does not do this. udp simply sends data packets over the network in a best effort manner and assumes the packets are well - received. ) an early problem noted with tcp's ack mechanism was it did not work well in large multicast group communications.


the first of these is that the context changes functional interpretations of the same behaviors, such as the way “ wright, right, right, rite, and write ” are interpreted based on the context of the sentence. “ right ” can be interpreted as a direction or as something good depending on the context. a second line of evidence says that errors are involved in human behavior as hierarchical organization.


in the japanese kantenji braille, the standard 8 - dot braille patterns 258, 1258, 2458, and 12458 are the patterns related to braille pattern dots - 146, since the two additional dots of kantenji patterns 0146, 1467, and 01467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, the quasi - commutative property is an extension or generalization of the general commutative property. this property is used in specific applications with various definitions.


the main reason for the design of this format is that it fits the maximum amount of data on a standard 80 - character - wide screen or printer, while still being very easy to read and skim visually. here the leftmost column represents the address at which the bytes represented by the following columns are located. cp / m and various dos systems ran in real mode on the x86 cpus, where addresses are composed of two parts ( base and offset ). in the above examples the final 00s are non - existent bytes beyond the end of the file. some dump tools display other characters so that it is clear they are beyond the end of the file, typically using spaces or asterisks, e. g. : or


in programming languages that support recursive data types, it is possible to type the y combinator by appropriately accounting for the recursion at the type level. the need to self - apply the variable x can be managed using a type ( rec a ), which is defined so as to be isomorphic to ( rec a - > a ). for example, in the following haskell code, we have in and out being the names of the two directions of the isomorphism, with types : which lets us write : or equivalently in ocaml : alternatively :


in the philippines, the data privacy act of 2012 mandated the creation of the national privacy commission that would monitor and maintain policies that involve information privacy and personal data protection in the country. modeled after the eu data protection directive and the asia - pacific economic cooperation ( apec ) privacy framework, the independent body would ensure compliance of the country with international standards set for data protection. the law requires government and private organizations composed of at least 250 employees or those which have access to the personal and identifiable information of at least 1000 people to appoint a data protection officer that would assist in regulating the management of personal information in such entities. in summary, the law identifies important points regarding the handling of personal information as follows : personal information must be collected for reasons that are specified, legitimate, and reasonable.


in mathematics, a supercommutative ( associative ) algebra is a superalgebra ( i. e. a z2 - graded algebra ) such that for any two homogeneous elements x, y we have y x = ( − 1 ) | x | | y | x y, { \ displaystyle yx = ( - 1 ) ^ { | x | | y | } xy, } where | x | denotes the grade of the element and is 0 or 1 ( in z2 ) according to whether the grade is even or odd, respectively. equivalently, it is a superalgebra where the supercommutator = x y − ( − 1 ) | x | | y | y x { \ displaystyle = xy - ( - 1 ) ^ { | x | | y | } yx } always vanishes. algebraic structures which supercommute in the above sense are sometimes referred to as skew - commutative associative algebras to emphasize the anti - commutation, or, to emphasize the grading, graded - commutative or, if the supercommutativity is understood, simply commutative. any commutative algebra is a supercommutative algebra if given the trivial gradation ( i. e. all elements are even ).


in mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. the word " permutation " also refers to the act or process of changing the linear order of an ordered set. permutations differ from combinations, which are selections of some members of a set regardless of order. for example, written as tuples, there are six permutations of the set { 1, 2, 3 }, namely ( 1, 2, 3 ), ( 1, 3, 2 ), ( 2, 1, 3 ), ( 2, 3, 1 ), ( 3, 1, 2 ), and ( 3, 2, 1 ). these are all the possible orderings of this three - element set.


this is possible because the logarithm of a product is the sum of the logarithms of the factors : provided that b, x and y are all positive and b = 1. the slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. the present - day notion of logarithms comes from leonhard euler, who connected them to the exponential function in the 18th century, and who also introduced the letter e as the base of natural logarithms. logarithmic scales reduce wide - ranging quantities to smaller scopes.


in usaid, the use of a program cycle, " codified in the automated directive systems ( ads ) 201, is usaid's operational model for planning, delivering, assessing, and adapting development programming in a given region or country to achieve more effective and sustainable results in order to advance u. s. foreign policy ". relatedly, within the agency there exists resources regarding adaptive management decision cycles.


as properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set { 1, 2, …, n } { \ displaystyle \ { 1, 2, \ ldots, n \ } } that are considered for studying permutations. in elementary combinatorics, the k - permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. when k is equal to the size of the set, these are the permutations of the set.


in meteorology a ridge or barometric ridge is an elongated area of relatively high atmospheric pressure compared to the surrounding environment, without being a closed circulation. it is associated with an area of maximum anticyclonic curvature of wind flow. the ridge originates in the center of an anticyclone and sandwiched between two low - pressure areas, and the locus of the maximum curvature is called the ridge line. this phenomenon is the opposite of a trough.


for example, in the multiset { a, a, b, b, b, c } the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6. nicolaas govert de bruijn coined the word multiset in the 1970s, according to donald knuth. : 694 however, the concept of multisets predates the coinage of the word multiset by many centuries.


in the svp, a basis of a vector space v and a norm n ( often l2 ) are given for a lattice l and one must find the shortest non - zero vector in v, as measured by n, in l. in other words, the algorithm should output a non - zero vector v such that ‖ v ‖ n = λ ( l ) { \ displaystyle \ | v \ | _ { n } = \ lambda ( l ) }. in the γ - approximation version svpγ, one must find a non - zero lattice vector of length at most γ ⋅ λ ( l ) { \ displaystyle \ gamma \ cdot \ lambda ( l ) } for given γ ≥ 1 { \ displaystyle \ gamma \ geq 1 }.


error correction does not seem to have a direct influence on learning a second language. instruction may affect the rate of learning, but the stages remain the same.


in probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take " on average " over an arbitrarily large number of occurrences – given that a certain set of " conditions " is known to occur. if the random variable can take on only a finite number of values, the " conditions " are that the variable can only take on a subset of those values. more formally, in the case when the random variable is defined over a discrete probability space, the " conditions " are a partition of this probability space.


in mathematics, knuth's up - arrow notation is a method of notation for very large integers, introduced by donald knuth in 1976. in his 1947 paper, r. l. goodstein introduced the specific sequence of operations that are now called hyperoperations. goodstein also suggested the greek names tetration, pentation, etc., for the extended operations beyond exponentiation. the sequence starts with a unary operation ( the successor function with n = 0 ), and continues with the binary operations of addition ( n = 1 ), multiplication ( n = 2 ), exponentiation ( n = 3 ), tetration ( n = 4 ), pentation ( n = 5 ), etc. various notations have been used to represent hyperoperations. one such notation is h n ( a, b ) { \ displaystyle h _ { n } ( a, b ) }. knuth's up - arrow notation ↑ { \ displaystyle \ uparrow } is another. for example : the single arrow ↑ { \ displaystyle \ uparrow } represents exponentiation ( iterated multiplication ) the double arrow ↑↑ { \ displaystyle \ uparrow \ uparrow } represents tetration ( iterated exponentiation ) the triple arrow ↑↑↑ { \ displaystyle \ uparrow \ uparrow \ uparrow } represents pentation ( iterated tetration ) the general definition of the up - arrow notation is as follows ( for a ≥ 0, n ≥ 1, b ≥ 0 { \ displaystyle a \ geq 0, n \ geq 1, b \ geq 0 } ) : here, ↑ n { \ displaystyle \ uparrow ^ { n } } stands for n arrows, so for example the square brackets are another notation for hyperoperations.


this is a pbe - it is a best - response for both sender and receiver. the sender's strategy is : never give. suppose the receiver's beliefs when receiving a gift is that the sender is a friend with probability q { \ displaystyle q }, where q { \ displaystyle q } is any number in { \ displaystyle }.


the number of correct digits roughly doubles with each step. this algorithm is first in the class of householder's methods, succeeded by halley's method. the method can also be extended to complex functions and to systems of equations.


in one special case two covariates, say j and k, are identical for each observation, so that x ( j ) = x ( k ) { \ displaystyle x _ { ( j ) } = x _ { ( k ) } }, where x ( j ), i = x ( k ), i { \ displaystyle x _ { ( j ), i } = x _ { ( k ), i } }. then the values of β j { \ displaystyle \ beta _ { j } } and β k { \ displaystyle \ beta _ { k } } that minimize the lasso objective function are not uniquely determined. in fact, if some β ^ { \ displaystyle { \ hat { \ beta } } } in which β ^ j β ^ k ≥ 0 { \ displaystyle { \ hat { \ beta } } _ { j } { \ hat { \ beta } } _ { k } \ geq 0 }, then if s ∈ { \ displaystyle s \ in } replacing β ^ j { \ displaystyle { \ hat { \ beta } } _ { j } } by s ( β ^ j + β ^ k ) { \ displaystyle s ( { \ hat { \ beta } } _ { j } + { \ hat { \ beta } } _ { k } ) } and β ^ k { \ displaystyle { \ hat { \ beta } } _ { k } } by ( 1 − s ) ( β ^ j + β ^ k ) { \ displaystyle ( 1 - s ) ( { \ hat { \ beta } } _ { j } + { \ hat { \ beta } } _ { k } ) }, while keeping all the other β ^ i { \ displaystyle { \ hat { \ beta } } _ { i } } fixed, gives a new solution, so the lasso objective function then has a continuum of valid minimizers. several variants of the lasso, including the elastic net regularization, have been designed to address this shortcoming.


whatever we may say something'is'obviously is not the'something'on the silent levels. " by making it a'mental'habit to find and keep one's bearings among the ordered stages, general semantics training seeks to sharpen internal orientation much as a gps device may sharpen external orientation. once trained, general semanticists affirm, a person will act, respond, and make decisions more appropriate to any given set of happenings.


given a data array x, the basic backus - gilbert inverse is : h θ = c − 1 g θ g θ t c − 1 g θ { \ displaystyle \ mathbf { h } _ { \ theta } = { \ frac { \ mathbf { c } ^ { - 1 } \ mathbf { g } _ { \ theta } } { \ mathbf { g } _ { \ theta } ^ { t } \ mathbf { c } ^ { - 1 } \ mathbf { g } _ { \ theta } } } } where c is the covariance matrix of the data, and gθ is an a priori constraint representing the source θ for which a solution is sought. regularization is implemented by " whitening " the covariance matrix : c ′ = c + λ i { \ displaystyle \ mathbf { c }'= \ mathbf { c } + \ lambda \ mathbf { i } } with c ′ replacing c in the equation for hθ. then, h θ t x { \ displaystyle \ mathbf { h } _ { \ theta } ^ { t } \ mathbf { x } } is an estimate of the activity of the source θ.


in some countries such as germany, the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with the first digit of the multiplier : 23958233 · 5830 — — — — — — — — — — — — — — — 119791165 191665864 71874699 00000000 — — — — — — — — — — — — — — — 139676498390 below pseudocode describes the process of above multiplication. it keeps only one row to maintain the sum which finally becomes the result. note that the'+ ='operator is used to denote sum to existing value and store operation ( akin to languages such as java and c ) for compactness.


{ \ cdot } \, } _ { i \ in i } a _ { i } } ). a standard way for building the disjoint union is to define a { \ displaystyle a } as the set of ordered pairs ( x, i ) { \ displaystyle ( x, i ) } such that x ∈ a i, { \ displaystyle x \ in a _ { i }, } and the injection a i → a { \ displaystyle a _ { i } \ to a } as x ↦ ( x, i ). { \ displaystyle x \ mapsto ( x, i ). }


in statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data.


we can show that c = 2 0 { \ displaystyle { \ mathfrak { c } } = 2 ^ { \ aleph _ { 0 } } }, this also being the cardinality of the set of all subsets of the natural numbers. the continuum hypothesis says that 1 = 2 0 { \ displaystyle \ aleph _ { 1 } = 2 ^ { \ aleph _ { 0 } } }, i. e. 2 0 { \ displaystyle 2 ^ { \ aleph _ { 0 } } } is the smallest cardinal number bigger than 0 { \ displaystyle \ aleph _ { 0 } }, i. e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers. the continuum hypothesis is independent of zfc, a standard axiomatization of set theory ; that is, it is impossible to prove the continuum hypothesis or its negation from zfc — provided that zfc is consistent. for more detail, see § cardinality of the continuum below.


for instance, the set of all integers ( including negative numbers ) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still ( only ) countably infinite. nevertheless, there are sets, such as the set of real numbers, that can be shown to be " too large " to admit a bijection with the natural numbers, and these sets are called " uncountable. " sets for which there exists a bijection between them are said to have the same cardinality, and in the most general sense counting a set can be taken to mean determining its cardinality.


in logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. in other words, it cannot be false. it cannot be untrue.


a line l in a projective plane π is a translation line if the group of all elations with axis l acts transitively on the points of the affine plane obtained by removing l from the plane π, πl ( the affine derivative of π ). a projective plane with a translation line is called a translation plane. the affine plane obtained by removing the translation line is called an affine translation plane. while it is often easier to work with projective planes, in this context several authors use the term translation plane to mean affine translation plane.