in some cases the two methods may yield essentially the same results. the basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set. a more advanced technique is to form a kernel out of the data, using a fixed kernel. the basis functions from the eigenvectors of the kernel matrix are thus non - linear in the location of the data ( see mercer's theorem and the kernel trick for more information ).


in molecular biology and genetics, dna annotation or genome annotation is the process of describing the structure and function of the components of a genome, by analyzing and interpreting them in order to extract their biological significance and understand the biological processes in which they participate. among other things, it identifies the locations of genes and all the coding regions in a genome and determines what those genes do. annotation is performed after a genome is sequenced and assembled, and is a necessary step in genome analysis before the sequence is deposited in a database and described in a published article. although describing individual genes and their products or functions is sufficient to consider this description as an annotation, the depth of analysis reported in literature for different genomes vary widely, with some reports including additional information that goes beyond a simple annotation.


in the java collections framework, the class list represents an ordered collection of objects of type myclass. upper bounds are specified using extends : a list extends myclass > is a list of objects of some subclass of myclass, i. e. any object in the list is guaranteed to be of type myclass, so one can iterate over it using a variable of type myclass however, it is not guaranteed that one can add any object of type myclass to that list : the converse is true for lower bounds, which are specified using super : a list super myclass > is a list of objects of some superclass of myclass, i. e. the list is guaranteed to be able to contain any object of type myclass, so one can add any object of type myclass : however, it is not guaranteed that one can iterate over that list using a variable of type myclass : in order to be able to do both add objects of type myclass to the list and iterate over it using a variable of type myclass, a list is needed, which is the only type of list that is both list extends myclass > and list super myclass >. the mnemonics pecs ( producer extends, consumer super ) from the book effective java by joshua bloch gives an easy way to remember when to use wildcards ( corresponding to covariance and contravariance ) in java.


in the field of nonparametric optimization, voronoi manifolds serve as valuable tools for reducing the sample size and selecting promising points. they help identify regions of interest where experiments or evaluations should be focused, leading to efficient optimization algorithms and improved convergence rates.


the reason is that, in any minimum - length partition, every maximal line - segment can be " pushed " until it hits one of the vertices of the boundary, without changing the total length. therefore, there are only o ( n 2 ) { \ displaystyle o ( n ^ { 2 } ) } candidates for a line segment in an optimal partition, and they can be checked efficiently using dynamic programming. : 166 – 167 if the raw polygon might have holes, even if they are degenerate holes ( i. e., single points ), the problem is np - hard.


binary logarithms are included in the standard c mathematical functions and other mathematical software packages. the integer part of a binary logarithm can be found using the find first set operation on an integer value, or by looking up the exponent of a floating point value. the fractional part of the logarithm can be calculated efficiently.


this objective is a quadratic form in b { \ displaystyle \ mathbf { b } }. taking the gradient of this quadratic form with respect to b { \ displaystyle \ mathbf { b } } and equating it to zero ( when b = β ^ { \ displaystyle \ mathbf { b } = { \ hat { \ beta } } } ) gives 2 x t ω − 1 x β ^ − 2 x t ω − 1 y = 0 { \ displaystyle 2 \ mathbf { x } ^ { \ mathsf { t } } \ mathbf { \ omega } ^ { - 1 } \ mathbf { x } { \ hat { \ beta } } - 2 \ mathbf { x } ^ { \ mathsf { t } } \ mathbf { \ omega } ^ { - 1 } \ mathbf { y } = 0 } therefore, the minimum of the objective function can be computed yielding the explicit formula : β ^ = ( x t ω − 1 x ) − 1 x t ω − 1 y. { \ displaystyle \ mathbf { \ hat { \ beta } } = \ left ( \ mathbf { x } ^ { \ mathsf { t } } \ mathbf { \ omega } ^ { - 1 } \ mathbf { x } \ right ) ^ { - 1 } \ mathbf { x } ^ { \ mathsf { t } } \ mathbf { \ omega } ^ { - 1 } \ mathbf { y }. } the quantity ω − 1 { \ displaystyle \ mathbf { \ omega } ^ { - 1 } } is known as the precision matrix ( or dispersion matrix ), a generalization of the diagonal weight matrix.


in robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. a regression analysis models the relationship between one or more independent variables and a dependent variable. standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise ( i. e. are not robust to assumption violations ). robust regression methods are designed to limit the effect that violations of assumptions by the underlying data - generating process have on regression estimates. for example, least squares estimates for regression models are highly sensitive to outliers : an outlier with twice the error magnitude of a typical observation contributes four ( two squared ) times as much to the squared error loss, and therefore has more leverage over the regression estimates. the huber loss function is a robust alternative to standard square error loss that reduces outliers'contributions to the squared error loss, thereby limiting their impact on regression estimates.


the number of iterations is then decoupled to the number of points ( each point can be considered more than once ). the incremental gradient method can be shown to provide a minimizer to the empirical risk. incremental techniques can be advantageous when considering objective functions made up of a sum of many terms e. g. an empirical error corresponding to a very large dataset.


there is an additive definition of the psi function as well. quoting from dickson, r. dedekind proved that, if n { \ displaystyle n } is decomposed in every way into a product a b { \ displaystyle ab } and if e { \ displaystyle e } is the g. c. d. of a, b { \ displaystyle a, b } then a ( a / e ) φ ( e ) = n p | n ( 1 + 1 p ) { \ displaystyle \ sum _ { a } ( a / e ) \ varphi ( e ) = n \ prod _ { p | n } \ left ( 1 + { \ frac { 1 } { p } } \ right ) } where a { \ displaystyle a } ranges over all divisors of n { \ displaystyle n } and p { \ displaystyle p } over the prime divisors of n { \ displaystyle n } and φ { \ displaystyle \ varphi } is the totient function.


in the field of networking, the government secure intranet ( gsi ) puts in place a secure link between central government departments. it is an ip - based virtual private network based on broadband technology introduced in april 1998 and further upgraded in february 2004. among other things, it offers a variety of advanced services including file transfer and search facilities, directory services, email exchange facilities ( both between network members and over the internet ) as well as voice and video services. an additional network is currently also under development : the public sector network ( psn ) will be the network to interconnect public authorities ( including departments and agencies in england ; devolved administrations and local governments ) and facilitate in particular sharing of information and services among each other.


which one ( s ) are appropriate depend on a variety of factors, such as : which assumptions ( if any ) may be made a priori about the distributions from which the data have been sampled? for example, in many situations it may be assumed that the underlying distributions are normal distributions. in other cases the data are categorical, coming from a discrete distribution over a nominal scale, such as which entry was selected from a menu. does the hypothesis being tested apply to the distributions as a whole, or just some population parameter, for example the mean or the variance? is the hypothesis being tested merely that there is a difference in the relevant population characteristics ( in which case a two - sided test may be indicated ), or does it involve a specific bias ( " a is better than b " ), so that a one - sided test can be used?


many scientists such as maxwell, heaviside and hertz unsuccessfully attempted to solve these problems by incorporating either fresnel or stokes'theories into maxwell's new electromagnetic laws. hendrik lorentz spent considerable effort along these lines. after working on this problem for a decade, the issues with stokes'theory caused him to abandon it and to follow fresnel's suggestion of a ( mostly ) stationary aether ( 1892, 1895 ).


in order to encrypt or decrypt data, use the standard block cipher mode of operation on all but the last two blocks of data. the following steps describe how to handle the last two blocks of the plaintext, called pn−1 and pn, where the length of pn−1 equals the block size of the cipher in bits, b ; the length of the last block, pn, is m bits ; and k is the key that is in use. m can range from 1 to b, inclusive, so pn could possibly be a complete block. the cbc mode description also makes use of the ciphertext block just previous to the blocks concerned, cn−2, which may in fact be the iv if the plaintext fits within two blocks.


well before any significant investments are made, the uncertainty is reduced to a level where the risk can be carried comfortably. in this kind of environment the uncertainty level decreases rapidly in the beginning and the cone shape is less obvious. the software business however is very volatile and there is an external pressure to decrease the uncertainty level over time.


in mathematics, a prime number p is called a chen prime if p + 2 is either a prime or a product of two primes ( also called a semiprime ). the even number 2p + 2 therefore satisfies chen's theorem. the chen primes are named after chen jingrun, who proved in 1966 that there are infinitely many such primes. this result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a chen prime.


in such a scenario, the second smallest eigenvalue ( λ 2 { \ displaystyle \ lambda _ { 2 } } ) of l { \ displaystyle l }, yields a lower bound on the optimal cost ( c { \ displaystyle c } ) of ratio - cut partition with c ≥ λ 2 n { \ displaystyle c \ geq { \ frac { \ lambda _ { 2 } } { n } } }. the eigenvector ( v 2 { \ displaystyle v _ { 2 } } ) corresponding to λ 2 { \ displaystyle \ lambda _ { 2 } }, called the fiedler vector, bisects the graph into only two communities based on the sign of the corresponding vector entry. division into a larger number of communities can be achieved by repeated bisection or by using multiple eigenvectors corresponding to the smallest eigenvalues. the examples in figures 1, 2 illustrate the spectral bisection approach.


in the bayesian ( or epistemological ) interpretation, probability measures a " degree of belief ". bayes'theorem links the degree of belief in a proposition before and after accounting for evidence. for example, suppose it is believed with 50 % certainty that a coin is twice as likely to land heads than tails. if the coin is flipped a number of times and the outcomes observed, that degree of belief will probably rise or fall, but might even remain the same, depending on the results. for proposition a and evidence b, p ( a ), the prior, is the initial degree of belief in a. p ( a | b ), the posterior, is the degree of belief after incorporating news that b is true. the quotient p ( b | a ) / p ( b ) represents the support b provides for a. for more on the application of bayes'theorem under the bayesian interpretation of probability, see bayesian inference.


in policy iteration ( howard 1960 ), step one is performed once, and then step two is performed once, then both are repeated until policy converges. then step one is again performed once and so on. ( policy iteration was invented by howard to optimize sears catalogue mailing, which he had been optimizing using value iteration. )


the type of co - ownership does not affect the right of co - owners to sell their fractional interest in the property to others during their lifetimes, but it does affect their power to will the property upon death to their devisees in the case of joint tenants. however, any joint tenant can change this by severing the joint tenancy. this occurs whenever a joint tenant transfers his or her fractional interest in the property. laws can vary from place to place, and the following general discussion will not be applicable in its entirety to all jurisdictions.


in the united kingdom the data protection act 1998 ( c 29 ) ( information commissioner ) implemented the eu directive on the protection of personal data. it replaced the data protection act 1984 ( c 35 ). the 2016 general data protection regulation supersedes previous protection acts. the data protection act 2018 ( c 12 ) updates data protection laws in the uk. it is a national law which complements the european union's general data protection regulation ( gdpr ).


with the definition given, ⟨ ρ ∗ ( g ) φ, ρ ( g ) v ⟩ = ⟨ ρ ( g − 1 ) t φ, ρ ( g ) v ⟩ = ( ρ ( g − 1 ) t φ ) t ρ ( g ) v = φ t ρ ( g − 1 ) ρ ( g ) v = φ t v = ⟨ φ, v ⟩. { \ displaystyle \ langle { \ rho } ^ { * } ( g ) \ varphi, \ rho ( g ) v \ rangle = \ langle \ rho ( g ^ { - 1 } ) ^ { t } \ varphi, \ rho ( g ) v \ rangle = ( \ rho ( g ^ { - 1 } ) ^ { t } \ varphi ) ^ { t } \ rho ( g ) v = \ varphi ^ { t } \ rho ( g ^ { - 1 } ) \ rho ( g ) v = \ varphi ^ { t } v = \ langle \ varphi, v \ rangle. }


in the 1970s through the early 1980s, paper tape was commonly used to transfer binary data for incorporation in either mask - programmable read - only memory ( rom ) chips or their erasable counterparts eproms. a significant variety of encoding formats were developed for use in computer and rom / eprom data transfer. encoding formats commonly used were primarily driven by those formats that eprom programming devices supported and included various ascii hex variants as well as a number of proprietary formats. a much more primitive as well as a much longer high - level encoding scheme was also used, bnpf ( begin - negative - positive - finish ), also written as bpnf.


in some cases, random necklaces can be split equally using fewer cuts. mathematicians noga alon, dor elboim, gabor tardos and janos pach studied the typical number of cuts required to split a random necklace between two thieves. in the model they considered, a necklace is chosen uniformly at random from the set of necklaces with t colors and m beads of each color. as m tends to infinity, the probability that the necklace can be split using ( t + 1 ) / 2 cuts or less tends to zero while the probability that it's possible to split with ( t + 1 ) / 2 + 1 cuts is bounded away from zero.


{ \ displaystyle ~ { \ frac { a - { \ sqrt { a ^ { 2 } - c } } } { 2 } } ~. } thus x and y are rational if and only if d = a 2 − c { \ displaystyle d = { \ sqrt { a ^ { 2 } - c } } ~ } is a rational number. for explicitly choosing the various signs, one must consider only positive real square roots, and thus assuming c > 0.


in some domains, a few dozen different source and target schema ( proprietary data formats ) may exist. an " exchange " or " interchange format " is often developed for a single domain, and then necessary routines ( mappings ) are written to ( indirectly ) transform / translate each and every source schema to each and every target schema by using the interchange format as an intermediate step. that requires a lot less work than writing and debugging the hundreds of different routines that would be required to directly translate each and every source schema directly to each and every target schema. examples of these transformative interchange formats include : standard interchange format for geospatial data ; data interchange format for spreadsheet data ; open document format for spreadsheets, charts, presentations and word processing documents ; gps exchange format or keyhole markup language for describing gps data ; and gdsii for integrated circuit layout.


an important example of normal variance - mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse gaussian distribution. the probability density function of a normal variance - mean mixture with mixing probability density g { \ displaystyle g } is f ( x ) = 0 ∞ 1 2 π σ 2 v exp ( − ( x − α − β v ) 2 2 σ 2 v ) g ( v ) d v { \ displaystyle f ( x ) = \ int _ { 0 } ^ { \ infty } { \ frac { 1 } { \ sqrt { 2 \ pi \ sigma ^ { 2 } v } } } \ exp \ left ( { \ frac { - ( x - \ alpha - \ beta v ) ^ { 2 } } { 2 \ sigma ^ { 2 } v } } \ right ) g ( v ) \, dv } and its moment generating function is m ( s ) = exp ( α s ) m g ( β s + 1 2 σ 2 s 2 ), { \ displaystyle m ( s ) = \ exp ( \ alpha s ) \, m _ { g } \ left ( \ beta s + { \ frac { 1 } { 2 } } \ sigma ^ { 2 } s ^ { 2 } \ right ), } where m g { \ displaystyle m _ { g } } is the moment generating function of the probability distribution with density function g { \ displaystyle g }, i. e. m g ( s ) = e ( exp ( s v ) ) = 0 ∞ exp ( s v ) g ( v ) d v. { \ displaystyle m _ { g } ( s ) = e \ left ( \ exp ( sv ) \ right ) = \ int _ { 0 } ^ { \ infty } \ exp ( sv ) g ( v ) \, dv. }


in mathematics, an uncountable set ( or uncountably infinite set ) is an infinite set that contains too many elements to be countable. the uncountability of a set is closely related to its cardinal number : a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.


in mathematics, two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent but not obviously equivalent. in particular, two definitions or axiomatizations of the same object are " cryptomorphic " if it is not obvious that they define the same object. examples of cryptomorphic definitions abound in matroid theory and others can be found elsewhere, e. g., in group theory the definition of a group by a single operation of division, which is not obviously equivalent to the usual three " operations " of identity element, inverse, and multiplication. this word is a play on the many morphisms in mathematics, but " cryptomorphism " is only very distantly related to " isomorphism ", " homomorphism ", or " morphisms ". the equivalence may in a cryptomorphism, if it is not actual identity, be informal, or may be formalized in terms of a bijection or equivalence of categories between the mathematical objects defined by the two cryptomorphic axiom systems.


one disk is allowed to spin freely, and the other is driven by a motor. mode locking occurs when the freely - spinning disk turns at a frequency that is a rational multiple of that of the driven rotator. the simplest mathematical model that exhibits mode - locking is the circle map, which attempts to capture the motion of the spinning disks at discrete time intervals.


historically, there have been several formalizations of rewriting in an abstract setting, each with its idiosyncrasies. this is due in part to the fact that some notions are equivalent, see below in this article. the formalization that is most commonly encountered in monographs and textbooks, and which is generally followed here, is due to gerard huet ( 1980 ).


the nimber addition and multiplication operations are associative and commutative. each nimber is its own negative. in particular for some pairs of ordinals, their nimber sum is smaller than either addend. the minimum excludant operation is applied to sets of nimbers.


in probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if x, y, and z are random variables on the same probability space, and the covariance of x and y is finite, then cov ( x, y ) = e ( cov ( x, y z ) ) + cov ( e ( x z ), e ( y z ) ). { \ displaystyle \ operatorname { cov } ( x, y ) = \ operatorname { e } ( \ operatorname { cov } ( x, y \ mid z ) ) + \ operatorname { cov } ( \ operatorname { e } ( x \ mid z ), \ operatorname { e } ( y \ mid z ) ). } the nomenclature in this article's title parallels the phrase law of total variance.


in some applications ( e. g., building data models from only partially observed data ) one wants to find the " nearest " correlation matrix to an " approximate " correlation matrix ( e. g., a matrix which typically lacks semi - definite positiveness due to the way it has been computed ). in 2002, higham formalized the notion of nearness using the frobenius norm and provided a method for computing the nearest correlation matrix using the dykstra's projection algorithm, of which an implementation is available as an online web api. this sparked interest in the subject, with new theoretical ( e. g., computing the nearest correlation matrix with factor structure ) and numerical ( e. g. usage the newton's method for computing the nearest correlation matrix ) results obtained in the subsequent years.


in statistics, the analogous process is usually dividing a difference ( a distance ) by a scale factor ( a measure of statistical dispersion ), which yields a dimensionless number, which is called normalization. most often, this is dividing errors or residuals by the standard deviation or sample standard deviation, respectively, yielding standard scores and studentized residuals.


however, it remains unproven as of 2022. the number of primes between prime squares is 2, 5, 6, 15, 9, 22, 11, 27,... oeis : a050216. legendre's conjecture that there is a prime between consecutive integer squares directly implies that there are at least two primes between prime squares for pn ≥ 3 since pn + 1 − pn ≥ 2.


in mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. when specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size. the ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at every step, thus enclosing a minimizer of a convex function.


the sequence of output subcommands required to accomplish the input command is generated by situations ( i. e., branching conditions ) that cause the fsa to transition from one output subcommand to the next. in step 4, each of the situations that are defined in step 3 are analyzed to reveal their dependencies on world and task states. this step identifies the detailed relationships between entities, events, and states of the world that cause a particular situation to be true.


in the balanced number partitioning problem, there are constraints on the number of items that can be allocated to each subset ( these are called cardinality constraints ). another variant is the multidimensional number partitioning.


the term is also used for other devices which can both transmit and receive through a communications channel, such as optical transceivers which transmit and receive light in optical fiber systems, and bus transceivers which transmit and receive digital data in computer data buses. radio transceivers are widely used in wireless devices. one large use is in two - way radios, which are audio transceivers used for bidirectional person - to - person voice communication.


in some texts, a trivial proof refers to a statement involving a material implication p→q, where the consequent q, is always true. here, the proof follows immediately by virtue of the definition of material implication in which as the implication is true regardless of the truth value of the antecedent p if the consequent is fixed as true. a related concept is a vacuous truth, where the antecedent p in a material implication p→q is false. in this case, the implication is always true regardless of the truth value of the consequent q – again by virtue of the definition of material implication.


in public transportation, schedule adherence or on - time performance refers to the level of success of the service ( such as a bus or train ) remaining on the published schedule. on time performance, sometimes referred to as on time running, is normally expressed as a percentage, with a higher percentage meaning more vehicles are on time. the level of on time performance for many transport systems is a very important measure of the effectiveness of the system.


for this reason, security and access control became a major focus of the multics project in 1965. another ongoing issue was properly handling computing resources : users spent most of their time staring at the terminal and thinking about what to input instead of actually using the resources of the computer, and a time - sharing system should give the cpu time to an active user during these periods. finally, the systems typically offered a memory hierarchy several layers deep, and partitioning this expensive resource led to major developments in virtual memory systems.


in networking jargon, a computer, phone, or internet of things device connected to a computer network is sometimes referred to as an end system or end station, because it sits at the edge of the network. the end user directly interacts with an end system that provides information or services. end systems that are connected to the internet are also referred to as internet hosts ; this is because they host ( run ) internet applications such as a web browser or an email retrieval program. the internet's end systems include some computers with which the end user does not directly interact. these include mail servers, web servers, or database servers.


in print, summation and product are represented by special symbols ; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. thus, the iterations of the four operations mentioned above are denoted,,, { \ displaystyle \ sum, \ \ prod, \ \ bigcup, } and { \ displaystyle \ bigcap }, respectively. more generally, iteration of a binary function is generally denoted by a slash : iteration of f { \ displaystyle f } over the sequence ( a 1, a 2 …, a n ) { \ displaystyle ( a _ { 1 }, a _ { 2 } \ ldots, a _ { n } ) } is denoted by f / ( a 1, a 2 …, a n ) { \ displaystyle f / ( a _ { 1 }, a _ { 2 } \ ldots, a _ { n } ) }, following the notation for reduce in bird – meertens formalism. in general, there is more than one way to extend a binary operation to operate on finite sequences, depending on whether the operator is associative, and whether the operator has identity elements.


hence the degree of ψ ℓ { \ displaystyle \ psi _ { \ ell } } is equal to either 1 2 ( l 2 − 1 ) { \ displaystyle { \ frac { 1 } { 2 } } ( l ^ { 2 } - 1 ) }, 1 2 ( l − 1 ) { \ displaystyle { \ frac { 1 } { 2 } } ( l - 1 ) }, or 0. rene schoof observed that working modulo the ℓ { \ displaystyle \ ell } th division polynomial allows one to work with all ℓ { \ displaystyle \ ell } - torsion points simultaneously. this is heavily used in schoof's algorithm for counting points on elliptic curves.


= λ e − λ t − e − λ t u = 1 x − 1 ( λ u t u − 1 ( u − 1 )! − λ u + 1 t u u! ) { \ displaystyle { \ begin { aligned } f ( t ) & { } = { \ frac { d } { dt } } \ pr ( t _ { x } \ leq t ) = { \ frac { d } { dt } } \ pr ( x _ { t } \ geq x ) = { \ frac { d } { dt } } ( 1 - \ pr ( x _ { t } \ leq x - 1 ) ) \ \ \ \ & { } = { \ frac { d } { dt } } \ left ( 1 - \ sum _ { u = 0 } ^ { x - 1 } \ pr ( x _ { t } = u ) \ right ) = { \ frac { d } { dt } } \ left ( 1 - \ sum _ { u = 0 } ^ { x - 1 } { \ frac { ( \ lambda t ) ^ { u } e ^ { - \ lambda t } } { u!


in the example that follows, there are exactly two complete lead - reductions that produce two very different results. the fact that the results are irreducible ( not only lead - irreducible ) is specific to the example, although this is rather common with such small examples. in this two variable example, the monomial ordering that is used is the lexicographic order with x > y, { \ displaystyle x > y, } and we consider the reduction of by g = { g 1, g 2 }, { \ displaystyle g = \ { g _ { 1 }, g _ { 2 } \ }, } with for the first reduction step, either the first or the second term of f may be reduced. however, the reduction of a term amounts to removing this term at the cost of adding new lower terms ; if it is not the first reducible term that is reduced, it may occur that a further reduction adds a similar term, which must be reduced again.


in the united states, the u. s. food and drug administration ( fda ) controls antimicrobial handsoaps and sanitizers as over - the - counter drugs ( otc ) because they are intended for topical anti - microbial use to prevent disease in humans. the fda requires strict labeling which informs consumers on proper use of this otc drug and dangers to avoid, including warning adults not to ingest, not to use in the eyes, to keep out of the reach of children, and to allow use by children only under adult supervision. according to the american association of poison control centers, there were nearly 12, 000 cases of hand sanitizer ingestion in 2006. if ingested, alcohol - based hand sanitizers can cause alcohol poisoning in small children.


they may be running traditionally in - house software or general purpose software such as dos. many of the newer ones have touch screens. they may be connected to computerized point of sale networks using any type of protocol. such systems may be accessed remotely for the purpose of obtaining records or troubleshooting. many businesses also use tablet computers as cash registers, utilizing the sale system as downloadable app - software.


in designing an artificial intelligence agent, it was soon realized that representing common - sense knowledge, knowledge that humans simply take for granted, was essential to make an ai that could interact with humans using natural language. cyc was meant to address this problem.


in statistics, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value ( parameter ) of interest. it can be defined as the proportion of instances where the interval surrounds the true value as assessed by long - run frequency.


the mse is the second moment ( about the origin ) of the error, and thus incorporates both the variance of the estimator ( how widely spread the estimates are from one data sample to another ) and its bias ( how far off the average estimated value is from the true value ). for an unbiased estimator, the mse is the variance of the estimator. like the variance, mse has the same units of measurement as the square of the quantity being estimated. in an analogy to standard deviation, taking the square root of mse yields the root - mean - square error or root - mean - square deviation ( rmse or rmsd ), which has the same units as the quantity being estimated ; for an unbiased estimator, the rmse is the square root of the variance, known as the standard error.


this first unit had been manufactured to the following specifications : 1, 400 w, 40 hz, 120 : 72 v, 11. 6 : 19. 4 a, ratio 1. 67 : 1, one - phase, shell form. in both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air ( see toroidal cores below ). the new transformers were 3. 4 times more efficient than the open - core bipolar devices of gaulard and gibbs. the zbd patents included two other major interrelated innovations : one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher ( initially 1, 400 to 2, 000 v ) than the voltage of utilization loads ( 100 v initially preferred ).


in nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point. given a hyperreal number x in r∗, the monad of x is the set monad ( x ) = { y ∈ r ∗ x − y is infinitesimal }. { \ displaystyle { \ text { monad } } ( x ) = \ { y \ in \ mathbb { r } ^ { * } \ mid x - y { \ text { is infinitesimal } } \ }. } if x is finite ( limited ), the unique real number in the monad of x is called the standard part of x. = = references = =


the first recall device in the united states was adopted in los angeles in 1903. typically, the process involves the collection of citizen petitions for the recall of an elected official ; if a sufficient number of valid signatures are collected and verified, a recall election is triggered. there have been four gubernatorial recall elections in u. s.


the linkage criterion determines the distance between sets of observations as a function of the pairwise distances between observations. some commonly used linkage criteria between two sets of observations a and b and a distance d are : some of these can only be recomputed recursively ( wpgma, wpgmc ), for many a recursive computation with lance - williams - equations is more efficient, while for other ( mini - max, hausdorff, medoid ) the distances have to be computed with the slower full formula. other linkage criteria include : the probability that candidate clusters spawn from the same distribution function ( v - linkage ). the product of in - degree and out - degree on a k - nearest - neighbour graph ( graph degree linkage ). the increment of some cluster descriptor ( i. e., a quantity defined for measuring the quality of a cluster ) after merging two clusters.


the following algorithm b doesn't have this disadvantage, but it also doesn't have the fast arithmetic modulo p { \ displaystyle p } algorithm a has in that case. algorithm b select a q { \ displaystyle q } - bit prime q { \ displaystyle q } so that q ≡ 7 mod 12 { \ displaystyle q \ equiv 7 \ { \ text { mod } } \ 12 }. find the roots r 1 { \ displaystyle r _ { 1 } } and r 2 { \ displaystyle r _ { 2 } } of x 2 − x + 1 mod q { \ displaystyle x ^ { 2 } - x + 1 \ { \ text { mod } } \ q }.


in mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle. let s { \ displaystyle s } be a set, and let ( x i ) { \ displaystyle ( x _ { i } ) } and ( y i ) { \ displaystyle ( y _ { i } ) }, i = 0, 1, 2, …, { \ displaystyle i = 0, 1, 2, \ ldots, } be two sequences in s. { \ displaystyle s. } the interleave sequence is defined to be the sequence x 0, y 0, x 1, y 1, … { \ displaystyle x _ { 0 }, y _ { 0 }, x _ { 1 }, y _ { 1 }, \ dots }.


clustered lasso is a generalization of fused lasso that identifies and groups relevant covariates based on their effects ( coefficients ). the basic idea is to penalize the differences between the coefficients so that nonzero ones cluster. this can be modeled using the following regularization : i < j p | β i − β j | ≤ t 2. { \ displaystyle \ sum _ { i


query - dependent methods attempt to measure the degree to which a page matches a specific query, independent of the importance of the page. query - dependent ranking is usually based on heuristics that consider the number and locations of matches of the various query words on the page itself, in the url or in any anchor text referring to the page. in webometrics, it is possible to rank institutions according to their presence in the web ( number of webpages ) and the impact of these contents, such as the webometrics ranking of world universities.


in the first loop, the original ( parent ) process forks 10 copies of itself. each of these child processes ( detected by the fact that fork ( ) returned zero ) prints a message, sleeps, and exits. all of the children are created at essentially the same time ( since the parent is doing very little in the loop ), so it is somewhat random when each of them gets scheduled for the first time - thus the scrambled order of their messages. during the loop, an array of child process ids is built.


in medicine, sampling is gathering of matter from the body to aid in the process of a medical diagnosis and / or evaluation of an indication for treatment, further medical tests or other procedures. in this sense, the sample is the gathered matter, and the sampling tool or sampler is the person or material to collect the sample. sampling is a prerequisite for many medical tests, but generally not for medical history, physical examination and radiologic tests.


bentley also proposed using range trees, which improved query time to o ( log d n + k ) { \ displaystyle o ( \ log ^ { d } n + k ) } but increased space to o ( n log d − 1 n ) { \ displaystyle o ( n \ log ^ { d - 1 } n ) }. dan willard used downpointers, a special case of fractional cascading to reduce the query time further to o ( log d − 1 n + k ) { \ displaystyle o ( \ log ^ { d - 1 } n + k ) }. while the above results were achieved in the pointer machine model, further improvements have been made in the word ram model of computation in low dimensions ( 2d, 3d, 4d ).


in mathematics, the metaplectic group mp2n is a double cover of the symplectic group sp2n. it can be defined over either real or p - adic numbers. the construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles. the metaplectic group has a particularly significant infinite - dimensional linear representation, the weil representation. it was used by andre weil to give a representation - theoretic interpretation of theta functions, and is important in the theory of modular forms of half - integral weight and the theta correspondence.


in mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. the class of completely regular semigroups forms an important subclass of the class of regular semigroups, the class of inverse semigroups being another such subclass. alfred h. clifford was the first to publish a major paper on completely regular semigroups though he used the terminology " semigroups admitting relative inverses " to refer to such semigroups. the name " completely regular semigroup " stems from lyapin's book on semigroups.


in the context of regulation ( eu ) no 910 / 2014 ( eidas ), a qualified digital certificate is a public key certificate issued by a trust service provider which has government - issued qualifications. the certificate is designed to ensure the authenticity and data integrity of an electronic signature and its accompanying message and / or attached data.


since relabels and saturating pushes increase φ, the total number of nonsaturating pushes must make up the difference of ( 2 | v | − 1 ) ( | v | − 2 ) + ( 2 | v | − 1 ) ( 2 | v | | e | ) ≤ 4 | v | 2 | e |. this results in a time bound of o ( v 2e ) for the nonsaturating push operations. in sum, the algorithm executes o ( v 2 ) relabels, o ( ve ) saturating pushes and o ( v 2e ) nonsaturating pushes. data structures can be designed to pick and execute an applicable operation in o ( 1 ) time. therefore, the time complexity of the algorithm is o ( v 2e ).


in statistical inference based on regression coefficients, yes ; in predictive modelling applications, correction is neither necessary nor appropriate. to understand this, consider the measurement error as follows. let y be the outcome variable, x be the true predictor variable, and w be an approximate observation of x. frost and thompson suggest, for example, that x may be the true, long - term blood pressure of a patient, and w may be the blood pressure observed on one particular clinic visit. regression dilution arises if we are interested in the relationship between y and x, but estimate the relationship between y and w. because w is measured with variability, the slope of a regression line of y on w is less than the regression line of y on x. does this matter?


in 2012, the court ruled that under the all writs act, the defendant was required to produce an unencrypted hard drive for the court. in many jurisdictions, the legal status of forced disclosure remains unclear. the 2016 fbi – apple encryption dispute concerns the ability of courts in the united states to compel manufacturers'assistance in unlocking cell phones whose contents are cryptographically protected. as a potential counter - measure to forced disclosure some cryptographic software supports plausible deniability, where the encrypted data is indistinguishable from unused random data ( for example such as that of a drive which has been securely wiped ).


in the zeroth part, chapter 0, conway introduces a specialized form of set notation, having the form { l | r }, where l and r are again of this form, built recursively, terminating in { | }, which is to be read as an analog of the empty set. given this object, axiomatic definitions for addition, subtraction, multiplication, division and inequality may be given. as long as one insists that l


codes such as marlowe operate with this approach. the binary collision approximation can also be extended to simulate dynamic composition changes of a material due to prolonged ion irradiation, i. e. due to ion implantation and sputtering. at low ion energies, the approximation of independent collisions between atoms starts to break down.


in mathematical group theory, a c - group is a group such that the centralizer of any involution has a normal sylow 2 - subgroup. they include as special cases cit - groups where the centralizer of any involution is a 2 - group, and ti - groups where any sylow 2 - subgroups have trivial intersection. the simple c - groups were determined by suzuki ( 1965 ), and his classification is summarized by gorenstein ( 1980, 16. 4 ). the classification of c - groups was used in thompson's classification of n - groups. the simple c - groups are the projective special linear groups psl2 ( p ) for p a fermat or mersenne prime the projective special linear groups psl2 ( 9 ) the projective special linear groups psl2 ( 2n ) for n≥2 the projective special linear groups psl3 ( q ) for q a prime power the suzuki groups sz ( 22n + 1 ) for n≥1 the projective unitary groups pu3 ( q ) for q a prime power


uncertainties can also be defined by the relative error ( δx ) / x, which is usually written as a percentage. most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, which is the positive square root of the variance. the value of a quantity and its error are then expressed as an interval x ± u. however, the most general way of characterizing uncertainty is by specifying its probability distribution.


in the japanese kantenji braille, the standard 8 - dot braille patterns 235, 1235, 2345, and 12345 are the patterns related to braille pattern dots - 124, since the two additional dots of kantenji patterns 0124, 1247, and 01247 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


so the parser should also use the rule a → w if ε is in fi ( w ) and it sees on the input stream a symbol that could follow a. therefore, we also need the follow - set of a, written as fo ( a ) here, which is defined as the set of terminals a such that there is a string of symbols αaaβ that can be derived from the start symbol. we use $ as a special terminal indicating end of input stream, and s as start symbol. computing the follow - sets for the nonterminals in a grammar can be done as follows : initialize fo ( s ) with { $ } and every other fo ( ai ) with the empty set if there is a rule of the form aj → waiw ', then if the terminal a is in fi ( w'), then add a to fo ( ai ) if ε is in fi ( w'), then add fo ( aj ) to fo ( ai ) if w'has length 0, then add fo ( aj ) to fo ( ai ) repeat step 2 until all fo sets stay the same. this provides the least fixed point solution to the following system : fo ( s ) { $ } fo ( a ) fi ( w ) · fo ( b ) for each rule of the form b →... a wnow we can define exactly which rules will appear where in the parsing table.


thus measuring leakage, or iddq testing, is a quick, inexpensive method for finding defective chips. increased leakage is a common failure mode resulting from non - catastrophic overstress of a semiconductor device, when the junction or the gate oxide suffers permanent damage not sufficient to cause a catastrophic failure. overstressing the gate oxide can lead to stress - induced leakage current.


altmetrics did not originally cover citation counts, but calculate scholar impact based on diverse online research output, such as social media, online news media, online reference managers and so on. it demonstrates both the impact and the detailed composition of the impact. altmetrics could be applied to research filter, promotion and tenure dossiers, grant applications and for ranking newly - published articles in academic search engines.


infiltrating organizations is an important tool because these institutions are already seen as legitimate in the eyes of the people and provide a platform to express their ideas. when infiltrating, the dissident identifies needs of the organization and then links those needs to solutions that his ideology can provide. this was a technique that the communist party usa employed.


{ \ displaystyle x _ { 0 }, x _ { 1 }, x _ { 2 },... } then x 0 { \ displaystyle x _ { 0 } } is the state which the machine starts in and x 10 { \ displaystyle x _ { 10 } } is the random variable describing its state after 10 transitions. the process continues forever, indexed by the natural numbers. an example of a stochastic process which is not a markov chain is the model of a machine which has states a and e and moves to a from either state with 50 % chance if it has ever visited a before, and 20 % chance if it has never visited a before ( leaving a 50 % or 80 % chance that the machine moves to e ).


in the united states house of representatives, a motion to recommit can be made with or without instructions. if the motion is made without instructions, the bill or resolution is simply sent back to the committee. if the motion is made with instructions and the motion is agreed to, the chairman of the committee in question will immediately report the bill or resolution back to the whole house with the new language. in this sense, a motion to recommit with instructions is effectively an amendment.


in telecommunication, a mobile vpn is a solution that provides data user mobility and ensures secure network access with predictable performance. data user mobility is defined as uninterrupted connectivity or the ability to stay connected and communicate to a possibly remote data network while changing the network access medium or points of attachment. in 2001, huawei launched a product named " mvpn ". in this case " mvpn " had a different meaning from the way that later industry sources would use the term. the huawei product was focused on delivering a seamless corporate phone system to users whether they were on desktop phones or mobile devices. although the web page is no longer available, the company advertised that their mvpn had the following advantages over a standard phone system : direct connectivity – the corporate network becomes part of mobile operator's network through direct connection private numbering plan – the communication is tailored to company organization corporate business group – all offices and employees are part of one common group, that includes all mobile and desk phones short dialing – a short number to access each employee, no meter on his mobile or desk phone smart divert – easy divert within company group groups and subgroups – several sub - groups could be defined within the group with different changing as well as with separate numbering plan calls control – certain destinations could be allowed or barred both on mobile and desk phones.


the internal language of closed symmetric monoidal categories is linear logic and the type system is the linear type system. many examples of closed monoidal categories are symmetric. however, this need not always be the case, as non - symmetric monoidal categories can be encountered in category - theoretic formulations of linguistics ; roughly speaking, this is because word - order in natural language matters.


in such games, however, it is often found that creativity is lowered and the words stray towards having obvious associations again. this game is sometimes known as " word for word ". sometimes, repeated words are forbidden or otherwise noted on a separate list for interest. a variant with an arbitrary name ( sometimes called ultra word association ) involves associating words in a grid, where the first word is placed in the top - left, and where each word must be placed adjacent to another one and must associate with all those words adjacent to it.


in the 1990s, noam elkies, followed by a. o. l. atkin devised improvements to schoof's basic algorithm by making a distinction among the primes ℓ 1, …, ℓ s { \ displaystyle \ ell _ { 1 }, \ ldots, \ ell _ { s } } that are used. a prime ℓ { \ displaystyle \ ell } is called an elkies prime if the characteristic equation of the frobenius endomorphism, 2 − t + q = 0 { \ displaystyle \ phi ^ { 2 } - t \ phi + q = 0 }, splits over f ℓ { \ displaystyle \ mathbb { f } _ { \ ell } }. otherwise ℓ { \ displaystyle \ ell } is called an atkin prime. elkies primes are the key to improving the asymptotic complexity of schoof's algorithm.


an example would be to trade the electric charge, q, ( related to the abelian group u ( 1 ) of electromagnetism ), for the new quantum number exp ( 2iπ q ). then this becomes a multiplicative quantum number by virtue of the charge being an additive quantum number. however, this route is usually followed only for discrete subgroups of u ( 1 ), of which z2 finds the widest possible use.


digitally modulated signals ( e. g. qam or psk ) are basically made of two cw carriers ( the i and q components, which are out - of - phase carriers ). in fact, the information ( bits or symbols ) is carried by given combinations of phase and / or amplitude of the i and q components.


available in several varieties ; analog, analog spread spectrum ( 100 khz bandwidth ), digital, and digital spread spectrum, most being sold today are low - cost analog models, which are still susceptible to eavesdropping. digital variants can still be scanned, but are received as a digital hiss and therefore are difficult to eavesdrop upon. digital transmission is immune to static interference but can experience signal fade ( brief silence ) as the phone goes out of range of the base.


in the nmos 6502 and derivatives ( e. g., 6510 ), the simultaneous assertion of a hardware interrupt line and execution of brk was not accounted for in the design — the brk instruction will be ignored in such a case. also, the status of the decimal mode flag in the processor status register is unchanged following an interrupt of any kind. this behavior can potentially result in a difficult to locate bug in the interrupt handler if decimal mode happens to be enabled at the time of an interrupt. these anomalies were corrected in all cmos versions of the processor.


there is no standard method for applying the task. the most commonly used one is a letter rating task, which involves having participants judge all the letters of the alphabet.


it has also been observed that misinformation and disinformation reappear on social media sites. a research study watched the process of thirteen rumors appearing on twitter and noticed that eleven of those same stories resurfaced multiple times, after time had passed. a social media app called parler has caused much chaos as well. right winged twitter users who were banned on the app moved to parler after the capitol hill riots, and the app was being used to plan and facilitate more illegal and dangerous activities.


in the contemporary literature, there are two primary ( and non - equivalent ) formulations of supervenience ( for both definitions let a and b be sets of properties ). ( 1 ) a - properties supervene on b - properties if and only if all things that are b - indiscernible are a - indiscernible. formally : x y ( x ∈ b ( x x ↔ x y ) → y ∈ a ( y x ↔ y y ) ) { \ displaystyle \ forall x \ forall y ( \ forall x _ { \ in b } ( xx \ leftrightarrow xy ) \ rightarrow \ forall y _ { \ in a } ( yx \ leftrightarrow yy ) ) } ( 2 ) a - properties supervene on b - properties if and only if anything that has an a - property has some b - property such that anything that has that b - property also has that a - property. formally : x x ∈ a ( x x → y ∈ b ( y x ∧ y ( y y → x y ) ) ) { \ displaystyle \ forall x \ forall x _ { \ in a } ( xx \ rightarrow \ exists y _ { \ in b } ( yx \ land \ forall y ( yy \ rightarrow xy ) ) ) } for example, if one lets a be a set of mental properties, lets b be a set of physical properties, and chooses a domain of discourse consisting of persons, then ( 1 ) says that any two persons who are physically indiscernible are mentally indiscernible, and ( 2 ) says that any person who has a mental property has some physical property such that any person with that physical property has that mental property.


the trade - off between exploration and exploitation is also faced in machine learning. in practice, multi - armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company.


in the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy - tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. a frequent cause of outliers is a mixture of two distributions, which may be two distinct sub - populations, or may indicate'correct trial'versus'measurement error'; this is modeled by a mixture model. in most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable.


in mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. weak orders are a generalization of totally ordered sets ( rankings without ties ) and are in turn generalized by ( strictly ) partially ordered sets and preorders. there are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic ( interconvertable with no loss of information ) : they may be axiomatized as strict weak orderings ( strictly partially ordered sets in which incomparability is a transitive relation ), as total preorders ( transitive binary relations in which at least one of the two possible relations exists between every pair of elements ), or as ordered partitions ( partitions of the elements into disjoint subsets, together with a total order on the subsets ). in many cases another representation called a preferential arrangement based on a utility function is also possible. weak orderings are counted by the ordered bell numbers. they are used in computer science as part of partition refinement algorithms, and in the c + + standard library.


in quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. an example of quantum information is the state of a qubit. an example of classical information is a text document transmitted over the internet.


in mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. a matrix b is said to be a square root of a if the matrix product bb is equal to a. some authors use the name square root or the notation a1 / 2 only for the specific case when a is positive semidefinite, to denote the unique matrix b that is positive semidefinite and such that bb = btb = a ( for real - valued matrices, where bt is the transpose of b ). less frequently, the name square root may be used for any factorization of a positive semidefinite matrix a as btb = a, as in the cholesky factorization, even if bb = a. this distinct meaning is discussed in positive definite matrix § decomposition.


in some languages and programming environments, the use of a case or switch statement is considered superior to an equivalent series of if else if statements because it is : easier to debug ( e. g. setting breakpoints on code vs. a call table, if the debugger has no conditional breakpoint capability ) easier for a person to read easier to understand, and consequently easier to maintain fixed depth : a sequence of " if else if " statements may yield deep nesting, making compilation more difficult ( especially in automatically generated code ) easier to verify that all values are handled. compilers can issue a warning if some enum values are not handled. additionally, an optimized implementation may execute much faster than the alternative, because it is often implemented by using an indexed branch table. for example, deciding program flow based on a single character's value, if correctly implemented, is vastly more efficient than the alternative, reducing instruction path lengths considerably.


in mathematics, the chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a ≤ b ≤ c. an algorithm similar to schensted's algorithm yields characterisation of the equivalence classes and a cross - section theorem. it was discovered by duchamp & krob ( 1994 ) during their classification of monoids with growth similar to that of the plactic monoid, and studied in detail by julien cassaigne, marc espie, daniel krob, jean - christophe novelli, and florent hivert in 2001. the chinese monoid has a regular language cross - section a ∗ ( b a ) ∗ b ∗ ( c a ) ∗ ( c b ) ∗ c ∗ { \ displaystyle a ^ { * } \ ( ba ) ^ { * } b ^ { * } \ ( ca ) ^ { * } ( cb ) ^ { * } c ^ { * } \ cdots } and hence polynomial growth of dimension n ( n + 1 ) 2 { \ displaystyle { \ frac { n ( n + 1 ) } { 2 } } }. the chinese monoid equivalence class of a permutation is the preimage of an involution under the map w ↦ w ∘ w − 1 { \ displaystyle w \ mapsto w \ circ w ^ { - 1 } } where ∘ { \ displaystyle \ circ } denotes the product in the iwahori - hecke algebra with q s = 0 { \ displaystyle q _ { s } = 0 }.


in some countries'online banking, the bank sends to the user a numbered list of otps that is printed on paper. other banks send plastic cards with actual otps obscured by a layer that the user has to scratch off to reveal a numbered otp. for every online transaction, the user is required to enter a specific otp from that list. some systems ask for the numbered otps sequentially, others pseudorandomly choose an otp to be entered.


in order to discuss the continuous - time markov decision process, we introduce two sets of notations : if the state space and action space are finite, s { \ displaystyle { \ mathcal { s } } } : state space ; a { \ displaystyle { \ mathcal { a } } } : action space ; q ( i j, a ) { \ displaystyle q ( i \ mid j, a ) } : s × a → s { \ displaystyle { \ mathcal { s } } \ times { \ mathcal { a } } \ rightarrow \ triangle { \ mathcal { s } } }, transition rate function ; r ( i, a ) { \ displaystyle r ( i, a ) } : s × a → r { \ displaystyle { \ mathcal { s } } \ times { \ mathcal { a } } \ rightarrow \ mathbb { r } }, a reward function. if the state space and action space are continuous, x { \ displaystyle { \ mathcal { x } } } : state space ; u { \ displaystyle { \ mathcal { u } } } : space of possible control ; f ( x, u ) { \ displaystyle f ( x, u ) } : x × u → x { \ displaystyle { \ mathcal { x } } \ times { \ mathcal { u } } \ rightarrow \ triangle { \ mathcal { x } } }, a transition rate function ; r ( x, u ) { \ displaystyle r ( x, u ) } : x × u → r { \ displaystyle { \ mathcal { x } } \ times { \ mathcal { u } } \ rightarrow \ mathbb { r } }, a reward rate function such that r ( x ( t ), u ( t ) ) d t = d r ( x ( t ), u ( t ) ) { \ displaystyle r ( x ( t ), u ( t ) ) \, dt = dr ( x ( t ), u ( t ) ) }, where r ( x, u ) { \ displaystyle r ( x, u ) } is the reward function we discussed in previous case.


examples are cell phones, which transmit and receive the two sides of a phone conversation using radio waves to a cell tower, cordless phones in which both the phone handset and the base station have transceivers to communicate both sides of the conversation, and land mobile radio systems like walkie - talkies and cb radios. another large use is in wireless modems in mobile networked computer devices such laptops, pads, and cellphones, which both transmit digital data to and receive data from a wireless router. aircraft carry automated microwave transceivers called transponders which, when they are triggered by microwaves from an air traffic control radar, transmit a coded signal back to the radar to identify the aircraft. satellite transponders in communication satellites receive digital telecommunication data from a satellite ground station, and retransmit it to another ground station.


to form the product of two 8 - bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right. for 8 - bit integers the table of quarter squares will have 29−1 = 511 entries ( one entry for the full range 0.. 510 of possible sums, the differences using only the first 256 entries in range 0.. 255 ) or 29−1 = 511 entries ( using for negative differences the technique of 2 - complements and 9 - bit masking, which avoids testing the sign of differences ), each entry being 16 - bit wide ( the entry values are from ( 0² / 4 ) = 0 to ( 510² / 4 ) = 65025 ). the quarter square multiplier technique has benefited 8 - bit systems that do not have any support for a hardware multiplier. charles putney implemented this for the 6502.


in the fourth year of his degree course richard's research project led him to using oxford's ferranti mercury computer to solve integrals. during a fellowship year in france at centre de mecanique ondulatoire appliquee, he was able to use more powerful computers. returning to oxford, he worked on ab initio computations and applied computational techniques to solving quantum mechanical problems in theoretical chemistry, in particular studying spin - orbit coupling. his influential paper third age of quantum chemistry ( 1979 ) marked the development of computational techniques for theoretical analysis whose precision equaled or surpassed experimental results.


by offering a quantity discount for a larger quantity purchased the seller is able to capture some of the consumer surplus but not all. this is because diminishing marginal utility may mean the consumer would not be willing to purchase an additional unit without a discount since the marginal utility received from the good or service is no longer greater than price. however, by offering a discount the seller can capture some of consumers surplus by encouraging them to purchase an additional unit at a discounted price.


optimization will generally focus on improving just one or two aspects of performance : execution time, memory usage, disk space, bandwidth, power consumption or some other resource. this will usually require a trade - off – where one factor is optimized at the expense of others. for example, increasing the size of cache improves run time performance, but also increases the memory consumption.


in telecommunications, effective transmission rate ( average rate of transmission, effective speed of transmission ) is the rate at which information is processed by a transmission facility. the effective transmission rate is calculated as ( a ) the measured number of units of data, such as bits, characters, blocks, or frames, transmitted during a significant measurement time interval divided by ( b ) the measurement time interval. the effective transmission rate is usually expressed as a number of units of data per unit time, such as bits per second or characters per second.


in statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always " better " than it ( or at least sometimes better and never worse ), in the precise sense of " better " defined below. this concept is analogous to pareto efficiency.


in statistics, the standard score is the number of standard deviations by which the value of a raw score ( i. e., an observed value or data point ) is above or below the mean value of what is being observed or measured. raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. it is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.


the presumed difficulty of this problem is important for the algorithms used in cryptography such as rsa public - key encryption and the rsa digital signature. many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. in 2019, fabrice boudot, pierrick gaudry, aurore guillevic, nadia heninger, emmanuel thome and paul zimmermann factored a 240 - digit ( 795 - bit ) number ( rsa - 240 ) utilizing approximately 900 core - years of computing power.


in mathematics, an iterated function is a function x → x ( that is, a function from some set x to itself ) which is obtained by composing another function f : x → x with itself a certain number of times. the process of repeatedly applying the same function is called iteration. in this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. for example on the image on the right : l = f { \ displaystyle { \ mathit { f } } \, } ( k ), m = f ∘ f { \ displaystyle { \ mathit { f } } \, \ circ { \ mathit { f } } \, } ( k ) = f 2 { \ displaystyle { \ mathit { f } } \ ; ^ { 2 } \, } ( k ), with the circle ‑ shaped symbol of function composition. iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics.


in mathematical logic, craig's theorem ( also known as craig's trick ) states that any recursively enumerable set of well - formed formulas of a first - order language is ( primitively ) recursively axiomatizable. this result is not related to the well - known craig interpolation theorem, although both results are named after the same logician, william craig.


in regional testing, 20 to 50 µl of liquid stimulus is presented to the anterior and posterior tongue using a pipette, soaked filter - paper disks, or cotton swabs. in whole mouth testing, small quantities ( 2 - 10 ml ) of solution are administered, and the patient is asked to swish the solution around in the mouth. threshold tests for sucrose ( sweet ), citric acid ( sour ), sodium chloride ( salty ), and quinine or caffeine ( bitter ) are frequently performed with natural stimuli. one of the most frequently used techniques is the " three - drop test. "


in the 1960s a metrication program was initiated in most english - speaking countries, resulting in either the partial or total displacement of the imperial system or the us customary system of measure in those countries. the current status of imperial and us customary units, as summarised by nist, is that " the si metric system is now the official system of units in the united kingdom, while the customary units are still predominantly used in the united states ". the situation is however not as clear - cut as this. in the united states, for example, the metric system is the predominant system of measure in certain fields such as automobile manufacture even though customary units are used in aircraft manufacture. in the united kingdom, metric units are required for almost all regulated use of units of measure except for a few specifically exempt areas such as road signs, speedometers and draught beer. metrication is also all but complete in the commonwealth countries of australia, india, new zealand and south africa ; metrication in canada has displaced the imperial system in many areas. the imperial and us customary systems of measurement use the si for their formal definitions, the yard being defined as 0. 9144 metres exactly, the pound avoirdupois as 0. 45359237 kilograms exactly while both systems of measure share the definition of the second.


in mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute galois group. it is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite groups.


in the japanese kantenji braille, the standard 8 - dot braille patterns 256, 1256, 2456, and 12456 are the patterns related to braille pattern dots - 145, since the two additional dots of kantenji patterns 0145, 1457, and 01457 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


an element of order 6 in the group s5 can be written in cycle notation as ( 1 2 ) ( 3 4 5 ). note that the same argument applies to the number 6, that is, g ( 6 ) = 6. there are arbitrarily long sequences of consecutive numbers n, n + 1, …, n + m on which the function g is constant. the integer sequence g ( 0 ) = 1, g ( 1 ) = 1, g ( 2 ) = 2, g ( 3 ) = 3, g ( 4 ) = 4, g ( 5 ) = 6, g ( 6 ) = 6, g ( 7 ) = 12, g ( 8 ) = 15,... ( sequence a000793 in the oeis ) is named after edmund landau, who proved in 1902 that lim n → ∞ ln ( g ( n ) ) n ln ( n ) = 1 { \ displaystyle \ lim _ { n \ to \ infty } { \ frac { \ ln ( g ( n ) ) } { \ sqrt { n \ ln ( n ) } } } = 1 } ( where ln denotes the natural logarithm ).


in the unl approach, information conveyed by natural language is represented sentence by sentence as a hypergraph composed of a set of directed binary labeled links ( referred to as relations ) between nodes or hypernodes ( the universal words, or simply uws ), which stand for concepts. uws can also be annotated with attributes representing context information. as an example, the english sentence ‘ the sky was blue?! ’ can be represented in unl as follows : in the example above, sky ( icl > natural world ) and blue ( icl > color ), which represent individual concepts, are uws ; " aoj " ( = attribute of an object ) is a directed binary semantic relation linking the two uws ; and " @ def ", " @ interrogative ", " @ past ", " @ exclamation " and " @ entry " are attributes modifying uws.


for a dijoin in the given graph, the corresponding set of edges forms a directed cut in the dual graph, and vice versa. this relationship between these two problems allows the feedback arc set problem to be solved efficiently for planar graphs, even though it is np - hard for other types of graphs. = = references = =


in professional usage, digital cameras offer many advantages in speed, precision, flexibility, ease, and cost. immediacy : image review and deletion are possible immediately ; lighting and composition can be assessed immediately, which ultimately conserves storage space. faster workflow : management ( color and file ), manipulation, and printing tools are more versatile than conventional film processes. however, batch processing of raw files can be time - consuming, even on a fast computer.


in the reiner – stanton – white paper, the following example is given : let α be a composition of n, and let w ( α ) be the set of all words of length n with αi letters equal to i. a descent of a word w is any index j such that w j > w j + 1 { \ displaystyle w _ { j } > w _ { j + 1 } }. define the major index maj ( w ) { \ displaystyle \ operatorname { maj } ( w ) } on words as the sum of all descents. the triple ( x n, c n − 1, 1 q q ) { \ displaystyle ( x _ { n }, c _ { n - 1 }, { \ frac { 1 } { _ { q } } } \ left _ { q } ) } exhibit a cyclic sieving phenomenon, where x n { \ displaystyle x _ { n } } is the set of non - crossing ( 1, 2 ) - configurations of.


in probability theory, the central limit theorem states conditions under which the average of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. directional statistics is the subdiscipline of statistics that deals with directions ( unit vectors in rn ), axes ( lines through the origin in rn ) or rotations in rn. the means and variances of directional quantities are all finite, so that the central limit theorem may be applied to the particular case of directional statistics. this article will deal only with unit vectors in 2 - dimensional space ( r2 ) but the method described can be extended to the general case.


this makes the reliable modification of static memory values more complex. the load address has to be determined and subtracted from a found memory address to obtain a static memory offset. this offset is often exactly the address of the static variable within the pie binary.


additionally, both of these services allow browsing of their classifications, via westlaw's west key numbers or lexis'headnotes. though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text ( though this may be computer - assisted ). these systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. in one study, ontological searching resulted in a precision rate of 82 % and a recall rate of 97 % among legal professionals. the legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction. the major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. as the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable.


i am her. subject + verb ( transitive ) + indirect object + direct objectexample : she made me a pie. this clause pattern is a derivative of s + v + o, transforming the object of a preposition into an indirect object of the verb, as the example sentence in transformational grammar is actually " she made a pie for me ". subject + verb ( transitive ) + object + object complementexample : they made him happy. they did not make " him ", and they did not make " happy " ; they made " him happy " — the object and its complement form a syntactical unit. sentences – which are composed of these clauses, in either " dependent " or " independent " form – also have patterns, as explained below.


in logics with double negation elimination ( where ¬ ¬ x ≡ x { \ displaystyle \ lnot \ lnot x \ equiv x } ) the complementary literal or complement of a literal l { \ displaystyle l } can be defined as the literal corresponding to the negation of l { \ displaystyle l }. we can write l { \ displaystyle { \ bar { l } } } to denote the complementary literal of l { \ displaystyle l }. more precisely, if l ≡ x { \ displaystyle l \ equiv x } then l { \ displaystyle { \ bar { l } } } is ¬ x { \ displaystyle \ lnot x } and if l ≡ ¬ x { \ displaystyle l \ equiv \ lnot x } then l { \ displaystyle { \ bar { l } } } is x { \ displaystyle x }.


in performance testing, it is often crucial for the test conditions to be similar to the expected actual use. however, in practice this is hard to arrange and not wholly possible, since production systems are subjected to unpredictable workloads. test workloads may mimic occurrences in the production environment as far as possible, but only in the simplest systems can one exactly replicate this workload variability. loosely - coupled architectural implementations ( e. g. : soa ) have created additional complexities with performance testing. to truly replicate production - like states, enterprise services or assets that share a common infrastructure or platform require coordinated performance testing, with all consumers creating production - like transaction volumes and load on shared infrastructures or platforms. because this activity is so complex and costly in money and time, some organizations now use tools to monitor and simulate production - like conditions ( also referred as " noise " ) in their performance testing environments ( pte ) to understand capacity and resource requirements and verify / validate quality attributes.


in the japanese kantenji braille, the standard 8 - dot braille patterns 23568, 123568, 234568, and 1234568 are the patterns related to braille pattern dots - 12456, since the two additional dots of kantenji patterns 012456, 124567, and 0124567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


as in the case of groups or magmas, the semigroup operation need not be commutative, so x · y is not necessarily equal to y · x ; a well - known example of an operation that is associative but non - commutative is matrix multiplication. if the semigroup operation is commutative, then the semigroup is called a commutative semigroup or ( less often than in the analogous case of groups ) it may be called an abelian semigroup. a monoid is an algebraic structure intermediate between semigroups and groups, and is a semigroup having an identity element, thus obeying all but one of the axioms of a group : existence of inverses is not required of a monoid.


in the 19th century, research into the subject started to intensify. notable developments in this century include the work of hans christian ørsted who discovered in 1820 that an electric current produces a magnetic field that will deflect a compass needle, of william sturgeon who, in 1825 invented the electromagnet, of joseph henry and edward davy who invented the electrical relay in 1835, of georg ohm, who in 1827 quantified the relationship between the electric current and potential difference in a conductor, of michael faraday ( the discoverer of electromagnetic induction in 1831 ), and of james clerk maxwell, who in 1873 published a unified theory of electricity and magnetism in his treatise electricity and magnetism. in 1782, georges - louis le sage developed and presented in berlin probably the world's first form of electric telegraphy, using 24 different wires, one for each letter of the alphabet. this telegraph connected two rooms. it was an electrostatic telegraph that moved gold leaf through electrical conduction.


in order to reduce encryption or signature verification time, it is useful to use a small public exponent ( e { \ displaystyle e } ). in practice, common choices for e { \ displaystyle e } are 3, 17 and 65537 ( 2 16 + 1 ) { \ displaystyle ( 2 ^ { 16 } + 1 ) }. these values for e are fermat primes, sometimes referred to as f 0, f 2 { \ displaystyle f _ { 0 }, f _ { 2 } } and f 4 { \ displaystyle f _ { 4 } } respectively ( f x = 2 2 x + 1 ) { \ displaystyle ( f _ { x } = 2 ^ { 2 ^ { x } } + 1 ) }. they are chosen because they make the modular exponentiation operation faster.


the blinking of the text cursor is usually temporarily suspended when it is being moved ; otherwise, the cursor may change position when it is not visible, making its location difficult to follow. the concept of a blinking cursor can be attributed to charles kiesling sr. via us patent 3531796, filed in august 1967. some interfaces use an underscore or thin vertical bar to indicate that the user is in insert mode, a mode where text will be inserted in the middle of the existing text, and a larger block to indicate that the user is in overtype mode, where inserted text will overwrite existing text. in this way, a block cursor may be seen as a piece of selected text one character wide, since typing will replace the text " in " the cursor with the new text.


when any two indices are interchanged, equal or not, the symbol is negated : if any two indices are equal, the symbol is zero. when all indices are unequal, we have : where p ( called the parity of the permutation ) is the number of pairwise interchanges of indices necessary to unscramble i1, i2,..., in into the order 1, 2,..., n, and the factor ( −1 ) p is called the sign, or signature of the permutation. the value ε1 2... n must be defined, else the particular values of the symbol for all permutations are indeterminate.


in multivariate statistics, spectral clustering techniques make use of the spectrum ( eigenvalues ) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. the similarity matrix is provided as an input and consists of a quantitative assessment of the relative similarity of each pair of points in the dataset. in application to image segmentation, spectral clustering is known as segmentation - based object categorization.


what stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value? the general solution to this full - information expected rank problem is unknown. the major difficulty is that the problem is fully history - dependent, that is, the optimal rule depends at every stage on all preceding values, and not only on simpler sufficient statistics of these. only bounds are known for the limiting value v as n goes to infinity, namely 1. 908 < v < 2. 329. it is known that there is some room to improve the lower bound by further computations for a truncated version of the problem. it is still not known how to improve on the upper bound which stems from the subclass of memoryless threshold rules.


since the posterior mean is cumbersome to calculate, the form of the mmse estimator is usually constrained to be within a certain class of functions. linear mmse estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. it has given rise to many popular estimators such as the wiener – kolmogorov filter and kalman filter.


in the 2010s, software has become a key business differentiator. as a result, organizations now expect software development teams to deliver more, and more innovative, software within shorter delivery cycles. to meet these demands, teams have turned to lean approaches, such as agile, devops, and continuous delivery, to try to speed up the systems development life cycle ( sdlc ). after accelerating other aspects of the delivery pipeline, teams typically find that their testing process is preventing them from achieving the expected benefits of their sdlc acceleration initiative.


interaction between 32 - bit addresses and two loop control instructions, bxh and bxle that treated their arguments as signed numbers when doing comparisons ( and which was said to be the reason tss used 31 - bit addressing on the model 67 ). : 26, note 85 input from key initial model 67 sites, which had debated the alternatives during the initial system design period, and had recommended 31 bits ( instead of the 32 - bit design that was ultimately chosen at the time ). : 8 – 9, note 21 certain machine instructions in this 31 - bit addressing mode alter the addressing mode bit.


in the dynamic topic model, only w t, d, n { \ displaystyle w _ { t, d, n } } is observable. learning the other parameters constitutes an inference problem. blei and lafferty argue that applying gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the gaussian and multinomial distributions. they propose the use of variational methods, in particular, the variational kalman filtering and the variational wavelet regression.


). roughly speaking, δ { \ displaystyle \ delta \, \! } minimizes this expectation of expected loss ( i. e., is a bayes rule ) if and only if it minimizes the expected loss for each x ∈ x { \ displaystyle x \ in { \ mathcal { x } } } separately ( i. e., is a generalized bayes rule ).


in mathematics, the levy metric is a metric on the space of cumulative distribution functions of one - dimensional random variables. it is a special case of the levy – prokhorov metric, and is named after the french mathematician paul levy.


for each ordinal α { \ displaystyle \ alpha }, α + 1 { \ displaystyle \ aleph _ { \ alpha + 1 } } is the least cardinal number greater than α { \ displaystyle \ aleph _ { \ alpha } }. the cardinality of the natural numbers is denoted aleph - null ( 0 { \ displaystyle \ aleph _ { 0 } } ), while the cardinality of the real numbers is denoted by " c { \ displaystyle { \ mathfrak { c } } } " ( a lowercase fraktur script " c " ), and is also referred to as the cardinality of the continuum. cantor showed, using the diagonal argument, that c > 0 { \ displaystyle { \ mathfrak { c } } > \ aleph _ { 0 } }.


fppf stands for fidelement plate de presentation finie, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat and of finite presentation. fpqc stands for fidelement plate et quasi - compacte, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat. in both categories, a covering family is defined be a family which is a cover on zariski open subsets.


passport, are by law one of the few primary documents for proving u. s. citizenship. these certificates are normally not carried on a day - to - day basis ; instead, they are used to procure other documents, such as a passport or driver's license, which are then carried and used as a primary means of identification.


in mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two - symbol substring of the word. equivalently, it is a language recognised by a local automaton, a particular kind of deterministic finite automaton. formally, a language l over an alphabet a is defined to be local if there are subsets r and s of a and a subset f of a×a such that a word w is in l if and only if the first letter of w is in r, the last letter of w is in s and no factor of length 2 in w is in f. this corresponds to the regular expression ( r a ∗ ∩ a ∗ s ) a ∗ f a ∗. { \ displaystyle ( ra ^ { * } \ cap a ^ { * } s ) \ setminus a ^ { * } fa ^ { * } \. } more generally, a k - testable language l is one for which membership of a word w in l depends only on the prefix, suffix and the set of factors of w of length k ; a language is locally testable if it is k - testable for some k. a local language is 2 - testable.


we merely abstain from both assumptions...


in order to decouple the real - time operating system platform from the application software, arinc 653 defines an api called application executive ( apex ). each application software is called a partition and has its own memory space. it also has a dedicated time slot allocated by the apex api. within each partition, multitasking is allowed.


in mathematics, economics, and computer science, the lattice of stable matchings is a distributive lattice whose elements are stable matchings. for a given instance of the stable matching problem, this lattice provides an algebraic description of the family of all solutions to the problem. it was originally described in the 1970s by john horton conway and donald knuth. by birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying partially ordered set. the elements of this set can be given a concrete structure as rotations, with cycle graphs describing the changes between adjacent stable matchings in the lattice.


in 1847 gabriel lame announced a solution of fermat's last theorem for all n > 2 { \ displaystyle n > 2 } ; that is, that the fermat equation has no solutions in nonzero integers, but it turned out that his solution hinged on the assumption that the cyclotomic ring z { \ displaystyle \ mathbb { z } } is a ufd. ernst kummer had shown three years before that this was not the case already for n = 23 { \ displaystyle n = 23 } ( the full, finite list of values for which z { \ displaystyle \ mathbb { z } } is a ufd is now known ). at the same time, kummer developed powerful new methods to prove fermat's last theorem at least for a large class of prime exponents n { \ displaystyle n } using what we now recognize as the fact that the ring z { \ displaystyle \ mathbb { z } } is a dedekind domain.


in realtime scheduling algorithms for periodic jobs, an acceptance test is needed before accepting a sporadic job with a hard deadline. one of the simplest acceptance tests for a sporadic job is calculating the amount of slack time between the release time and deadline of the job.


however, this naming scheme was quite temporary, lasting for a few years during the early 1980s. although the 8086 was primarily developed for embedded systems and small multi - user or single - user computers, largely as a response to the successful 8080 - compatible zilog z80, the x86 line soon grew in features and processing power. today, x86 is ubiquitous in both stationary and portable personal computers, and is also used in midrange computers, workstations, servers, and most new supercomputer clusters of the top500 list. a large amount of software, including a large list of x86 operating systems are using x86 - based hardware.


in the star, new instructions essentially wrote the loops for the user. the user told the machine where in memory the list of numbers was stored, then fed in a single instruction a ( 1.. 1000000 ) = addv b ( 1.. 1000000 ), c ( 1.. 1000000 ). at first glance it appears the savings are limited ; in this case the machine fetches and decodes only a single instruction instead of 1, 000, 000, thereby saving 1, 000, 000 fetches and decodes, perhaps one - fourth of the overall time. the real savings are not so obvious.


property is in a person's presence when it is within the area of their immediate control. the property has to be close enough to the victim's person that the victim could have prevented its taking if he / she had not been placed in fear or intimidation. by force or threat of force – the use of force or threat of force is the defining element of robbery. for there to be robbery there must be " force or fear " in perpetrating the theft.


some of these databases may be shared among several companies, each paying every time a name is " extracted ". it is for this reason that mobile telephone callers may appear as " wireless caller ", or the central office location of the number. if the call originates on a pots line ( a standard loop - start line ), then caller id is provided by the service provider's local switch.


the application of biotechnology to basic science ( for example through the human genome project ) has also dramatically improved our understanding of biology and as our scientific knowledge of normal and disease biology has increased, our ability to develop new medicines to treat previously untreatable diseases has increased as well. genetic testing allows the genetic diagnosis of vulnerabilities to inherited diseases, and can also be used to determine a child's parentage ( genetic mother and father ) or in general a person's ancestry. in addition to studying chromosomes to the level of individual genes, genetic testing in a broader sense includes biochemical tests for the possible presence of genetic diseases, or mutant forms of genes associated with increased risk of developing genetic disorders. genetic testing identifies changes in chromosomes, genes, or proteins.


in the 19th century it became a common technique to gain insight into integer solutions of polynomial equations using rings of algebraic numbers of higher degree. for instance, fix a positive integer m { \ displaystyle m }. in the attempt to determine which integers are represented by the quadratic form x 2 + m y 2 { \ displaystyle x ^ { 2 } + my ^ { 2 } }, it is natural to factor the quadratic form into ( x + − m y ) ( x − − m y ) { \ displaystyle ( x + { \ sqrt { - m } } y ) ( x - { \ sqrt { - m } } y ) }, the factorization taking place in the ring of integers of the quadratic field q ( − m ) { \ displaystyle \ mathbb { q } ( { \ sqrt { - m } } ) }. similarly, for a positive integer n { \ displaystyle n } the polynomial z n − y n { \ displaystyle z ^ { n } - y ^ { n } } ( which is relevant for solving the fermat equation x n + y n = z n { \ displaystyle x ^ { n } + y ^ { n } = z ^ { n } } ) can be factored over the ring z { \ displaystyle \ mathbb { z } }, where ζ n { \ displaystyle \ zeta _ { n } } is a primitive n - th root of unity.


in mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series n = 1 ∞ a n { \ displaystyle \ sum _ { n = 1 } ^ { \ infty } a _ { n } }.


in the interpretation above, the only partition of { 1, 2, 3 } { \ textstyle \ { 1, 2, 3 \ } } into 1 set can have its set ordered in 6 ways : l ( 3, 2 ) { \ textstyle l ( 3, 2 ) } is equal to 6, because there are six partitions of { 1, 2, 3 } { \ textstyle \ { 1, 2, 3 \ } } into two ordered parts : l ( n, n ) { \ textstyle l ( n, n ) } is always 1 because the only way to partition { 1, 2, …, n } { \ textstyle \ { 1, 2, \ ldots, n \ } } into n { \ displaystyle n } non - empty subsets results in subsets of size 1, that can only be permuted in one way. in the more recent literature, karamata – knuth style notation has taken over. lah numbers are now often written as


the intuitive meaning of a stack is that it is a fibred category such that " all possible gluings work ". the specification of gluings requires a definition of coverings with regard to which the gluings can be considered. it turns out that the general language for describing these coverings is that of a grothendieck topology. thus a stack is formally given as a fibred category over another base category, where the base has a grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the grothendieck topology.


it is a sharper bound than the first - or second - moment - based tail bounds such as markov's inequality or chebyshev's inequality, which only yield power - law bounds on tail decay. however, when applied to sums the chernoff bound requires the random variables to be independent, a condition that is not required by either markov's inequality or chebyshev's inequality ( although chebyshev's inequality does require the random variables to be pairwise independent ). the chernoff bound is related to the bernstein inequalities. it is also used to prove hoeffding's inequality, bennett's inequality, and mcdiarmid's inequality.


this language became quite popular in the early 1980s, and thus may also have been instrumental in spreading the style outside parc. upper camel case ( or " pascal case " ) is used in wolfram language in computer algebraic system mathematica for predefined identifiers. user defined identifiers should start with a lower case letter. this avoids the conflict between predefined and user defined identifiers both today and in all future versions. c # variable names are recommended to follow the lower camel case convention.


properties of time - aggregated network snapshots are able to be studied in terms of f ( x ) { \ displaystyle f ( x ) }. for example, since each node j { \ displaystyle j } after t { \ displaystyle t } timesteps will have on average m η x i t { \ displaystyle m \ eta x _ { i } t } outgoing links, the degree distribution after t { \ displaystyle t } timesteps in the time - aggregated network will be related to the activity - potential distribution by p t ( k ) f ( k m η t ). { \ displaystyle p _ { t } ( k ) \ propto f \ left ( { \ frac { k } { m \ eta t } } \ right ). } spreading behavior according to the sis epidemic model was investigated on activity - driven networks, and the following condition was derived for large - scale outbreaks to be possible : β λ > 2 ⟨ a ⟩ ⟨ a ⟩ + ⟨ a 2 ⟩, { \ displaystyle { \ frac { \ beta } { \ lambda } } > { \ frac { 2 \ langle a \ rangle } { \ langle a \ rangle + { \ sqrt { \ langle a ^ { 2 } \ rangle } } } }, } where β { \ displaystyle \ beta } is the per - contact transmission probability, λ { \ displaystyle \ lambda } is the per - timestep recovery probability, and ( ⟨ a ⟩ { \ displaystyle \ langle a \ rangle }, ⟨ a 2 ⟩ { \ displaystyle \ langle a ^ { 2 } \ rangle } ) are the first and second moments of the random activity - rate a j { \ displaystyle a _ { j } }.


in the 17th century conrad henfling writing to leibniz about music theory and the tuning of musical instruments makes use of the euclidean algorithm in his reasoning. viggo brun investigated the use of euclidean algorithm in terms of constructing scales up to 4 different size intervals. erv wilson explored both using ratios andscale steps of which kraig grady applied torhythms within long meters.


in principle, it would be possible to inflate the number of bytes in an encoding by padding the code point with leading 0s. to encode the euro sign € from the above example in four bytes instead of three, it could be padded with leading 0s until it was 21 bits long – 000 000010 000010 101100, and encoded as 11110000 10000010 10000010 10101100 ( or f0 82 82 ac in hexadecimal ). this is called an overlong encoding.


his device was the foundation for further developments in analog computing. the differential analyser, a mechanical analog computer designed to solve differential equations by integration using wheel - and - disc mechanisms, was conceptualized in 1876 by james thomson, the brother of the more famous lord kelvin. he explored the possible construction of such calculators, but was stymied by the limited output torque of the ball - and - disk integrators. in a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output.


in anti addition, two substituents are added to opposite sides ( or faces ) of a double bond or triple bond, once again resulting in a decrease in bond order and increase in number of substituents. the classical example of this is bromination ( any halogenation ) of alkenes. an anti addition reaction results in a trans - isomer of the products, as the substituents are on opposite faces of the bond.