Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically "redundant", repeating information present within the noun. Count-classifiers can be used stylistically, though, and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun 课 kè "class" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier 门 (門) mén or 节 (節) jié is used.One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects. An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind. Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse, to introduce major characters or items in a story or conversation, or to foreground important information and objects by making them bigger and more salient. In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.


Sampling is a foundation of hip hop music, which emerged when producers in the 1980s began sampling funk and soul records, particularly drum breaks. It has influenced many other genres of music, particularly electronic music and pop. Samples such as the Amen break, the "Funky Drummer" drum break and the orchestra hit have been used in thousands of recordings, and James Brown, Loleatta Holloway, Fab Five Freddy and Led Zeppelin are among the most sampled artists.


In proof compression, an area of mathematical logic, LowerUnivalents is an algorithm used for the compression of propositional resolution proofs. LowerUnivalents is a generalised algorithm of the LowerUnits, and it is able to lower not only units but also subproofs of non-unit clauses, provided that they satisfy some additional conditions. == References ==


The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible.


Part of the settlement agreement for this case, Mink v. University of Chicago, attorneys for the plaintiffs negotiated for the university to provide free medical exams for all offspring exposed to DES in utero during the 1950 experiments as well as treat the daughters of any women involved who develop DES-associated vaginal or cervical cancer.As of February 1991, there were over a thousand pending legal actions against DES manufacturers. There are over 300 companies that manufactured DES according to the same formula and the largest barrier to recovery is determining which manufacturer supplied the drug in each particular case.


Once a system has been commissioned it should be either put immediately into service or drained down and dried. If either of these options is not possible then the system should be flushed though regularly until it is put into use. It should not be left to stand for more than a week.


In number theory, the Moser–de Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4. Equivalently, they are the numbers whose binary representations are nonzero only in even positions. The Moser–de Bruijn numbers in this sequence grow in proportion to the square numbers. They are the squares for a modified form of arithmetic without carrying.


In telecommunication contracts it is frequent the practice to lock the use of a sim card of one operator with a phone acquired through the same mobile operator. Obstructing the unlocking of the phone may be illegal if the consumer is entitled to it.


The intangible and esoteric Outer Planes—the realms of ideals, philosophies, and gods—stand in contrast to the Inner Planes, which compose the material building blocks of reality and the realms of energy and matter. All Outer Planes are spatially infinite but are composed of features and locations of finite scope. Many of these planes are often split into a collection of further infinites called layers, which are essentially sub-planes that represent one particular facet or theme of the plane.


In probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral χ 2 {\displaystyle \chi ^{2}} distribution) is a noncentral generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically) a chi-squared distribution; important examples of such tests are the likelihood-ratio tests.


Such a core ontology is a key pre-requisite to a more complete foundation ontology, or a more general philosophical sense of ontology. Most applicable to teaching, e.g. the Longmans defining dictionary of the simplest meanings of 2,000 English words is used to define the 4,000 most basic English idioms—this is a core glossary of the English language, which permits access to the core ontology (the idioms). Core ontologies is a concept that is used in information science as well. For example, CIDOC-CRM and CORA are considered as core ontologies.


Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the radix complement (as described below) is also valuable in number theory, such as in Midy's theorem.


Some models of smartphones allow the user to enter letters into the device’s dialing window to allow the completion of phonewords. Numerous Blackberry models allow this feature by using the ALT key when pressing a key to select the letter, and not the number on the key. On older landline telephones, the O, Q and Z sometimes vary in placement or are omitted entirely; this is not an issue for most mobile telephones as all 26 letters must be provided to support short message service transmission. The dialing of 1 or 0 instead of I or O in phonewords can lead to misdialed calls; one such typosquatting incident targeted 1-800-HOLIDAY (+1-800-465-4329, the toll-free direct reservations line for Holiday Inn) by subscribing 1-800-H0LIDAY (+1-800-405-4329, the same number with 'o' replaced by 'zero') to a rival vendor which stood to collect a profitable travel agent's commission.


Other classifiers work by comparing observations to previous observations by means of a similarity or distance function. An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category.


In statistics, a proper linear model is a linear regression model in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple regression analysis is the most common example of a proper linear model. Unit-weighted regression is the most common example of an improper linear model.


In nonrelativistic classical mechanics, a closed system is a physical system that doesn't exchange any matter with its surroundings, and isn't subject to any net force whose source is external to the system. A closed system in classical mechanics would be equivalent to an isolated system in thermodynamics. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment.


While performing these operations, there may be scenarios where the same element is being searched by one thread and is being deleted by another. In such cases, the output may be erroneous. The thread searching the element may have a hit, whereas the other thread may delete it just after that time.


In the classical setting, we aim at partitioning the vertices of a hypergraph H = ( V , E ) {\displaystyle {\mathcal {H}}=(V,{\mathcal {E}})} into two classes in such a way that ideally each hyperedge contains the same number of vertices in both classes. A partition into two classes can be represented by a coloring χ: V → { − 1 , + 1 } {\displaystyle \chi \colon V\rightarrow \{-1,+1\}} . We call −1 and +1 colors. The color-classes χ − 1 ( − 1 ) {\displaystyle \chi ^{-1}(-1)} and χ − 1 ( + 1 ) {\displaystyle \chi ^{-1}(+1)} form the corresponding partition.


In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite.


In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, a sound tone, or a physical artifact, such as a meter ruler. The outcome of the comparison can result in one of the following: no significant error being noted on the device under test a significant error being noted but no adjustment made an adjustment made to correct the error to an acceptable levelStrictly speaking, the term "calibration" means just the act of comparison and does not include any subsequent adjustment. The calibration standard is normally traceable to a national or international standard held by a metrology body.


Step 8: For every class of equinumerous classes, create its successor. Step 9: Order the numbers: The process of creating a successor requires the relation " . .


{\displaystyle \max _{\left\{c_{t}\right\}_{t=0}^{\infty }}\mathbb {E} {\bigg (}\sum _{t=0}^{\infty }\beta ^{t}u({\color {OliveGreen}c_{t}}){\bigg )}.} The expectation E {\displaystyle \mathbb {E} } is taken with respect to the appropriate probability measure given by Q on the sequences of r's. Because r is governed by a Markov process, dynamic programming simplifies the problem significantly.


This representation was translated to a computational model and an anytime algorithm for belief revision was developed.Ginsberg–Fagin–Ullman–Vardi the maximal subsets of K ∪ { P } {\displaystyle K\cup \{P\}} that are consistent and contain P {\displaystyle P} are combined by disjunction;Nebel similar to the above, but a priority among formulae can be given, so that formulae with higher priority are less likely to being retracted than formulae with lower priority.A different realization of the foundational approach to belief revision is based on explicitly declaring the dependences among beliefs. In the truth maintenance systems, dependence links among beliefs can be specified. In other words, one can explicitly declare that a given fact is believed because of one or more other facts; such a dependency is called a justification. Beliefs not having any justifications play the role of non-derived beliefs in the non-deductively closed knowledge base approach.


Fix an integer m. Let ej denote the number of units in the right order of Ij and let Bij denote the number of α in Ij−1Ii with reduced norm N(α) equal to mN(Ii)/N(Ij). The Brandt matrix B(m) is the H×H matrix with entries Bij. Up to conjugation by a permutation matrix it is independent of the choice of representatives Ij; it is dependent only on the level of the order O.


In structured programming, stack resource management is done simply by nesting code sufficiently to handle all cases. This requires only a single return at the end of the code, and can result in heavily nested code if many resources must be acquired, which is considered an anti-pattern by some – the Arrow Anti Pattern, due to the triangular shape from the successive nesting.


This structure is specified, e.g., in a file format or protocol and distinguishes valid from invalid input. An effective fuzzer generates semi-valid inputs that are "valid enough" in that they are not directly rejected by the parser, but do create unexpected behaviors deeper in the program and are "invalid enough" to expose corner cases that have not been properly dealt with. For the purpose of security, input that crosses a trust boundary is often the most useful. For example, it is more important to fuzz code that handles the upload of a file by any user than it is to fuzz the code that parses a configuration file that is accessible only to a privileged user.


Maximum weighted matchings do not have to be stable, but in some applications a maximum weighted matching is better than a stable one. The matching with contracts problem is a generalization of matching problem, in which participants can be matched with different terms of contracts. An important special case of contracts is matching with flexible wages.


Extensions that were busy or rang “no answer” would forward to the message center onto a device called a “call director”. The call director had a button for each extension in the company which would flash when that person's extension forwarded to the message center. A little label next to the button told the operator whose extension it was. As wireless communication technologies increased in the late 1980s, the Pager service providers created a subscription service offered in a variety of plans and options to meet the needs of a subscriber and the type of device used. In general, all pagers are given unique telephone numbers so that callers could dial in and send a numeric message, such as their callback number or a numerically coded special message, such as room numbers to report to, etc. However, alphanumeric pagers could only receive text messages when the message sender had installed software on their PC to dial into the publicly accessible modems operated by the paging service provider to then transmit their message over-the-air through the network of radio towers.


If S {\displaystyle S} is also separable, then P ( S ) {\displaystyle {\mathcal {P}}(S)} is metrizable and separable, for example by the Lévy–Prokhorov metric. If S {\displaystyle S} is also compact or Polish, so is P ( S ) {\displaystyle {\mathcal {P}}(S)} . If S {\displaystyle S} is separable, it naturally embeds into P ( S ) {\displaystyle {\mathcal {P}}(S)} as the (closed) set of Dirac measures, and its convex hull is dense. There are many "arrow notations" for this kind of convergence: the most frequently used are P n ⇒ P {\displaystyle P_{n}\Rightarrow P} , P n ⇀ P {\displaystyle P_{n}\rightharpoonup P} , P n → w P {\displaystyle P_{n}\xrightarrow {w} P} and P n → D P {\displaystyle P_{n}\xrightarrow {\mathcal {D}} P} .


In the 1990s, an epidemic of "cloning" cost the cellular carriers millions of dollars. An eavesdropper with specialized equipment could intercept a handset's ESN (Electronic Serial Number) and MDN or CTN (Mobile Directory Number or Cellular Telephone Number). The Electronic Serial Number, a 12-digit number sent by the handset to the cellular system for billing purposes, uniquely identified that phone on the network. The system then allowed or disallowed calls and/or features based on its customer file.


In the background of the technology looked to address the following issues: The development of non-removable SIM technology - a new generation of SIM-cards like MFF which are soldered into the device. The appearance and support by mobile operators of the concept of ABC (always best connected) – the opportunity get quality connections from any mobile operator at any point in time. The explosive growth of the Internet of Things (IoT) - according to Gartner about 8.4 billion connections in 2017 (up 31% from 2016). The cost and effort required to swap a SIM in a device that has been deployed in the field.


The main criteria included: A large selection of publication items (journal articles, books, dataset, software) that agree with the writing and reading practices of scientific communities. Fully documented data sources. Transparent and reproducible process for the calculation of the metrics and other indices.


In some programming languages, e.g. Java, the term conditional operator refers to short circuit boolean operators && and ||. The second expression is evaluated only when the first expression is not sufficient to determine the value of the whole expression.


Harvey writes that the asymptotic time complexity of this algorithm is O(n2 log(n)2 + ε) and claims that this implementation is significantly faster than implementations based on other methods. Using this implementation Harvey computed Bn for n = 108. Harvey's implementation has been included in SageMath since version 3.1. Prior to that, Bernd Kellner computed Bn to full precision for n = 106 in December 2002 and Oleksandr Pavlyk for n = 107 with Mathematica in April 2008. * Digits is to be understood as the exponent of 10 when Bn is written as a real number in normalized scientific notation.A possible algorithm for computing Bernoulli numbers in the Julia programming language is given by


The example C code below illustrates how structure objects are dynamically allocated and referenced. The standard C library provides the function malloc() for allocating memory blocks from the heap. It takes the size of an object to allocate as a parameter and returns a pointer to a newly allocated block of memory suitable for storing the object, or it returns a null pointer if the allocation failed. The code below illustrates how memory objects are dynamically deallocated, i.e., returned to the heap or free store. The standard C library provides the function free() for deallocating a previously allocated memory block and returning it back to the heap.


Although she developed many techniques for establishing the non-consecutivity condition, she did not succeed in her strategic goal. She also worked to set lower limits on the size of solutions to Fermat's equation for a given exponent p {\displaystyle p} , a modified version of which was published by Adrien-Marie Legendre.


In the beginning there was Sendmail and many other mail delivery agents soon followed (Postfix etc.) Once email spam and computer virus problems started becoming prevalent in the early 1990s. These critical Internet infrastructure systems had to be patched and the underlying protocols changed -or in some cases ignored- to deal with these issues. Thus was born the messaging platform. Large telecommunication operators and internet service providers needed flexible, easily deployed and scaled messaging systems for quickly growing messaging services and cell phone networks (for examples see SMS and BlackBerry.)


With the area of the four triangles removed from both side of the equation what remains is a 2 + b 2 = c 2 . {\displaystyle a^{2}+b^{2}=c^{2}.} In another proof rectangles in the second box can also be placed such that both have one corner that correspond to consecutive corners of the square.


He follows a similar method for the other eleven categories, then represents them in the following table: These categories, then, are the fundamental, primary, or native concepts of the understanding. These flow from, or constitute the mechanism of understanding and its nature, and are inseparable from its activity. Therefore, for human thought, they are universal and necessary, or a priori.


This filter prevents payloads such as and its URI-encoded form %3Cscript%3Ealert%281%29%3C%2Fscript%3E. However, %253Cscript%253Ealert%25281%2529%253C%252Fscript%253E, which is the double-URI-encoded form of , will bypass this filter. When double-URI-encoded payload %253Cscript%253Ealert%25281%2529%253C%252Fscript%253E is used, the value of $_GET will be %3Cscript%3Ealert%281%29%3C%2Fscript%3E which doesn't contain any illegal character and thus passes through the htmlentities function without any change and will be given to the urldecode function which returns , resulting in a successful attack.


In medicine (oncology and other fields), performance status is an attempt to quantify cancer patients' general well-being and activities of daily life. This measure is used to determine whether they can receive chemotherapy, whether dose adjustment is necessary, and as a measure for the required intensity of palliative care. It is also used in oncological randomized controlled trials as a measure of quality of life.


In some applications, the elements of the set being permuted will be compared with each other. This requires that the set S has a total order so that any two elements can be compared. The set {1, 2, ..., n} is totally ordered by the usual "≤" relation and so it is the most frequently used set in these applications, but in general, any totally ordered set will do. In these applications, the ordered arrangement view of a permutation is needed to talk about the positions in a permutation. There are a number of properties that are directly related to the total ordering of S.


However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. Euclidean distance matrices are closely related to Gram matrices (matrices of dot products, describing norms of vectors and angles between them). The latter are easily analyzed using methods of linear algebra.


It can be extended to infinite-dimensional vector spaces as the L2 norm or L2 distance. The Euclidean distance gives Euclidean space the structure of a topological space, the Euclidean topology, with the open balls (subsets of points at less than a given distance from a given point) as its neighborhoods.Other common distances on Euclidean spaces and low-dimensional vector spaces include: Chebyshev distance, which measures distance assuming only the most significant dimension is relevant. Manhattan distance, which measures distance following only axis-aligned directions. Minkowski distance, a generalization that unifies Euclidean distance, Manhattan distance, and Chebyshev distance.For points on surfaces in three dimensions, the Euclidean distance should be distinguished from the geodesic distance, the length of a shortest curve that belongs to the surface. In particular, for measuring great-circle distances on the earth or other spherical or near-spherical surfaces, distances that have been used include the haversine distance giving great-circle distances between two points on a sphere from their longitudes and latitudes, and Vincenty's formulae also known as "Vincent distance" for distance on a spheroid.


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


In order to split a secret into several shares, Blakley's scheme specifies the secret as a point in n-dimensional space, and gives out shares that correspond to hyperplanes that intersect the secret point. Any n such hyperplanes will specify the point, while fewer than n hyperplanes will leave at least one degree of freedom, and thus leave the point unspecified.In contrast, Shamir's secret sharing scheme represents the secret as the y-intercept of an n-degree polynomial, and shares correspond to points on the polynomial.


Then, for all t ≥ 0 {\displaystyle t\geq 0} Pr { λ max ( H ( z ) − E H ( z ) ) ≥ t } ≤ d ⋅ e − t 2 / 8 σ 2 , {\displaystyle \Pr \left\{\lambda _{\text{max}}\left(\mathbf {H} (\mathbf {z} )-\mathbb {E} \,\mathbf {H} (\mathbf {z} )\right)\geq t\right\}\leq d\cdot e^{-t^{2}/8\sigma ^{2}},} where z = ( Z 1 , … , Z n ) {\displaystyle \mathbf {z} =(Z_{1},\ldots ,Z_{n})} . An improvement of this result was established in (Paulin, Mackey & Tropp 2013) (see also (Paulin, Mackey & Tropp 2016)): for all t ≥ 0 {\displaystyle t\geq 0} Pr { λ max ( H ( z ) − E H ( z ) ) ≥ t } ≤ d ⋅ e − t 2 / σ 2 , {\displaystyle \Pr \left\{\lambda _{\text{max}}\left(\mathbf {H} (\mathbf {z} )-\mathbb {E} \,\mathbf {H} (\mathbf {z} )\right)\geq t\right\}\leq d\cdot e^{-t^{2}/\sigma ^{2}},} where z = ( Z 1 , … , Z n ) {\displaystyle \mathbf {z} =(Z_{1},\ldots ,Z_{n})} and σ 2 = ‖ ∑ k A k 2 ‖ . {\displaystyle \sigma ^{2}={\bigg \Vert }\sum _{k}\mathbf {A} _{k}^{2}{\bigg \Vert }.}


In polymer chemistry, the term prepolymer or pre-polymer, refers to a monomer or system of monomers that have been reacted to an intermediate-molecular mass state. This material is capable of further polymerization by reactive groups to a fully cured, high-molecular-mass state. As such, mixtures of reactive polymers with un-reacted monomers may also be referred to as pre-polymers. The term "pre-polymer" and "polymer precursor" may be interchanged.


For example, in the term ( λ x . x Ω ) ( λ y . I ) {\displaystyle (\lambda x.x\Omega )(\lambda y.I)} with Ω , I {\displaystyle \Omega ,I} defined here, the leftmost redex of the in-order traversal is Ω {\displaystyle \Omega } while the leftmost-outermost redex is the entire expression.Applicative order reduction refers to leftmost-innermost reduction.


In mathematics and probability, the Borell–TIS inequality is a result bounding the probability of a deviation of the uniform norm of a centered Gaussian stochastic process above its expected value. The result is named for Christer Borell and its independent discoverers Boris Tsirelson, Ildar Ibragimov, and Vladimir Sudakov. The inequality has been described as "the single most important tool in the study of Gaussian processes."


In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges are referred to as k-cut. The goal is to find the minimum-weight k-cut. This partitioning can have applications in VLSI design, data-mining, finite elements and communication in parallel computing.


Symbols are concatenated together according to recursive rules, in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form.


In regular English verbs, the past tense and past participle have the same form. This is also true of most irregular verbs that follow a variation of the weak conjugation, as can be seen in the list below. Differences between the past tense and past participle (as in sing–sang–sung, rise–rose–risen) generally appear in the case of verbs that continue the strong conjugation, or in a few cases weak verbs that have acquired strong-type forms by analogy—as with show (regular past tense showed, strong-type past participle shown). However, even some strong verbs have identical past tense and participle, as in cling–clung–clung.


In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant precisely when, for all m < n σ ( m ) m < σ ( n ) n {\displaystyle {\frac {\sigma (m)}{m}}<{\frac {\sigma (n)}{n}}} where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... (sequence A004394 in the OEIS). For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5.


To express the constraint that all items must be allocated, add an n-ary constraint for each item (where n is the number of agents), with an infinite cost if no variable related to this item is "1".The problem can be solved using the following local search algorithm. All agents are ordered lexicographically (e.g. by their name or index). Each agent also orders its variables lexicographically.


In telecommunication, a call-second is a unit used to measure communications traffic density, equivalent to one call with a duration of one second. Traffic is measured independent of users. For example, one user making two 75-second calls is equivalent to two users each making one 75-second call, as each case produces 150 call-seconds of traffic.


During the Vedic period, gods aid humans against demons. By that, gods secure their own place in heaven, using humans as tools to defeat their cosmic enemies.Asura, in the earliest hymns of the Rigveda, originally meant any supernatural spirit, either good or bad. Since the /s/ of the Indic linguistic branch is cognate with the /h/ of the Early Iranian languages, the word asura, representing a category of celestial beings, is a cognate with Old Persian Ahura.


Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is used to determine a score for making a prediction. The vector space associated with these vectors is often called the feature space. In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed.


In the field of computer science recently more specific types of modeling languages have emerged.


In the 1920s, William Giauque and Herrick L. Johnston discovered the stable isotopes of oxygen. Isotopes were not well understood at the time; James Chadwick would not discover the neutron until 1932. Two systems were in use for classifying them, based on chemical and physical properties. The latter was determined using the mass spectrograph.


In the context of process-driven applications, three categories of process exist:


The protection thus granted has proven to be incomplete. Consequently, over the course of the 20th century, case law has extended liability for recklessness to other cases, in particular by admitting that § 823 paragraph 1 BGB aims to protect a "general right to personality" and a "right to the company" or by recognising, alongside tort liability, the theory of culpa in contrahendo. Although Boris Starck makes no express reference to it, there are serious reasons to think that this right strongly inspired him in his elaboration of the theory of the guarantee.


These numbers may surprise many, because the market is perceived as desktop computers. x86 designs dominate desktop and notebook computer sales, but such computers are only a tiny fraction of the computers now sold. Most people in industrialised countries own more computers in embedded systems in their car and house, than on their desks.


Facebook estimated the existence of up to 60 million troll bots actively spreading misinformation on their platform, and has taken measures to stop the spread of misinformation, resulting in a decrease, though misinformation continues to exist on the platform. A research report by NewsGuard found there is a very high level (~20% in their probes of videos about relevant topics) of online misinformation delivered – to a mainly young user base – with TikTok, whose (essentially unregulated) usage is increasing as of 2022.Spontaneous spread of misinformation on social media usually occurs from users sharing posts from friends or mutually-followed pages.


Some disadvantages are that the datasets are often huge and difficult to keep up to date. Another problem with this method is that it is costly to compile such a warehouse.Standardized formats for different types of data (ex: protein data) are now emerging due to the influence of groups like the Proteomics Standards Initiative (PSI). Some data warehousing projects even require the submission of data in one of these new formats.


In signal processing, multidimensional empirical mode decomposition (multidimensional EMD) is an extension of the one-dimensional (1-D) EMD algorithm to a signal encompassing multiple dimensions. The Hilbert–Huang empirical mode decomposition (EMD) process decomposes a signal into intrinsic mode functions combined with the Hilbert spectral analysis, known as the Hilbert–Huang transform (HHT). The multidimensional EMD extends the 1-D EMD algorithm into multiple-dimensional signals. This decomposition can be applied to image processing, audio signal processing, and various other multidimensional signals.


The effect is that i2 uses the correct (the more recent) value of Register 1: the commit/store was made immediately and not pipelined. With forwarding enabled, the Instruction Decode/Execution (ID/EX) stage of the pipeline now has two inputs: the value read from the register specified (in this example, the value 6 from Register 1), and the new value of Register 1 (in this example, this value is 3) which is sent from the next stage Instruction Execute/Memory Access (EX/MEM). Added control logic is used to determine which input to use.


For example, simply typed lambda calculus can be seen as a language with a single non-basic type constructor—the function type constructor. Product types can generally be considered "built-in" in typed lambda calculi via currying. Abstractly, a type constructor is an n-ary type operator taking as argument zero or more types, and returning another type.


stock market is too narrow, omitting all sorts of other domestic and international asset classes. Thus another occasional choice would be the use of international indexes, such as the MSCI EAFE. However, even these indexes have returns that are surprisingly similar to the stock market.


Key relevance is the measure of similarity between the key and the optimal size needed to fit the lock, or it is the similarity between a duplicate key and the original it is seeking to replicate. Key relevance cannot be deduced from a key code, since the key code merely refers to a central authoritative source for designed shapes and sizes of keys. Typical modern keys require a key relevance of approximately 0.03 millimetres (0.0012 in) to 0.07 millimetres (0.0028 in) (accuracy within 0.75% to 1.75%) in order to operate.


In mathematics, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions: k > 3 the row and column sums of K are each equal to b, where b ≥ 2 there exists no row of the (m − k)-by-k submatrix formed by the rows not included in K with a row sum greater than b.The following is an example of a K submatrix where k = 5 and b = 2:  . {\displaystyle {\begin{bmatrix}1&1&0&0&0\\0&1&1&0&0\\0&0&1&1&0\\0&0&0&1&1\\1&0&0&0&1\end{bmatrix}}.} == References ==


In reporting result of horse races winning margins are commonly abbreviated:


In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group.Let G {\displaystyle G} be a finitely generated group. Then, for each integer n {\displaystyle n} define a n ( G ) {\displaystyle a_{n}(G)} to be the number of subgroups H {\displaystyle H} of index n {\displaystyle n} in G {\displaystyle G} . Similarly, if G {\displaystyle G} is a topological group, s n ( G ) {\displaystyle s_{n}(G)} denotes the number of open subgroups U {\displaystyle U} of index n {\displaystyle n} in G {\displaystyle G} .


The correct proof was published in May 1995. The proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques not available to Fermat.


These are for informational purposes only, and are called by a variety of names, such as Lot Book Report, Plat Certificate, 300-foot Radius Report, Ownership & Lien Report and others. These informational searches are used mainly in two instances: Ownership & Lien Report. Is informational, coming from examining the current owner's vesting deed forward and examining: owed taxes, new encumbrances on record, name searches on parties in title.


The parameters of a logistic regression are most commonly estimated by maximum-likelihood estimation (MLE). This does not have a closed-form expression, unlike linear least squares; see § Model fitting. Logistic regression by MLE plays a similarly basic role for binary or categorical responses as linear regression by ordinary least squares (OLS) plays for scalar responses: it is a simple, well-analyzed baseline model; see § Comparison with linear regression for discussion. The logistic regression as a general statistical model was originally developed and popularized primarily by Joseph Berkson, beginning in Berkson (1944), where he coined "logit"; see § History.


Now supporting VESA Local Bus and using the Am486 with up to 100 MHz clock speed. A SC450 with 33 MHze.g. was used in the Nokia 9000 Communicator.


At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs.Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering.


In the context of games for many 8-bit computers, users could load games into memory and, before launching them, modify specific memory addresses in order to cheat, getting an unlimited number of lives, immunity, invisibility, etc. Such modifications were performed using POKE statements. The Commodore 64, ZX Spectrum and Amstrad CPC also allowed players with one of the relevant cartridges (such as Action Replay or Multiface) to freeze the running program, enter POKEs, and resume. For example, in Knight Lore for the ZX Spectrum, immunity can be achieved with the following command: In this case, the value 201 corresponds to a RET instruction, so that the game returns from a subroutine early before triggering collision detection.


In the System/360, other than the 360/67, and early System/370 architectures, the general-purpose registers were 32 bits wide, the machine did 32-bit arithmetic operations, and addresses were always stored in 32-bit words, so the architecture was considered 32-bit, but the machines ignored the top 8 bits of the address resulting in 24-bit addressing. With the System/370-XA architecture and the IBM Enterprise Systems Architecture, in addition to a 24-bit addressing mode for compatibility with older applications, there is a 31-bit addressing mode, in which only the high order bit (bit 0) in the word is ignored for addressing. An exception is that mode-switching instructions also use bit 0. There were at least two reasons that IBM did not implement the 32-bit addressing of the 360/67 The loop control instructions BXH and BXLE did signed comparisons. Much of the existing software used bit 0 as an end-of-list indicator.The 64-bit z/Architecture also supports 24-bit and 31-bit addressing modes for compatibility with older applications.


In mathematics, a *-ring is a ring with a map *: A → A that is an antiautomorphism and an involution. More precisely, * is required to satisfy the following properties: (x + y)* = x* + y* (x y)* = y* x* 1* = 1 (x*)* = xfor all x, y in A. This is also called an involutive ring, involutory ring, and ring with involution. The third axiom is implied by the second and fourth axioms, making it redundant. Elements such that x* = x are called self-adjoint.Archetypical examples of a *-ring are fields of complex numbers and algebraic numbers with complex conjugation as the involution.


If some processors in a large grid of processors fail (become inactive), then it may also be necessary to inactivate other processors with too few active neighbors, in order to preserve the high connectivity of the remaining network. The analysis of bootstrap percolation can be used to determine the failure probability that can be tolerated by the system. == References ==


Convolutionally encoded block codes typically employ termination. The arbitrary block length of convolutional codes can also be contrasted to classic block codes, which generally have fixed block lengths that are determined by algebraic properties.


In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences OEIS: A023200 and OEIS: A046132 in OEIS) below 1000 are: (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 443), (457, 461), (463,467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971)


Another example would be to measure the productivity of a software development team in terms of lines of source code written. This approach can easily add large amounts of dubious code, thereby inflating the line count but adding little value in terms of systemic improvement. A similar problem arises when a footballer kicks a ball uselessly to build up their statistics.


In the 17th century, the method of exhaustion led to the rectification by geometrical methods of several transcendental curves: the logarithmic spiral by Evangelista Torricelli in 1645 (some sources say John Wallis in the 1650s), the cycloid by Christopher Wren in 1658, and the catenary by Gottfried Leibniz in 1691. In 1659, Wallis credited William Neile's discovery of the first rectification of a nontrivial algebraic curve, the semicubical parabola. The accompanying figures appear on page 145. On page 91, William Neile is mentioned as Gulielmus Nelius.


In search engines, autocomplete user interface features provide users with suggested queries or results as they type their query in the search box. This is also commonly called autosuggest or incremental search. This type of search often relies on matching algorithms that forgive entry errors such as phonetic Soundex algorithms or the language independent Levenshtein algorithm.


In symbolic programming languages, it is easy to have patterns as arguments to functions or as elements of data structures. A consequence of this is the ability to use patterns to declaratively make statements about pieces of data and to flexibly instruct functions how to operate. For instance, the Mathematica function Compile can be used to make more efficient versions of the code. In the following example the details do not particularly matter; what matters is that the subexpression {{com, Integer}} instructs Compile that expressions of the form com can be assumed to be integers for the purposes of compilation: Mailboxes in Erlang also work this way. The Curry–Howard correspondence between proofs and programs relates ML-style pattern matching to case analysis and proof by exhaustion.


In order to state the paradox it is necessary to understand that the cardinal numbers are totally ordered, so that one can speak about one being greater or less than another. Then Cantor's paradox is: This fact is a direct consequence of Cantor's theorem on the cardinality of the power set of a set. Another consequence of Cantor's theorem is that the cardinal numbers constitute a proper class. That is, they cannot all be collected together as elements of a single set. Here is a somewhat more general result.


In plant biology, the perforations in a perforate leaf are also described as fenestrae, and the leaf is called a fenestrate leaf. The leaf window is also known as a fenestra, and is a translucent structure that transmits light, as in Fenestraria. Examples of fenestrate structures in the fungal kingdom include the symmetrically arranged gaps in the indusium ("skirt") of the mushroom Phallus duplicatus, and the thallus of the coral lichen Pulchrocladia retipora.


In the contexts of software architecture, service-orientation and service-oriented architecture, the term service refers to a software functionality, or a set of software functionalities (such as the retrieval of specified information or the execution of a set of operations) with a purpose that different clients can reuse for different purposes, together with the policies that should control its usage (based on the identity of the client requesting the service, for example). OASIS defines a service as "a mechanism to enable access to one or more capabilities, where the access is provided using a prescribed interface and is exercised consistent with constraints and policies as specified by the service description".


Reduced heat production and lower overheating risk Redesigned pipeline, supporting faster clock speeds (target up to 1 GHz) Longer: 8 (vs 5) stages Out-of-order completion for some operations (e.g., stores) Dynamic branch prediction/folding (like XScale) Cache misses don't block execution of non-dependent instructions. Load/store parallelism ALU parallelism 64-bit data pathsJTAG debug support (for halting, stepping, breakpoints, and watchpoints) was simplified. The EmbeddedICE module was replaced with an interface which became part of the ARMv7 architecture.


In the C programming language, the standard input, output, and error streams are attached to the existing Unix file descriptors 0, 1 and 2 respectively. In a POSIX environment the definitions STDIN_FILENO, STDOUT_FILENO or STDERR_FILENO should be used instead rather than magic numbers. File pointers stdin, stdout, and stderr are also provided. Ken Thompson (designer and implementer of the original Unix operating system) modified sort in Version 5 Unix to accept "-" as representing standard input, which spread to other utilities and became a part of the operating system as a special file in Version 8. Diagnostics were part of standard output through Version 6, after which Dennis M. Ritchie created the concept of standard error.


In the Erdős–Rényi model, the average degree ⟨ k ⟩ {\displaystyle \langle k\rangle } of a graph with n vertices and N edges is given by ⟨ k ⟩ = 2 N n {\displaystyle \langle k\rangle ={\frac {2N}{n}}} . The condition for the emergence of a giant component is: ⟨ k ⟩ = 1 {\displaystyle {\left\langle k\right\rangle =1}} . Thus, one link is sufficient for its emergence of the giant component. If expressing the condition in terms of p {\displaystyle {p}} , one obtains: P c = 1 N − 1 ≈ 1 N {\displaystyle {P_{c}={\frac {1}{N-1}}\approx {\frac {1}{N}}}} (1) Where N {\displaystyle {N}} is the number of nodes, P c {\displaystyle {P_{c}}} is the probability of clustering. Therefore, the larger a network, the smaller p {\displaystyle {p}} is sufficient for the giant component.


In real mode each logical address points directly into a physical memory location, every logical address consists of two 16 bit parts: The segment part of the logical address contains the base address of a segment with a granularity of 16 bytes, i.e. a segment may start at physical address 0, 16, 32, ..., 220-16. The offset part of the logical address contains an offset inside the segment, i.e. the physical address can be calculated as physical_address: = segment_part × 16 + offset (if the address line A20 is enabled), respectively (segment_part × 16 + offset) mod 220 (if A20 is off) Every segment has a size of 216 bytes.


In peer-to-peer file sharing, the strength of a swarm depends on user behaviour, as peers ideally upload more than they download. This is done by seeding, and there are different motivations to do this. There are two popular motivations to seed, of which one is the reputation-based incentive mechanism and the other is the tit for tat mechanism. As the name reveals, the former is based on the reputation of a peer, meaning that those peers who have a good reputation will get a better treatment from the uploader.


In the first year 24 technical standards committees were created. A year later, AENOR assumed the representation of Spain before the European organizations (CENELEC, ETSI) and international (ISO, IEC). Nowadays, AENOR has more than 200 technical standards committees involving nearly 6,000 experts in the field.


In telecommunications, the hybrid (H-) ternary line code is a line code that operates on a hybrid principle combining the binary non-return-to-zero-level (NRZL) and the polar return-to-zero (RZ) codes. The H-ternary code has three levels for signal representation; these are positive (+), zero (0), and negative (−). These three levels are represented by three states. The state of the line code could be in any one of these three states.


In most territories, access to mobile satellite service is managed by traditional telecom companies and specialized resellers which market hardware, software and network access to end users, although occasionally some constellation operators also market service directly to end users. Some companies providing commercial access: Avanti Globalsat Group Iridium Communications Inmarsat Telespazio Thuraya Vizada


Operator error and a faulty shutdown system led to a sudden, massive spike in the neutron multiplication rate, a sudden decrease in the neutron period, and a consequent increase in neutron population; thus, core heat flux increased rapidly beyond the design limits of the reactor. This caused the water coolant to flash to steam, causing a sudden overpressure within the reactor core (the first of the two major explosions that occurred), leading to granulation of the upper portion of the core and the ejection of the upper biological shield atop the core along with core debris from the reactor building in a widely dispersed pattern. The lower portion of the reactor remained somewhat intact; the graphite neutron moderator was exposed to oxygen-containing air; heat from the power excursion in addition to residual heat flux from the remaining fuel rods left without coolant induced oxidation in the moderator and in the opened fuel rods; this in turn evolved more heat and contributed to the melting of more of the fuel rods and the outgassing of the fission products contained therein.


In order to determine where each channel is located in the stream of data being received, each set of 24 channels is aligned in a frame. The frame is 192 bits long (8 * 24), and is terminated with a 193rd bit, the framing bit, which is used to find the end of the frame. In order for the framing bit to be located by receiving equipment, a predictable pattern is sent on this bit.


In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed by Joel Spencer. He used a branching process to formally prove the optimal achievable bound under some side conditions. The other algorithm is called the Rödl nibble and was proposed by Vojtěch Rödl et al. They showed that the achievable packing by the Rödl nibble is in some sense close to that of the random greedy algorithm.


Reduction of surface tension increases cavitation, so the solution usually contains a good wetting agent (surfactant). Aqueous cleaning solutions contain detergents, wetting agents and other components, which have a large influence on the cleaning process. The correct composition of the solution is very dependent upon the item cleaned.


In the fair item allocation problem, classic allocation procedures such as adjusted winner and envy-graph are not RM. Moreover, even the Nash-optimal rule, which is RM in cake-cutting, is not RM in item allocation. In contrast, round-robin item allocation is RM. Moreover, round-robin can be adapted to yield picking sequences appropriate for agents with different entitlements; all these picking sequences are RM too.


In most functional programming languages, such as Scheme, nested functions are a common way of implementing algorithms with loops in them. A simple (tail) recursive inner function is created, which behaves as the algorithm's main loop, while the outer function performs startup actions that only need to be done once. In more complex cases, a number of mutually recursive functions may be created as inner functions.


That is, if tones x, y, and z form a rising sequence of tones, then the measure of the interval from x to y plus the measure of the interval from y to z should equal the measure of the interval from x to z. Such a measure is given by the cent, which divides the octave into 1200 equal intervals (12 semitones of 100 cents each). Mathematically, given tones with frequencies f1 and f2, the number of cents in the interval from f1 to f2 is | 1200 log 2  f 1 f 2 | . {\displaystyle \left|1200\log _{2}{\frac {f_{1}}{f_{2}}}\right|.} The millioctave is defined in the same way, but with a multiplier of 1000 instead of 1200.


The axiom schema of Replacement can also be formulated in terms of the ranges of such set functions. If both the domain A {\displaystyle A} and choosen codomain C {\displaystyle C} are sets, then the above predicate only involves bounded quantifiers. Common notions such as injectivity and surjectivity can be expressed in a bounded fashion as well, and thus so is bijectivity.


In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's Analytical Engine, a bit was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a paper card or tape. The first electrical devices for discrete logic (such as elevator and traffic light control circuits, telephone switches, and Konrad Zuse's computer) represented bits as the states of electrical relays which could be either "open" or "closed". When relays were replaced by vacuum tubes, starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a mercury delay line, charges stored on the inside surface of a cathode-ray tube, or opaque spots printed on glass discs by photolithographic techniques. In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory, magnetic tapes, drums, and disks, where a bit was represented by the polarity of magnetization of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other.


In six columns the classes of traffic handled at the station was shown as follows:Column 1 - G = Goods Traffic Column 1 - G* = Coal Class, Mineral and Station-to-Station Traffic in Truck Loads. Column 2 - P = Passenger, Parcels & Miscellaneous Traffic. Column 2 - P* = Passenger, but not Parcels & Miscellaneous Traffic. Column 2 - P† = Parcels & Miscellaneous Traffic (i.e. not Passengers).


{\displaystyle \lambda _{\text{piv}}={\sqrt {\frac {\int e(\lambda )\lambda \,\mathrm {d} \lambda }{\int e(\lambda )\lambda ^{-1}\,\mathrm {d} \lambda }}}.} For a response function expressed in the quantum-efficiency convention, it is: λ piv = ∫ e ( λ ) d λ ∫ e ( λ ) λ − 2 d λ . {\displaystyle \lambda _{\text{piv}}={\sqrt {\frac {\int e(\lambda )\,\mathrm {d} \lambda }{\int e(\lambda )\lambda ^{-2}\,\mathrm {d} \lambda }}}.}


Supported modulation formats on the PDSCH are QPSK, 16QAM and 64QAM. The Physical Multicast Channel (PMCH) is used for broadcast transmission using a Single Frequency Network The Physical Broadcast Channel (PBCH) is used to broadcast the basic system information within the cellAnd the following signals: The synchronization signals (PSS and SSS) are meant for the UE to discover the LTE cell and do the initial synchronization. The reference signals (cell specific, MBSFN, and UE specific) are used by the UE to estimate the DL channel. Positioning reference signals (PRS), added in release 9, meant to be used by the UE for OTDOA positioning (a type of multilateration)


In the following examples indentation and formatting are critical for parsing the code: expressions are terminated by the end of the line, lists of expressions need to be on the same level of indentation. This feature, named the off-side rule, is also found in other languages such as Haskell and Python. Communication between processes work through named channels. One process outputs data to a channel via !


In the Japanese kantenji braille, the standard 8-dot Braille patterns 3567, 13567, 34567, and 134567 are the patterns related to Braille pattern dots-2345, since the two additional dots of kantenji patterns 02345, 23457, and 023457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R: A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given by (a, c) ∈ S o R ⇔ for some b ∈ B, (a, b) ∈ R and (b, c) ∈ S.Rel has also been called the "category of correspondences of sets".


In some publications, the author responsible for new names and nomenclatural acts is not stated directly in the original source, but can sometimes be inferred from reliable external evidence. Recommendation 51D of the Code states: "...if the authorship is known or inferred from external evidence, the name of the author, if cited, should be enclosed in square brackets to show the original anonymity".


In diagnostic labs, MIC test results are used to grade microbes as "S" (susceptible or responding to a standard dosing regimen), "I" (intermediate or requiring increased exposure) or "R" (resistant). These grades are assigned based on agreed upon values called breakpoints. Breakpoints are published by standards development organizations such as the U.S.


In order theory it is common to define a pointwise partial order on functions. With A, B posets, the set of functions A → B can be ordered by f ≤ g if and only if (∀x ∈ A) f(x) ≤ g(x). Pointwise orders also inherit some properties of the underlying posets. For instance if A and B are continuous lattices, then so is the set of functions A → B with pointwise order. Using the pointwise order on functions one can concisely define other important notions, for instance: A closure operator c on a poset P is a monotone and idempotent self-map on P (i.e. a projection operator) with the additional property that idA ≤ c, where id is the identity function. Similarly, a projection operator k is called a kernel operator if and only if k ≤ idA.An example of an infinitary pointwise relation is pointwise convergence of functions—a sequence of functions with converges pointwise to a function f {\displaystyle f} if for each x {\displaystyle x} in X {\displaystyle X}


In text-based indexing or large vocabulary continuous speech recognition (LVCSR), the audio file is first broken down into recognizable phonemes. It is then run through a dictionary that can contain several hundred thousand entries and matched with words and phrases to produce a full text transcript. A user can then simply search a desired word term and the relevant portion of the audio content will be returned. If the text or word could not be found in the dictionary, the system will choose the next most similar entry it can find. The system uses a language understanding model to create a confidence level for its matches. If the confidence level be below 100 percent, the system will provide options of all the found matches.


The quantity ½(b − a)=0.125 is then added to the horizontal side of the square and subtracted from the vertical side. The resulting line segments are the sides of the desired rectangle.One difficulty in reconstructing Old Babylonian geometric diagrams is that known tablets never include diagrams in solutions—even in geometric solutions where explicit constructions are described in text—although diagrams are often included in formulations of problems.


{\displaystyle \forall x\forall y(x+y\leq z)\to \forall x\forall y(x+y=0).} This formula has one free variable, z.The axioms for ordered abelian groups can be expressed as a set of sentences in the language. For example, the axiom stating that the group is commutative is usually written ( ∀ x ) ( ∀ y )  . {\displaystyle (\forall x)(\forall y).}


In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.


In which case, there may be multiple and more complex ways to structure the argument of the proof. The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural numbers is clearly possible, by the most usual formulation of mathematical induction; but the scope of the method can include well-ordered induction of any kind.


In the Geometry paper, set on the second morning of the papers for candidates for the Gold Medal in the General Examination of the University of Dublin in October 1820, the following three problems appear. Question 10. Three equilateral triangles are thus constructed on the sides of a given triangle, A, B, D, the lines joining their centres, C, C', C" form an equilateral triangle. Question 11.


The result was documented in CSC-STD-004-85. Two relatively independent components of robustness were defined: Assurance Level and Functionality. Both were specified with a degree of precision that warranted significant confidence in certifications based on these criteria.


In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model: 495 ) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers, and job service times are exponentially distributed. It is a generalisation of the M/M/1 queue which considers only a single server. The model with infinitely many servers is the M/M/∞ queue.


In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.


In recent years most of the technology used in the various MIPS generations has been offered as semiconductor intellectual property cores (IP cores), as building blocks for embedded processor designs. Both 32-bit and 64-bit basic cores are offered, known as the 4K and 5K. These cores can be mixed with add-in units such as floating-point units (FPU), single instruction, multiple data (SIMD) systems, various input/output (I/O) devices, etc. MIPS cores have been commercially successful, now having many consumer and industrial uses.


In the data stream model, some or all of the input is represented as a finite sequence of integers (from some finite domain) which is generally not available for random access, but instead arrives one at a time in a "stream". If the stream has length n and the domain has size m, algorithms are generally constrained to use space that is logarithmic in m and n. They can generally make only some small constant number of passes over the stream, sometimes just one.


Then Pr  ≥ ( ∑ i = 1 n Pr  ) 2 ∑ i = 1 n ∑ j = 1 n Pr  . {\displaystyle \Pr\geq {\frac {\left(\sum _{i=1}^{n}\Pr\right)^{2}}{\sum _{i=1}^{n}\sum _{j=1}^{n}\Pr}}.}


In the alphabetic sequence c is identical either to k (in front of a, o, u or consonant or as the last letter of the word) or to z (in front of e or i). The letter y is identical to i.


This also is a known, computed quantity, and it varies by sample and by out-of-sample test space. In the context of gradient descent algorithms, it is common to introduce a factor of 1 / 2 {\displaystyle 1/2} to the MSE for ease of computation after taking the derivative. So a value which is technically half the mean of squared errors may be called the MSE.


Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility.


The arithmetical hierarchy and polynomial hierarchy classify the degree to which problems are respectively computable and computable in polynomial time. For instance, the level Σ 0 0 = Π 0 0 = Δ 0 0 {\displaystyle \Sigma _{0}^{0}=\Pi _{0}^{0}=\Delta _{0}^{0}} of the arithmetical hierarchy classifies computable, partial functions. Moreover, this hierarchy is strict such that at any other class in the arithmetic hierarchy classifies strictly uncomputable functions.


In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo of an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is −1. Its value at zero is 0. The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity. Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol.


In systems engineering, dependability is a measure of a system's availability, reliability, maintainability, and in some cases, other characteristics such as durability, safety and security. In real-time computing, dependability is the ability to provide services that can be trusted within a time-period. The service guarantees must hold even when the system is subject to attacks or natural failures. The International Electrotechnical Commission (IEC), via its Technical Committee TC 56 develops and maintains international standards that provide systematic methods and tools for dependability assessment and management of equipment, services, and systems throughout their life cycles. The IFIP Working Group 10.4 on "Dependable Computing and Fault Tolerance" plays a role in synthesizing the technical community's progress in the field and organizes two workshops each year to disseminate the results. Dependability can be broken down into three elements: Attributes - a way to assess the dependability of a system Threats - an understanding of the things that can affect the dependability of a system Means - ways to increase a system's dependability


Prediction: For every state in S(k) of the form (X → α • Y β, j) (where j is the origin position as above), add (Y → • γ, k) to S(k) for every production in the grammar with Y on the left-hand side (Y → γ). Scanning: If a is the next symbol in the input stream, for every state in S(k) of the form (X → α • a β, j), add (X → α a • β, j) to S(k+1). Completion: For every state in S(k) of the form (Y → γ •, j), find all states in S(j) of the form (X → α • Y β, i) and add (X → α Y • β, i) to S(k).Duplicate states are not added to the state set, only new ones.


When the true working-correlation is known, consistency does not require MCAR. Huber-White standard errors improve the efficiency of Liang Zeger GEE in the absence of serial Autocorrelation but may remove the marginal interpretation. GEE estimates the average response over the population ("population-averaged" effects) with Liang Zeger Standard Errors, and in individuals using Huber White Standard Errors also known as "robust standard error" or "sandwich variance" estimates.


In radio systems, TDMA is usually used alongside frequency-division multiple access (FDMA) and frequency-division duplex (FDD); the combination is referred to as FDMA/TDMA/FDD. This is the case in both GSM and IS-136 for example. Exceptions to this include the DECT and Personal Handy-phone System (PHS) micro-cellular systems, UMTS-TDD UMTS variant, and China's TD-SCDMA, which use time-division duplexing, where different time slots are allocated for the base station and handsets on the same frequency. A major advantage of TDMA is that the radio part of the mobile only needs to listen and broadcast for its own time slot.


In mathematics, effective dimension is a modification of Hausdorff dimension and other fractal dimensions that places it in a computability theory setting. There are several variations (various notions of effective dimension) of which the most common is effective Hausdorff dimension. Dimension, in mathematics, is a particular way of describing the size of an object (contrasting with measure and other, different, notions of size).


In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of "almost everywhere" in measure theory.


Crashes can be easily identified and might indicate potential vulnerabilities (e.g., denial of service or arbitrary code execution). However, the absence of a crash does not indicate the absence of a vulnerability. For instance, a program written in C may or may not crash when an input causes a buffer overflow.


In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes. Projection is one way, very obvious in visual terms when three-dimensional objects are projected into two dimensions (for example in one of our eyes); in looking at classical statuary the folds of drapery are amongst the most obvious features. Singularities of this kind include caustics, very familiar as the light patterns at the bottom of a swimming pool. Other ways in which singularities occur is by degeneration of manifold structure. The presence of symmetry can be good cause to consider orbifolds, which are manifolds that have acquired "corners" in a process of folding up, resembling the creasing of a table napkin.


In order for a game to be in normal form, we are provided with the following data: There is a finite set I of players, each player is denoted by i. Each player i has a finite k number of pure strategies S i = { 1 , 2 , … , k } . {\displaystyle S_{i}=\{1,2,\ldots ,k\}.} A pure strategy profile is an association of strategies to players, that is an I-tuple s → = ( s 1 , s 2 , … , s I ) {\displaystyle {\vec {s}}=(s_{1},s_{2},\ldots ,s_{I})} such that s 1 ∈ S 1 , s 2 ∈ S 2 , … , s I ∈ S I {\displaystyle s_{1}\in S_{1},s_{2}\in S_{2},\ldots ,s_{I}\in S_{I}} A payoff function is a function u i: S 1 × S 2 × … × S I → R . {\displaystyle u_{i}:S_{1}\times S_{2}\times \ldots \times S_{I}\rightarrow \mathbb {R} .}


The relationship between the two covariant return types is usually one which allows substitution of the one type with the other, following the Liskov substitution principle. This usually implies that the return types of the overriding methods will be subtypes of the return type of the overridden method. The above example specifically illustrates such a case. If substitution is not allowed, the return type is invariant and causes a compile error. Another example of covariance with the help of built in Object and String class of Java:


In some cases, the 'cake' to be divided has a negative value. For example, it might be piece of lawn that has to be mowed, or a piece of wasteland that has to be cleaned. Then, the cake is a 'heterogeneous bad' rather than a 'heterogeneous good'. Some procedures for envy-free cake-cutting can be adapted to work for a bad cake, but the adaptation is often not trivial. See envy-free chore division for more details.


In a similar fashion, cross-multiplier 2 states that fPC = (1/2) —while cross-multiplier 3 states that fPD = (1/2)  . Returning to the first multiplier, it can now be seen also to be fPQ = (1/2) , which, after substituting multipliers 2 and 3, resumes its original form. In much of the following, the grand-parental generation is referred to as (t-2) , the parent generation as (t-1) , and the "target" generation as t.


In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form F n = 2 2 n + 1 , {\displaystyle F_{n}=2^{2^{n}}+1,} where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... (sequence A000215 in the OEIS).If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023, the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS); heuristics suggest that there are no more.


Then it checks if p ( r 1 , … , r m ) = f k ( r 1 , … , r m ) {\displaystyle p(r_{1},\dots ,r_{m})=f_{k}(r_{1},\dots ,r_{m})} If they are equal then V accepts, otherwise V rejects.This is the end of the protocol description. If ψ is true then V will accept when P follows the protocol. Likewise if P ~ {\displaystyle {\tilde {P}}} is a malicious prover which lies, and if ψ is false, then P ~ {\displaystyle {\tilde {P}}} will need to lie at phase 0 and send some value for f0.


In the PEM model, there is no direct communication network between the P processors. The processors have to communicate indirectly over the main memory. If multiple processors try to access the same block in main memory concurrently read/write conflicts occur. Like in the PRAM model, three different variations of this problem are considered: Concurrent Read Concurrent Write (CRCW): The same block in main memory can be read and written by multiple processors concurrently.


He named them after his advisor Wolfgang Gröbner. In 2007, Buchberger received the Association for Computing Machinery's Paris Kanellakis Theory and Practice Award for this work. However, the Russian mathematician Nikolai Günther had introduced a similar notion in 1913, published in various Russian mathematical journals.


Since many users do not have unlimited web space, either as a paid service, or through an ISP offering, video hosting services are becoming increasingly popular, especially with the explosion in popularity of blogs, internet forums and other interactive pages. The mass market for camera phones and smartphones has increased the supply of user-generated video. Traditional methods of personal video distribution, such as making a DVD to show to friends at home, are unsuited to the low resolution and high volume of camera phone clips. In contrast, current broadband Internet connections are well suited to serving the quality of video shot on mobile phones. Most people do not own web servers, and this has created demand for user-generated video content hosting.


In the following, the '1' flag bits indicate the beginning of each segment. 1 2 3 4 5 6 input 1 0 0 1 0 1 flag bits 1 3 6 4 9 6 segmented scan + {\displaystyle {\begin{array}{|rrrrrr|l|}1&2&3&4&5&6&{\text{input}}\\\hline 1&0&0&1&0&1&{\text{flag bits}}\\\hline 1&3&6&4&9&6&{\text{segmented scan +}}\\\end{array}}} Group11 = 1 3 = 1 + 2 6 = 1 + 2 + 3Group24 = 4 9 = 4 + 5Group36 = 6An alternative method used by High Performance Fortran is to begin a new segment at every transition of flag value. An advantage of this representation is that it is useful with both prefix and suffix (backwards) scans without changing its interpretation. In HPF, Fortran logical data type is used to represent segments. So the equivalent flag array for the above example would be as follows: 1 2 3 4 5 6 input T T T F F T flag values 1 3 6 4 9 6 segmented scan + {\displaystyle {\begin{array}{|rrrrrr|l|}1&2&3&4&5&6&{\text{input}}\\\hline T&T&T&F&F&T&{\text{flag values}}\\\hline 1&3&6&4&9&6&{\text{segmented scan +}}\\\end{array}}} == References ==


In mathematics, a square-difference-free set is a set of natural numbers, no two of which differ by a square number. Hillel Furstenberg and András Sárközy proved in the late 1970s the Furstenberg–Sárközy theorem of additive number theory showing that, in a certain sense, these sets cannot be very large. In the game of subtract a square, the positions where the next player loses form a square-difference-free set.


A person intercepting an ESN/MDN pair could clone the combination onto a different phone and use it in other areas for making calls without paying. Cellular phone cloning became possible with off-the-shelf technology in the 1990s. Would-be cloners required three key items: A radio receiver, such as the Icom PCR-1000, that could tune into the Reverse Channel (the frequency on which AMPS phones transmit data to the tower) A PC with a sound card and a software program called Banpaia A phone that could easily be used for cloning, such as the Oki 900The radio, when tuned to the proper frequency, would receive the signal transmitted by the cell phone to be cloned, containing the phone's ESN/MDN pair.


In operating systems, feedback vertex sets play a prominent role in the study of deadlock recovery. In the wait-for graph of an operating system, each directed cycle corresponds to a deadlock situation. In order to resolve all deadlocks, some blocked processes have to be aborted. A minimum feedback vertex set in this graph corresponds to a minimum number of processes that one needs to abort.


It is often denoted Hom(V, k), or, when the field k is understood, V ∗ {\displaystyle V^{*}} ; other notations are also used, such as V ′ {\displaystyle V'} , V # {\displaystyle V^{\#}} or V ∨ . {\displaystyle V^{\vee }.} When vectors are represented by column vectors (as is common when a basis is fixed), then linear functionals are represented as row vectors, and their values on specific vectors are given by matrix products (with the row vector on the left).


In the Prolog syntactical convention a symbol starting with an upper case letter is a variable name; a symbol that starts with a lowercase letter is a function symbol; the comma is used as the logical and operator. For mathematical notation, x,y,z are used as variables, f,g as function symbols, and a,b as constants. The most general unifier of a syntactic first-order unification problem of size n may have a size of 2n. For example, the problem ( ( ( a ∗ z ) ∗ y ) ∗ x ) ∗ w ≐ w ∗ ( x ∗ ( y ∗ ( z ∗ a ) ) ) {\displaystyle (((a*z)*y)*x)*w\doteq w*(x*(y*(z*a)))} has the most general unifier { z ↦ a , y ↦ a ∗ a , x ↦ ( a ∗ a ) ∗ ( a ∗ a ) , w ↦ ( ( a ∗ a ) ∗ ( a ∗ a ) ) ∗ ( ( a ∗ a ) ∗ ( a ∗ a ) ) } {\displaystyle \{z\mapsto a,y\mapsto a*a,x\mapsto (a*a)*(a*a),w\mapsto ((a*a)*(a*a))*((a*a)*(a*a))\}} , cf. picture. In order to avoid exponential time complexity caused by such blow-up, advanced unification algorithms work on directed acyclic graphs (dags) rather than trees.


With the second method, a service provider sends a personalised OTAC (e.g. an enciphered token) to an authenticated email address; when the user types the OTAC into the website, the server authenticates the user. A web application can generate a unique personal identification number (PIN) that the user can input into the desktop client, the desktop client, in turn, uses that code to authenticate itself to the web application. This form of authentication is particularly useful in web applications that do not have an internal username/password store but instead use SAML for authentication.


These identifications are routinely done in mathematics. They can be expressed formally in Cartesian coordinates as with basis vectors in the tangent spaces defined by Here p and q are any two events and the second basis vector identification is referred to as parallel transport. The first identification is the canonical identification of vectors in the tangent space at any point with vectors in the space itself.


. . , − ∞ , m i n d − 1 } {\displaystyle k_{min}=\{-\infty ,min_{0},-\infty ,min_{1},...,-\infty ,min_{d-1}\}} k m a x = { m a x 0 , + ∞ , m a x 1 , + ∞ , .


Decimal megabytes were used for disk capacity by the CDC in 1974. The Seagate ST-412, one of several types installed in the IBM PC/XT, had a capacity of 10027008 bytes when formatted as 306 × 4 tracks and 32 256-byte sectors per track, which was quoted as "10 MB".


In the application of the Strahler stream order to hydrology, each segment of a stream or river within a river network is treated as a node in a tree, with the next segment downstream as its parent. When two first-order streams come together, they form a second-order stream. When two second-order streams come together, they form a third-order stream. Streams of lower order joining a higher order stream do not change the order of the higher stream.


In most computer programming, a programmer keeps a program's intended results in mind and painstakingly constructs a program to achieve those results. Inferential programming refers to (still mostly hypothetical) techniques and technologies enabling the inverse. This would allow describing an intended result to a computer, using a metaphor such as a fitness function, a test specification, or a logical specification, and then the computer, on its own, would construct a program needed to meet the supplied criteria.


In mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. It is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms — in order that a consistent body of propositions may be derived deductively from these statements. Thereafter, the proof of any proposition should be, in principle, traceable back to these axioms.


In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback are error correcting codes designed to work in the presence of feedback from the receiver to the sender.


Owen, New York: Marcel Dekker, pp. 149–193. See also "Confusion Over Measures of Evidence (p's) Versus Errors (a's) in Classical Statistical Testing," Raymond Hubbard and M. J. Bayarri, The American Statistician, August 2003, Vol.


In the context of national or homeland security, law enforcement, or social control policy, trusted systems provide conditional prediction about the behavior of people or objects prior to authorizing access to system resources. For example, trusted systems include the use of "security envelopes" in national security and counterterrorism applications, "trusted computing" initiatives in technical systems security, and credit or identity scoring systems in financial and anti-fraud applications. In general, they include any system in which probabilistic threat or risk analysis is used to assess "trust" for decision-making before authorizing access or for allocating resources against likely threats (including their use in the design of systems constraints to control behavior within the system); or deviation analysis or systems surveillance is used to ensure that behavior within systems complies with expected or authorized parameters.The widespread adoption of these authorization-based security strategies (where the default state is DEFAULT=DENY) for counterterrorism, anti-fraud, and other purposes is helping accelerate the ongoing transformation of modern societies from a notional Beccarian model of criminal justice based on accountability for deviant actions after they occur to a Foucauldian model based on authorization, preemption, and general social compliance through ubiquitous preventative surveillance and control through system constraints.In this emergent model, "security" is not geared towards policing but to risk management through surveillance, information exchange, auditing, communication, and classification. These developments have led to general concerns about individual privacy and civil liberty, and to a broader philosophical debate about appropriate social governance methodologies.


In non-canonical mode, data are accumulated in a buffer (which may or may not be the line editing buffer — some implementations having separate "processed input" and "raw input" queues) and become "available for reading" according to the values of two input control parameters, the c_cc and c_cc members of the termios data structure. Both are unsigned quantities (because cc_t is required to be an alias for an unsigned type). The former specifies a minimum number of characters, and the latter specifies a timeout in tenths of a second.


Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spaces in their own right is called point-set topology or general topology.


In the United States, many government regulations simply have categories for "off-highway vehicles" which are loosely defined and often result in SUVs (along with pick-up trucks and minivans) being classified as light trucks. For example, corporate average fuel economy (CAFE) regulations previously included "permit greater cargo-carrying capacity than passenger carrying volume" in the definition for trucks, resulting in SUVs being classified as light trucks.This classification as trucks allowed SUVs to be regulated less strictly than passenger cars under the Energy Policy and Conservation Act for fuel economy, and the Clean Air Act for emissions. However, from 2004 onwards, the United States Environmental Protection Agency (EPA) began to hold sport utility vehicles to the same tailpipe emissions standards as cars for criteria pollutants, though not greenhouse gas emissions standards as they were not set until 2010. In 2011, the CAFE regulations were changed to classify small, two-wheel-drive SUVs as passenger cars.However, the licensing and traffic enforcement regulations in the United States vary from state to state, and an SUV may be classified as a car in some states but as a truck in others.


In several Linux operating systems, the Software Updater program updates installed software and their associated packages with important software updates for security or with recommended patches. It also informs users when updates are available, listing them in alphabetical order for users to choose which updates to install, if any. It was originally written for Ubuntu, although it is now part of other APT-based systems.


It turns out that one can define simple formulas for P and its inverse (Cate & Twigg, 1977). First: P ( a ) = { M N − 1 if a = M N − 1 , N a mod ( M N − 1 ) otherwise , {\displaystyle P(a)={\begin{cases}MN-1&{\text{if }}a=MN-1,\\Na{\bmod {(}}MN-1)&{\text{otherwise}},\end{cases}}} where "mod" is the modulo operation. Second, the inverse permutation is given by: P − 1 ( a ′ ) = { M N − 1 if a ′ = M N − 1 , M a ′ mod ( M N − 1 ) otherwise .


The active set at x 0 {\displaystyle x_{0}} is made up of those constraints g i ( x 0 ) {\displaystyle g_{i}(x_{0})} that are active at the current point (Nocedal & Wright 2006, p. 308). The active set is particularly important in optimization theory, as it determines which constraints will influence the final result of optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search.


For example, consider the plaintext: crypto is short for cryptography. "crypto" is a repeated string, and the distance between the occurrences is 20 characters. If we line up the plaintext with a 6-character keyword "abcdef" (6 does not divide into 20): abcdefabcdefabcdefabcdefabcdefabc crypto is short for cryptography.


In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of supporting hyperplanes of A from the origin. The support function is a convex function on R n {\displaystyle \mathbb {R} ^{n}} . Any non-empty closed convex set A is uniquely determined by hA. Furthermore, the support function, as a function of the set A, is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition. Due to these properties, the support function is one of the most central basic concepts in convex geometry.


In protected mode a segment cannot be both writable and executable. Therefore, when implementing the Tiny memory model the code segment register must point to the same physical address and have the same limit as the data segment register. This defeated one of the features of the 80286, which makes sure data segments are never executable and code segments are never writable (which means that self-modifying code is never allowed). However, on the 80386, with its paged memory management unit it is possible to protect individual memory pages against writing.Memory models are not limited to 16-bit programs.


An ideal network structure has a vine and cluster structure, providing access to many different clusters and structural holes.Networks rich in structural holes are a form of social capital in that they offer information benefits. The main player in a network that bridges structural holes is able to access information from diverse sources and clusters. For example, in business networks, this is beneficial to an individual's career because he is more likely to hear of job openings and opportunities if his network spans a wide range of contacts in different industries/sectors. This concept is similar to Mark Granovetter's theory of weak ties, which rests on the basis that having a broad range of contacts is most effective for job attainment.


Less common are unilateral contracts, in which one party makes a promise, but the other side does not promise anything. In these cases, those accepting the offer are not required to communicate their acceptance to the offeror. In a reward contract, for example, a person who has lost a dog could promise a reward if the dog is found, through publication or orally.


More generally the transition rates are given in form of a finite measure c Λ ( η , d ξ ) {\displaystyle c_{\Lambda }(\eta ,d\xi )} on S Λ {\displaystyle S^{\Lambda }} . The generator L {\displaystyle L} of an IPS has the following form. First, the domain of L {\displaystyle L} is a subset of the space of "observables", that is, the set of real valued continuous functions on the configuration space Ω {\displaystyle \Omega } .


There are many key distribution schemes in the literature that are designed to maintain an easy and at the same time secure communication among sensor nodes. The most accepted method of key distribution in WSNs is key predistribution, where secret keys are placed in sensor nodes before deployment. When the nodes are deployed over the target area, the secret keys are used to create the network. For more info see: key distribution in wireless sensor networks.


In the following example expressed in C, a program has two variables which are adjacent in memory: an 8-byte-long string buffer, A, and a two-byte big-endian integer, B. Initially, A contains nothing but zero bytes, and B contains the number 1979. Now, the program attempts to store the null-terminated string "excessive" with ASCII encoding in the A buffer. "excessive" is 9 characters long and encodes to 10 bytes including the null terminator, but A can take only 8 bytes.


Woodall's conjecture, an unsolved problem in this area, states that in any directed graph the minimum number of edges in a dicut (the unweighted minimum closure) equals the maximum number of disjoint dijoins that can be found in the graph (a packing of dijoins). A fractional weighted version of the conjecture, posed by Jack Edmonds and Rick Giles, was refuted by Alexander Schrijver. In the other direction, the Lucchesi–Younger theorem states that the minimum size of a dijoin equals the maximum number of disjoint dicuts that can be found in a given graph. == References ==


In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy.


In the fall of 2004, the exam became computerized; the MAT is now solely a computer-based test (CBT).Out of the 120 questions, only 100 count in the test-taker's score. The remaining 20 questions are experimental. There is no way for test-takers to identify any of the 20 experimental questions on a given test form, as the two types of questions are intermingled. Tests taken before October 2004 were scored simply by the number of questions the test-taker answered correctly, with a range from 0-100.


In practice, most failures can be traced back to some type of human error, for example in: Management decisions (e.g. in budgeting, timing, and required tasks) Systems Engineering: Use studies (load cases) Systems Engineering: Requirement analysis / setting Systems Engineering: Configuration control Assumptions Calculations / simulations / FEM analysis Design Design drawings Testing (e.g. incorrect load settings or failure measurement) Statistical analysis Manufacturing Quality control Maintenance Maintenance manuals Training Classifying and ordering of information Feedback of field information (e.g. incorrect or too vague) etc.However, humans are also very good at detecting such failures, correcting for them, and improvising when abnormal situations occur. Therefore, policies that completely rule out human actions in design and production processes to improve reliability may not be effective. Some tasks are better performed by humans and some are better performed by machines.Furthermore, human errors in management; the organization of data and information; or the misuse or abuse of items, may also contribute to unreliability. This is the core reason why high levels of reliability for complex systems can only be achieved by following a robust systems engineering process with proper planning and execution of the validation and verification tasks. This also includes careful organization of data and information sharing and creating a "reliability culture", in the same way that having a "safety culture" is paramount in the development of safety critical systems.


This can be used to handle queries in the following fashion: when we look up cell T for some k, we can check if k is in the range {1, ..., m}: if it is not, then T is uninitialized. Otherwise, we check V], and verify that the first component of this pair is equal to k. If it is not, then T is uninitialized (and just happened by accident to fall in the range {1, ..., m}). Otherwise, we know that T is indeed one of the initialized cells, and the corresponding value is the second component of the pair.


In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form lim m → ∞ lim n → ∞ a n , m = lim m → ∞ ( lim n → ∞ a n , m ) {\displaystyle \lim _{m\to \infty }\lim _{n\to \infty }a_{n,m}=\lim _{m\to \infty }\left(\lim _{n\to \infty }a_{n,m}\right)} , lim y → b lim x → a f ( x , y ) = lim y → b ( lim x → a f ( x , y ) ) {\displaystyle \lim _{y\to b}\lim _{x\to a}f(x,y)=\lim _{y\to b}\left(\lim _{x\to a}f(x,y)\right)} ,or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value depends only on the other variable, and then one takes the limit as the other variable approaches some number.


The definition of the term named entity is therefore not strict and often has to be explained in the context in which it is used.Certain hierarchies of named entity types have been proposed in the literature. BBN categories, proposed in 2002, is used for question answering and consists of 29 types and 64 subtypes. Sekine's extended hierarchy, proposed in 2002, is made of 200 subtypes. More recently, in 2011 Ritter used a hierarchy based on common Freebase entity types in ground-breaking experiments on NER over social media text.