In the bin covering problem, the bin size is bounded from below: the goal is to maximize the number of bins used such that the total size in each bin is at least a given threshold. In the fair indivisible chore allocation problem (a variant of fair item allocation), the items represent chores, and there are different people each of whom attributes a different difficulty-value to each chore. The goal is to allocate to each person a set of chores with an upper bound on its total difficulty-value (thus, each person corresponds to a bin). Many techniques from bin packing are used in this problem too.In the guillotine cutting problem, both the items and the "bins" are two-dimensional rectangles rather than one-dimensional numbers, and the items have to be cut from the bin using end-to-end cuts. In the selfish bin packing problem, each item is a player who wants to minimize its cost.There is also a variant of bin packing in which the cost that should be minimized is not the number of bins, but rather a certain concave function of the number of items in each bin.Other variants are two-dimensional bin packing, three-dimensional bin packing, bin packing with delivery,


In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.


In the field of computational biology, a planted motif search (PMS) also known as a (l, d)-motif search (LDMS) is a method for identifying conserved motifs within a set of nucleic acid or peptide sequences. PMS is known to be NP-complete. The time complexities of most of the planted motif search algorithms depend exponentially on the alphabet size and l. The PMS problem was first introduced by Keich and Pevzner.The problem of identifying meaningful patterns (e.g., motifs) from biological data has been studied extensively since they play a vital role in understanding gene function, human disease, and may serve as therapeutic drug targets.


In that paper, a "similarity ratio" is given over bitmaps, where each bit of a fixed-size array represents the presence or absence of a characteristic in the plant being modelled. The definition of the ratio is the number of common bits, divided by the number of bits set (i.e. nonzero) in either sample. Presented in mathematical terms, if samples X and Y are bitmaps, X i {\displaystyle X_{i}} is the ith bit of X, and ∧ , ∨ {\displaystyle \land ,\lor } are bitwise and, or operators respectively, then the similarity ratio T s {\displaystyle T_{s}} is T s ( X , Y ) = ∑ i ( X i ∧ Y i ) ∑ i ( X i ∨ Y i ) {\displaystyle T_{s}(X,Y)={\frac {\sum _{i}(X_{i}\land Y_{i})}{\sum _{i}(X_{i}\lor Y_{i})}}} If each sample is modelled instead as a set of attributes, this value is equal to the Jaccard coefficient of the two sets.


In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F242 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements. The elements of W are called code words.


In terms of the diagram above (Oxelheim, 1990), the options are: Option (a): A stable exchange rate and free capital flows (but not an independent monetary policy because setting a domestic interest rate that is different from the world interest rate would undermine a stable exchange rate due to appreciation or depreciation pressure on the domestic currency). Option (b): An independent monetary policy and free capital flows (but not a stable exchange rate). Option (c): A stable exchange rate and independent monetary policy (but no free capital flows, which would require the use of capital controls).Currently, Eurozone members have chosen the first option (a) after the introduction of the euro.


Designers also experimented with using large sets of internal registers. The goal was to cache intermediate results in the registers under the control of the compiler. This also reduced the number of addressing modes and orthogonality.


In the presence of the axiom of choice, any cardinal number can be well-ordered, and then the following are equivalent for a cardinal κ {\displaystyle \kappa }: κ {\displaystyle \kappa } is a regular cardinal. If κ = ∑ i ∈ I λ i {\displaystyle \kappa =\sum _{i\in I}\lambda _{i}} and λ i < κ {\displaystyle \lambda _{i}<\kappa } for all i {\displaystyle i} , then | I | ≥ κ {\displaystyle |I|\geq \kappa } . If S = ⋃ i ∈ I S i {\displaystyle S=\bigcup _{i\in I}S_{i}} , and if | I | < κ {\displaystyle |I|<\kappa } and | S i | < κ {\displaystyle |S_{i}|<\kappa } for all i {\displaystyle i} , then | S | < κ {\displaystyle |S|<\kappa } .


Apple's Macintosh Central European encoding does not include the entire Gaj's Latin alphabet. Instead, a separate codepage, called MacCroatian encoding, is used. EBCDIC also has a Latin-2 encoding.The preferred character encoding for Croatian today is either the ISO 8859-2, or the Unicode encoding UTF-8 (with two bytes or 16 bits necessary to use the letters with diacritics). However, as of 2010, one can still find programs as well as databases that use CP1250, CP852 or even CROSCII. Digraphs ⟨dž⟩, ⟨lj⟩ and ⟨nj⟩ in their upper case, title case and lower case forms have dedicated Unicode code points as shown in the table below, However, these are included chiefly for backwards compatibility with legacy encodings which kept a one-to-one correspondence with Cyrillic; modern texts use a sequence of characters.


Many choices made at software design time cannot be directly expressed in today's implementation languages like C# and Java. These design choices (known by names like Design Pattern, Design Contract, Refactoring, Effective Programming Idioms, Blueprints, etc.) must be implemented via programming and naming conventions, because they go beyond the built-in functionality of production programming languages.


Personal information such as contact numbers of friends and family can also be stored on the SIM by the subscriber.After subscribers sign up, information about their identity (telephone number) and what services they are allowed to access are stored in a "SIM record" in the Home Location Register (HLR). Once the SIM card is loaded into the phone and the phone is powered on, it will search for the nearest mobile phone mast (also called a Base Transceiver Station/BTS) with the strongest signal in the operator's frequency band. If a mast can be successfully contacted, then there is said to be coverage in the area.


In mathematics, more specifically in linear algebra, the spark of a m × n {\displaystyle m\times n} matrix A {\displaystyle A} is the smallest integer k {\displaystyle k} such that there exists a set of k {\displaystyle k} columns in A {\displaystyle A} which are linearly dependent. If all the columns are linearly independent, s p a r k ( A ) {\displaystyle \mathrm {spark} (A)} is usually defined to be 1 more than the number of rows. The concept of matrix spark finds applications in error-correction codes, compressive sensing, and matroid theory, and provides a simple criterion for maximal sparsity of solutions to a system of linear equations. The spark of a matrix is NP-hard to compute.


In the area of classical computer vision, scale-space theory has established itself as a theoretical framework for early vision, with Gaussian derivatives constituting a canonical model for the first layer of receptive fields. With the introduction of deep learning, there has also been work on also using Gaussian derivatives or Gaussian kernels as a general basis for receptive fields in deep networks. Using the transformation properties of the Gaussian derivatives and Gaussian kernels under scaling transformations, it is in this way possible to obtain scale covariance/equivariance and scale invariance of the deep network to handle image structures at different scales in a theoretically well-founded manner. There have also been approaches developed to obtain scale covariance/equivariance and scale invariance by learned filters combined with multiple scale channels. Specifically, using the notions of scale covariance/equivariance and scale invariance, it is possible to make deep networks operate robustly at scales not spanned by the training data, thus enabling scale generalization.


However, particularly when considering data analysis, it is common to use the term "categorical data" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables. A categorical variable that can take on exactly two values is termed a binary variable or a dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables; categorical variables are often assumed to be polytomous unless otherwise specified.


These segments had to be contiguous when resident in RAM, requiring additional computation and movement to remedy fragmentation.Ferranti's Atlas, and the Atlas Supervisor developed at the University of Manchester, (1962), was the first system to implement memory paging. Subsequent early machines, and their operating systems, supporting paging include the IBM M44/44X and its MOS operating system (1964),, the SDS 940 and the Berkeley Timesharing System (1966), a modified IBM System/360 Model 40 and the CP-40 operating system (1967), the IBM System/360 Model 67 and operating systems such as TSS/360 and CP/CMS (1967), the RCA 70/46 and the Time Sharing Operating System (1967), the GE 645 and Multics (1969), and the PDP-10 with added BBN-designed paging hardware and the TENEX operating system (1969). Those machines, and subsequent machines supporting memory paging, use either a set of page address registers or in-memory page tables to allow the processor to operate on arbitrary pages anywhere in RAM as a seemingly contiguous logical address space. These pages became the units exchanged between disk and RAM.


In the context of group theory, a sequence G 0 → f 1 G 1 → f 2 G 2 → f 3 ⋯ → f n G n {\displaystyle G_{0}\;{\xrightarrow {\ f_{1}\ }}\;G_{1}\;{\xrightarrow {\ f_{2}\ }}\;G_{2}\;{\xrightarrow {\ f_{3}\ }}\;\cdots \;{\xrightarrow {\ f_{n}\ }}\;G_{n}} of groups and group homomorphisms is said to be exact at G i {\displaystyle G_{i}} if im  ( f i ) = ker  ( f i + 1 ) {\displaystyle \operatorname {im} (f_{i})=\ker(f_{i+1})} . The sequence is called exact if it is exact at each G i {\displaystyle G_{i}} for all 1 ≤ i < n {\displaystyle 1\leq i


Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary ω-rule.Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers.


However, the benefit is that minimal functionality is still possible on hosts that otherwise would be unable to support HID. The only devices supported in boot protocol are Keyboard – Any of the first 256 key codes ("Usages") defined in the HID Usage Tables, Usage Page 7 can be reported by a keyboard using the boot protocol, but most systems only handle a subset of these keys. Most systems support all 104 keys on the IBM AT-101 layout, plus the three extra keys designed for Microsoft Windows 95 (the left and right Windows key, and the Menu key).


Note that this terminology is not standardized and some authors will use rate where this article uses order (e.g., ). In practice, the rate and order of convergence provide useful insights when using iterative methods for calculating numerical approximations.


There are constants C 1 , C 2 > 0 {\displaystyle C_{1},C_{2}>0} so that the following two conditions are satisfied: For all n, ‖ p n ‖ ≥ C 1 ‖ ∇ f ( x n ) ‖ {\displaystyle \|\mathbf {p} _{n}\|\geq C_{1}\,\|\nabla f(\mathbf {x} _{n})\|} . Here, ‖ y ‖ {\displaystyle \|y\|} is the Euclidean norm of y {\displaystyle y} . (This assures that if p n = 0 {\displaystyle \mathbf {p} _{n}=0} , then also ∇ f ( x n ) = 0 {\displaystyle \nabla f(\mathbf {x} _{n})=0} .


Nevertheless, most of the interesting results on cardinality and its arithmetic can be expressed merely with =c. The goal of a cardinal assignment is to assign to every set A a specific, unique set that is only dependent on the cardinality of A. This is in accordance with Cantor's original vision of cardinals: to take a set and abstract its elements into canonical "units" and collect these units into another set, such that the only thing special about this set is its size.


Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples. Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics; and in philosophy.


In order to mitigate risk on vulnerable clients, some WPA2-enabled Wi-Fi access points have configuration options that can disable EAPOL-Key frame re-transmission during key installation. Attackers cannot cause re-transmissions with a delayed frame transmission, thereby denying them access to the network, provided TDLS is not enabled. One disadvantage of this method is that, with poor connectivity, key reinstallation failure may cause failure of the Wi-Fi link.


In programming for telephony, concatenation is used to provide dynamic audio feedback to a user. For example, in a "time of day" speaking clock, concatenation is used to give the correct time by playing the appropriate recordings concatenated together. For example: "At the tone the time will be" "Eight" "Thirty" "Five" "and" "Twenty" "Five" "Seconds"The recordings themselves exist separately, but playing them one after the other provides a grammatically correct sentence to the listener.


The composition of two ring homomorphisms is a ring homomorphism. It follows that the class of all rings forms a category with ring homomorphisms as the morphisms (cf. the category of rings). In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.


The first fifty nonhypotenuse numbers are: 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 31, 32, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84 (sequence A004144 in the OEIS)Although nonhypotenuse numbers are common among small integers, they become more-and-more sparse for larger numbers. Yet, there are infinitely many nonhypotenuse numbers, and the number of nonhypotenuse numbers not exceeding a value x scales asymptotically with x/√log x.The nonhypotenuse numbers are those numbers that have no prime factors of the form 4k+1. Equivalently, they are the number that cannot be expressed in the form K ( m 2 + n 2 ) {\displaystyle K(m^{2}+n^{2})} where K, m, and n are all positive integers. A number whose prime factors are not all of the form 4k+1 cannot be the hypotenuse of a primitive integer right triangle (one for which the sides do not have a nontrivial common divisor), but may still be the hypotenuse of a non-primitive triangle.The nonhypotenuse numbers have been applied to prove the existence of addition chains that compute the first n {\displaystyle n} square numbers using only n + o ( n ) {\displaystyle n+o(n)} additions.


In mathematics, an interprime is the average of two consecutive odd primes. For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are: 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, ... (sequence A024675 in the OEIS)Interprimes cannot be prime themselves (otherwise the primes would not have been consecutive).There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2018 may be the 388342-digit n = 2996863034895 · 21290000, where n + 1 is the largest known twin prime.


In regions such as North America and Europe, Musa fruits offered for sale can be divided into "bananas" and "plantains" (cooking banana), based on their intended use as food. Thus the banana producer and distributor Chiquita produces publicity material for the American market which says that "a plantain is not a banana". The stated differences are that plantains are more starchy and less sweet; they are eaten cooked rather than raw; they have thicker skin, which may be green, yellow or black; and they can be used at any stage of ripeness.


In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology).


Let A be a set of probability distributions over an alphabet X, and let q be an arbitrary distribution over X (where q may or may not be in A). Suppose we draw n i.i.d. samples from q, represented by the vector x n = x 1 , x 2 , … , x n {\displaystyle x^{n}=x_{1},x_{2},\ldots ,x_{n}} .


Events can be both mutually exclusive and collectively exhaustive. In the case of flipping a coin, flipping a head and flipping a tail are also mutually exclusive events. Both outcomes cannot occur for a single trial (i.e., when a coin is flipped only once). The probability of flipping a head and the probability of flipping a tail can be added to yield a probability of 1: 1/2 + 1/2 =1.


In stochastic (or "on-line") gradient descent, the true gradient of Q ( w ) {\displaystyle Q(w)} is approximated by a gradient at a single sample: w := w − η ∇ Q i ( w ) . {\displaystyle w:=w-\eta \nabla Q_{i}(w).} As the algorithm sweeps through the training set, it performs the above update for each training sample. Several passes can be made over the training set until the algorithm converges.


Such address translations are carried out by the segmentation unit of the CPU. The last segment, FFFFh (65535), begins at linear address FFFF0h (1048560), 16 bytes before the end of the 20 bit address space, and thus, can access, with an offset of up to 65,536 bytes, up to 65,520 (65536−16) bytes past the end of the 20 bit 8088 address space. On the 8088, these address accesses were wrapped around to the beginning of the address space such that 65535:16 would access address 0 and 65533:1000 would access address 952 of the linear address space.


In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (by the use of sharing).The benefits of lazy evaluation include: The ability to define control flow (structures) as abstractions instead of primitives. The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms. The ability to define partially-defined data structures where some elements are errors.


Whenever the data changes from one address to another address, from an address to a command, or from one command to another command, the data frames must be separated by at least 6 clear zero crossings (or "000000"). The sequence of six zeros resets the device decoder hardware.


In the algebraic theory of semigroups, in constructing special classes, attention is focused only on those properties, restrictions and conditions which can be expressed in terms of the binary operations in the semigroups and occasionally on the cardinality and similar properties of subsets of the underlying set. The underlying sets are not assumed to carry any other mathematical structures like order or topology. As in any algebraic theory, one of the main problems of the theory of semigroups is the classification of all semigroups and a complete description of their structure.


When the method is applied to a sufficient number of people over the course of a project, the objections raised above become addressed: The sample size ceases to be small and usability problems that arise with only occasional users are found. The value of the method lies in the fact that specific design problems, once encountered, are never seen again because they are immediately eliminated, while the parts that appear successful are tested over and over. While it's true that the initial problems in the design may be tested by only five users, when the method is properly applied, the parts of the design that worked in that initial test will go on to be tested by 50 to 100 people.


In the early 1990s, US social economist James D. Montgomery contributed to economic theories of network structures in the labour market. In 1991, Montgomery incorporated network structures in an adverse selection model to analyze the effects of social networks on labour market outcomes. In 1992, Montgomery explored the role of "weak ties", which he defined as non-frequent and transitory social relations in the labour market. He demonstrated that weak ties are positively correlated with higher wages and higher aggregate employment rates.


Special values, where all contributing Catalan numbers equal 1, are  s n ( x ) = ( − 1 ) n 2 n . {\displaystyle s_{n}(x)={\frac {(-1)^{n}}{2^{n}}}.} s n ( x ) = ( − 1 ) n n ( n − 1 ) ( n − 2 ) 2 n .


However, legal rules sometimes exempt people from the obligation to give evidence and legal rules disqualify people from serving as witnesses under some circumstances. Privilege rules give the holder of the privilege a right to prevent a witness from giving testimony. These privileges are ordinarily (but not always) designed to protect socially valued types of confidential communications.


In the case of backpropagation based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it can learn any continuous function on compact subsets of Rn as shown by the universal approximation theorem, thus it can have an arbitrary decision boundary.


It guarantees that the allocation is envy-free up to at most one item (EF1). Moreover, if the instance is ordered (- all agents rank the items in the same order), then the outcome is EFX, and guarantees to each agent at least 2 n 3 n − 1 {\displaystyle {\frac {2n}{3n-1}}} of his maximin share. If the items are chores, then a similar algorithm guarantees 4 n − 1 3 n {\displaystyle {\frac {4n-1}{3n}}} MMS.


In record-oriented file systems files are stored as a collection of records. They are typically associated with mainframe and minicomputer operating systems. Programs read and write whole records, rather than bytes or arbitrary byte ranges, and can seek to a record boundary but not within records.


In software development, a bug bash is a procedure where all the developers, testers, program managers, usability researchers, designers, documentation folks, and even sometimes marketing people, put aside their regular day-to-day duties and "pound on the product"—that is, each exercises the product in every way they can think of. Because each person will use the product in slightly different (or very different) ways, and the product is getting a great deal of use in a short amount of time, this approach may reveal bugs relatively quickly.The use of bug-bashing sessions is one possible tool in the testing methodology TMap (test management approach). Bug-bashing sessions are usually announced to the organization some days or weeks ahead of time. The test management team may specify that only some parts of the product need testing.


"Tables exist. "Both of these propositions are a posteriori: any justification of them would require one's experience.


For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously. P(A|B) may or may not be equal to P(A), i.e., the unconditional probability or absolute probability of A. If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other.


Cantor mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace topology). By a theorem of L. E. J. Brouwer, this is equivalent to being perfect nonempty, compact metrizable and zero dimensional.


It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("∀x", "∀(x)", or sometimes by "(x)" alone). Universal quantification is distinct from existential quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is encoded as U+2200 ∀ FOR ALL in Unicode, and as \forall in LaTeX and related formula editors.


Hill climbing finds optimal solutions for convex problems – for other problems it will find only local optima (solutions that cannot be improved upon by any neighboring configurations), which are not necessarily the best possible solution (the global optimum) out of all possible solutions (the search space). Examples of algorithms that solve convex problems by hill-climbing include the simplex algorithm for linear programming and binary search. : 253 To attempt to avoid getting stuck in local optima, one could use restarts (i.e. repeated local search), or more complex schemes based on iterations (like iterated local search), or on memory (like reactive search optimization and tabu search), or on memory-less stochastic modifications (like simulated annealing).


In metadata, property equivalence is the statement that two properties have the same property extension or values. This usually (but not always) implies that the two properties have the same semantics or meaning. Technically it only implies that the data elements have the same values. Property equivalence is one of the three ways that a metadata registry can store equivalence mappings to other metadata registries.


In systemic functional grammar (SFG), a nominal group is a group of words that represents or describes an entity, for example The nice old English police inspector who was sitting at the table with Mr Morse. Grammatically, the wording "The nice old English police inspector who was sitting at the table with Mr Morse" can be understood as a nominal group (a description of someone), which functions as the subject of the information exchange and as the person being identified as "Mr Morse". A nominal group is widely regarded as synonymous with noun phrase in other grammatical models. However, there are two major differences between the functional notion of a nominal group and the formal notion of a noun phrase that must be taken into account.


In mathematics, and particularly general topology, the half-disk topology is an example of a topology given to the set X {\displaystyle X} , given by all points ( x , y ) {\displaystyle (x,y)} in the plane such that y ≥ 0 {\displaystyle y\geq 0} . The set X {\displaystyle X} can be termed the closed upper half plane. To give the set X {\displaystyle X} a topology means to say which subsets of X {\displaystyle X} are "open", and to do so in a way that the following axioms are met: The union of open sets is an open set. The finite intersection of open sets is an open set. The set X {\displaystyle X} and the empty set ∅ {\displaystyle \emptyset } are open sets.


In practice, humans routinely make conceptual, linguistic, and probabilistic generalizations from small amounts of data. There is some debate about the utility of various tools of statistical inference in understanding the mind, but it is commonly accepted that the human mind is somehow an exceptionally apt prediction machine, and that action-oriented processes underlying this phenomenon, whatever they might entail, are at the core of cognition. Probabilistic inferences and generalization play central roles in concepts and categories and language learning, and infant studies are commonly used to understand the developmental trajectory of humans' intuitive statistical toolkit(s).


In the early 1980s the term FCAPS was introduced within the first Working Drafts (N1719) of ISO 10040, the Open Systems Interconnection (OSI) Systems Management Overview (SMO) standard. At that time the intention was to define five separate protocol standards, one for each functional area. Since initial experiences showed that these protocols would become very similar, the ISO working group responsible for the development of these protocols (ISO/TC97/SC16/WG4, later renamed into ISO-IEC/JTC1/SC21/WG4) decided to create a single protocol for all five areas instead. This protocol is called common management information protocol (CMIP). In the 1990s the ITU-T, as part of their work on Telecommunications Management Network (TMN), further refined the FCAPS as part of the TMN recommendation on Management Functions (M.3400). The idea of FCAPS turned out to be very useful for teaching network management functions; most textbooks therefore start with a section that explains the FCAPS.


The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same type of operator. Consider the expression a ~ b ~ c. If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c. If the operator has right associativity, the expression would be interpreted as a ~ (b ~ c). If the operator is non-associative, the expression might be a syntax error, or it might have some special meaning.


If so, it then attempts to expand the macro, treating the items in the tail of the s-expression as arguments without compiling code to evaluate them, and this process is repeated recursively until no macro invocations remain. If it is not a syntactic keyword, the compiler compiles code to evaluate the arguments in the tail of the s-expression and then to evaluate the variable represented by the symbol at the head of the s-expression and call it as a procedure with the evaluated tail expressions passed as arguments to it. Most Scheme implementations also provide additional macro systems.


For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. A bijective function from a set to itself is also called a permutation, and the set of all permutations of a set forms the symmetric group. Bijective functions are essential to many areas of mathematics including the definitions of isomorphisms, homeomorphisms, diffeomorphisms, permutation groups, and projective maps.


In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or nodes. Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\displaystyle A_{i,j}} is filled with 1 if node j {\displaystyle j} has a link to node i {\displaystyle i} , and 0 otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of column "j" by a number of k j = Σ i = 1 N A i , j {\displaystyle k_{j}=\Sigma _{i=1}^{N}A_{i,j}} where k j {\displaystyle k_{j}} is the total number of outgoing links from node j to all other nodes. The columns having zero matrix elements, corresponding to dangling nodes, are replaced by a constant value 1/N.


Events are also represented as terms. The effects of events are given using the predicates Initiates and Terminates. In particular, I n i t i a t e s ( e , f , t ) {\displaystyle {\mathit {Initiates}}(e,f,t)} means that, if the event represented by the term e is executed at time t, then the fluent f will be true after t. The Terminates predicate has a similar meaning, with the only difference being that f will be false after t.


Our hypothesis might specify the probability distribution of X {\displaystyle X} precisely, or it might only specify that it belongs to some class of distributions. Often, we reduce the data to a single numerical statistic, e.g., T {\displaystyle T} , whose marginal probability distribution is closely connected to a main question of interest in the study. The p-value is used in the context of null hypothesis testing in order to quantify the statistical significance of a result, the result being the observed value of the chosen statistic T {\displaystyle T} .


In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist which contain only elements a and b, but vary in the multiplicities of their elements: The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset. In the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.


In the above moment-cumulant formula E  ( X 1 ⋯ X n ) = ∑ π ∏ B ∈ π κ ( X i: i ∈ B ) {\displaystyle \operatorname {E} (X_{1}\cdots X_{n})=\sum _{\pi }\prod _{B\,\in \,\pi }\kappa (X_{i}:i\in B)} for joint cumulants, one sums over all partitions of the set { 1, ..., n }. If instead, one sums only over the noncrossing partitions, then, by solving these formulae for the κ {\displaystyle \kappa } in terms of the moments, one gets free cumulants rather than conventional cumulants treated above. These free cumulants were introduced by Roland Speicher and play a central role in free probability theory. In that theory, rather than considering independence of random variables, defined in terms of tensor products of algebras of random variables, one considers instead free independence of random variables, defined in terms of free products of algebras.The ordinary cumulants of degree higher than 2 of the normal distribution are zero. The free cumulants of degree higher than 2 of the Wigner semicircle distribution are zero. This is one respect in which the role of the Wigner distribution in free probability theory is analogous to that of the normal distribution in conventional probability theory.


1997 nr 89 poz. 555.) provides means of protecting against self-incrimination, including lack of penalization for refusing to answer any question which would enable law enforcement agencies to obtain access to potential evidence, which could be used against testifying person.


Often the principal components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the explanatory variables) are selected as regressors. However, for the purpose of predicting the outcome, the principal components with low variances may also be important, in some cases even more important.One major use of PCR lies in overcoming the multicollinearity problem which arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the low-variance principal components in the regression step.


It can be accomplished by planting a significant news story indirectly in the media, or presenting it favorably through press releases or corporate anniversary parties. Examples include newspaper and magazine articles, TVs and radio presentations, charitable contributions, speeches, issue advertising, seminars. Word of mouth is also a type of publicity, which transform from the person-to-person storytelling to social media influencers, or bloggers promotions today.


In order to handle such conflicts correctly, the pipeline must be provided with extra circuitry or logic that detects them and takes the appropriate action. Strategies for doing so include: Stalling: Every affected stage, such as A, is halted until the dependency is resolved—that is, until the required information is available and/or the required state has been achieved. Reordering items: Instead of stalling, stage A may put item Y aside and look for any subsequent item Z in its input stream that does not have any dependencies pending with any earlier item.


In the definitions provided below, let ω {\displaystyle \omega } denote the set of natural numbers ( N {\displaystyle \mathbb {N} } ) and A , B . . . {\displaystyle A,B...} denote subsets of ω {\displaystyle \omega } .


Consequently, lawmakers aim to devise definitions and categories which are sufficiently precise, so that they are not open to different interpretations. For this purpose, it is critically important to remove fuzziness, and differences of interpretation are typically resolved through a court ruling based on evidence. Alternatively, some other procedure is devised which permits the correct distinction to be discovered and made. In administration, archiving and accounting, fuzziness problems in interpretation and boundary problems can arise, because it is not clear to what category exactly a case, item, document, transaction or piece of data belongs. In principle, each case, event or item must be allocated to the correct category in a procedure, but it may be, that it is difficult to make the appropriate or relevant distinctions.


In the early days of Java (before the HotSpot VM was implemented in Java 1.3 in 2000) there were some criticisms of performance. Benchmarks typically reported Java as being about 50% slower than C (a language which compiles to native code).Java's performance has improved substantially since the early versions. Performance of JIT compilers relative to native compilers has in some optimized tests been shown to be quite similar.Java bytecode can either be interpreted at run time by a virtual machine, or it can be compiled at load time or runtime into native code which runs directly on the computer's hardware. Interpretation is slower than native execution, and compilation at load time or runtime has an initial performance penalty for the compilation. Modern performant JVM implementations all use the compilation approach, so after the initial startup time the performance is equivalent to native code.


In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist.


That is, even elements always commute. Odd elements, on the other hand, always anticommute.


In the false fame experiment, participants are presented with a list of non-famous names. Later, they are presented with the same names as before, with new non-famous and famous people. The participants then have to determine which names are famous, and the typical finding is that the old non-famous names are often misidentified as famous.


In symmetric-key schemes, the encryption and decryption keys are the same. Communicating parties must have the same key in order to achieve secure communication. The German Enigma Machine utilized a new symmetric-key each day for encoding and decoding messages. In public-key encryption schemes, the encryption key is published for anyone to use and encrypt messages.


In the basic five-bit biquinary code of the UNIVAC-LARC, 15 combinations are allowed, any one of which may be stored may be stored in any digit position in storage.


In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation: X n + Y n = Z n . {\displaystyle X^{n}+Y^{n}=Z^{n}.\ } Therefore, in terms of the affine plane its equation is: x n + y n = 1. {\displaystyle x^{n}+y^{n}=1.\ } An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa. But by Fermat's Last Theorem it is now known that (for n > 2) there are no nontrivial integer solutions to the Fermat equation; therefore, the Fermat curve has no nontrivial rational points.


In software development, version control is a class of systems responsible for managing changes to computer programs or other collections of information such that revisions have a logical and consistent organization. The following tables include general and technical information on notable version control and software configuration management (SCM) software. For SCM software not suitable for source code, see Comparison of open-source configuration management software.


In project management, a schedule is a listing of a project's milestones, activities, and deliverables. Usually dependencies and resources are defined for each task, then start and finish dates are estimated from the resource allocation, budget, task duration, and scheduled events. A schedule is commonly used in the project planning and project portfolio management parts of project management. Elements on a schedule may be closely related to the work breakdown structure (WBS) terminal elements, the Statement of work, or a Contract Data Requirements List.


Note that if X and X1, X2, ... are random variables corresponding to these distribution functions, then the Helly–Bray theorem does not imply that E(Xn) → E(X), since g(x) = x is not a bounded function. In fact, a stronger and more general theorem holds. Let P and P1, P2, ... be probability measures on some set S. Then Pn converges weakly to P if and only if ∫ S g d P n → n → ∞ ∫ S g d P , {\displaystyle \int _{S}g\,dP_{n}\quad {\xrightarrow{}}\quad \int _{S}g\,dP,} for all bounded, continuous and real-valued functions on S.


In order to guarantee safety (also called "consistency"), Paxos defines three properties and ensures the first two are always held, regardless of the pattern of failures: Validity (or non-triviality) Only proposed values can be chosen and learned. Agreement (or consistency, or safety) No two distinct learners can learn different values (or there can't be more than one decided value) Termination (or liveness) If value C has been proposed, then eventually learner L will learn some value (if sufficient processors remain non-faulty).Note that Paxos is not guaranteed to terminate, and thus does not have the liveness property. This is supported by the Fischer Lynch Paterson impossibility result (FLP) which states that a consistency protocol can only have two of safety, liveness, and fault tolerance. As Paxos's point is to ensure fault tolerance and it guarantees safety, it cannot also guarantee liveness.


In some languages, string literals may contain placeholders referring to variables or expressions in the current context, which are evaluated (usually at run time). This is referred to as variable interpolation, or more generally string interpolation. Languages that support interpolation generally distinguish strings literals that are interpolated from ones that are not. For example, in sh-compatible Unix shells (as well as Perl and Ruby), double-quoted (quotation-delimited, ") strings are interpolated, while single-quoted (apostrophe-delimited, ') strings are not.


Thus for S = a ⋅ 10 2 n {\displaystyle S=a\cdot 10^{2n}}: S ≈ ( − 190 a + 20 + 10 ) ⋅ 10 n {\displaystyle {\sqrt {S}}\approx \left({\frac {-190}{a+20}}+10\right)\cdot 10^{n}} The floating division need be accurate to only one decimal digit, because the estimate overall is only that accurate, and can be done mentally. A hyperbolic estimate is better on average than scalar or linear estimates.


Software developers can use these models as a basis for the implementation of software architectures and applications. This approach to domain analysis is sometimes called model-driven engineering. In information science, the term "domain analysis" was suggested in 1995 by Birger Hjørland and H. Albrechtsen.


The in situ in ISCR is just Latin for "in place", signifying that ISCR is a chemical reduction reaction that occurs at the site of the contamination. Like ISCO, it is able to decontaminate many compounds, and, in theory, ISCR could be more effective in ground water remediation than ISCO. Chemical reduction is one half of a redox reaction, which results in the gain of electrons. One of the reactants in the reaction becomes oxidized, or loses electrons, while the other reactant becomes reduced, or gains electrons. In ISCR, reducing compounds, compounds that accept electrons given by other compounds in a reaction, are used to change the contaminants into harmless compounds.


Important algorithms in computational group theory include: the Schreier–Sims algorithm for finding the order of a permutation group the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration the product-replacement algorithm for finding random elements of a groupTwo important computer algebra systems (CAS) used for group theory are GAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important. Some achievements of the field include: complete enumeration of all finite groups of order less than 2000 computation of representations for all the sporadic groups


In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to Datalog. Least fixed-point logic was first studied systematically by Yiannis N. Moschovakis in 1974, and it was introduced to computer scientists in 1979, when Alfred Aho and Jeffrey Ullman suggested fixed-point logic as an expressive database query language.


The genitive plural, however is hjartna showing a-breaking instead of u-breaking. Some borrowings may exhibit similar behaviour, e.g, singular drama, plural drömu. Most of these are words for organs.An almost exhaustive list of neuter weak nouns follows: auga (eye) bjúga (a type of sausage) eista (testicle) eyra (ear) hjarta (heart) hnoða (a woollen ball, most often encountered in fairy-tales) lunga (lung) milta (spleen) nýra (kidney)Then there are a small number of borrowings like firma, drama, þema etc. none of which require translation.


In mathematics, a Tamari lattice, introduced by Dov Tamari (1962), is a partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses; for instance, for a sequence of four objects abcd, the five possible groupings are ((ab)c)d, (ab)(cd), (a(bc))d, a((bc)d), and a(b(cd)). Each grouping describes a different order in which the objects may be combined by a binary operation; in the Tamari lattice, one grouping is ordered before another if the second grouping may be obtained from the first by only rightward applications of the associative law (xy)z = x(yz). For instance, applying this law with x = a, y = bc, and z = d gives the expansion (a(bc))d = a((bc)d), so in the ordering of the Tamari lattice (a(bc))d ≤ a((bc)d).


In mathematical optimization, the push–relabel algorithm (alternatively, preflow–push algorithm) is an algorithm for computing maximum flows in a flow network. The name "push–relabel" comes from the two basic operations used in the algorithm. Throughout its execution, the algorithm maintains a "preflow" and gradually converts it into a maximum flow by moving flow locally between neighboring nodes using push operations under the guidance of an admissible network maintained by relabel operations. In comparison, the Ford–Fulkerson algorithm performs global augmentations that send flow following paths from the source all the way to the sink.The push–relabel algorithm is considered one of the most efficient maximum flow algorithms.


In practice, many functions of interest are computable by machines that always halt. A machine that uses only finite memory on any particular input can be forced to halt for every input by restricting its flow control capabilities so that no input will ever cause the machine to enter an infinite loop. As a trivial example, a machine implementing a finitary decision tree will always halt. It is not required that the machine be entirely free of looping capabilities, however, to guarantee halting.


A positive voltage is applied to the anode. This voltage, combined with the high magnetic field between the tips of the internal and external cathodes allow a plasma to start. Ions from the plasma are repelled by the anode electric field. This creates an ion beam.


From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called nonvarieties, are sometimes included among the algebraic structures by tradition. Concrete examples of each structure will be found in the articles listed.


In the case of one continuous (or at least with bounded variation) compactly supported scaling function with orthogonal shifts, one may make a number of deductions. The proof of existence of this class of functions is due to Ingrid Daubechies. Assuming the scaling function has compact support, then V 0 ⊂ V − 1 {\displaystyle V_{0}\subset V_{-1}} implies that there is a finite sequence of coefficients a k = 2 ⟨ ϕ ( x ) , ϕ ( 2 x − k ) ⟩ {\displaystyle a_{k}=2\langle \phi (x),\phi (2x-k)\rangle } for | k | ≤ N {\displaystyle |k|\leq N} , and a k = 0 {\displaystyle a_{k}=0} for | k | > N {\displaystyle |k|>N} , such that ϕ ( x ) = ∑ k = − N N a k ϕ ( 2 x − k ) . {\displaystyle \phi (x)=\sum _{k=-N}^{N}a_{k}\phi (2x-k).}


In 1999, MIPS Technologies replaced the previous versions of the MIPS architecture with two architectures, the 32-bit MIPS32 (based on MIPS II with some added features from MIPS III, MIPS IV, and MIPS V) and the 64-bit MIPS64 (based on MIPS V) for licensing. Nippon Electric Corporation (NEC), Toshiba, and SiByte (later acquired by Broadcom) each obtained licenses for the MIPS64 as soon as it was announced.


In the HPCC implementation, by default, most ECL constructs will execute in parallel across the hardware being used. Many of the primitives also have a LOCAL option to specify that the operation is to occur locally on each node.


The system used a third-party service to identify content being distributed illegally. Users were then informed that their accounts were being used for possible copyright infringement and were provided with information about ways to get authorized content online. Users who received multiple notices of infringement faced "mitigations measures," such as temporary slowing of their Internet service, but the system did not include termination of subscriber accounts.


A similar result also holds in some closed networks. Examples of product-form networks where the arrival theorem does not hold include reversible Kingman networks and networks with a delay protocol.Mitrani offers the intuition that "The state of node i as seen by an incoming job has a different distribution from the state seen by a random observer. For instance, an incoming job can never see all 'k jobs present at node i, because it itself cannot be among the jobs already present."


The benchmark visible when pH7CMS is on the development mode. Better search experiences with the new SISE (Smart Intuitive Search Engine) and better translation are now done.


The iterations converge to the fixed point of the IFS. Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter. The "chaos game" method plots points in random order all over the attractor.


In statistics a quasi-maximum likelihood estimate (QMLE), also known as a pseudo-likelihood estimate or a composite likelihood estimate, is an estimate of a parameter θ in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihood function, but in discussing the consistency and (asymptotic) variance-covariance matrix, we assume some parts of the distribution may be mis-specified. In contrast, the maximum likelihood estimate maximizes the actual log likelihood function for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihood function. A common way to form such a simplified function is to use the log-likelihood function of a misspecified model that treats certain data values as being independent, even when in actuality they may not be.


In online analytical processing (OLAP), data cubes are a common arrangement of business data suitable for analysis from different perspectives through operations like slicing, dicing, pivoting, and aggregation.


We want to give unit A a 20% probability of selection, unit B a 40% probability, and so on up to unit E (100%). Assuming we maintain alphabetical order, we allocate each unit to the following interval: A: 0 to 0.2 B: 0.2 to 0.6 (= 0.2 + 0.4) C: 0.6 to 1.2 (= 0.6 + 0.6) D: 1.2 to 2.0 (= 1.2 + 0.8) E: 2.0 to 3.0 (= 2.0 + 1.0) If our random start was 0.156, we would first select the unit whose interval contains this number (i.e. A). Next, we would select the interval containing 1.156 (element C), then 2.156 (element E). If instead our random start was 0.350, we would select from points 0.350 (B), 1.350 (D), and 2.350 (E).


In recent years, Searle's main interlocutor on issues of social ontology has been Tony Lawson. Although their accounts of social reality are similar, there are important differences. Lawson emphasizes the notion of social totality whereas Searle prefers to refer to institutional facts. Furthermore, Searle believes that emergence implies causal reduction whereas Lawson argues that social totalities cannot be completely explained by the causal powers of their components. Searle also places language at the foundation of the construction of social reality, while Lawson believes that community formation necessarily precedes the development of language and, therefore, there must be the possibility for non-linguistic social structure formation. The debate is ongoing and takes place additionally through regular meetings of the Centre for Social Ontology at the University of California, Berkeley and the Cambridge Social Ontology Group at the University of Cambridge.


A Boolean function with multiple outputs, f: { 0 , 1 } k → { 0 , 1 } m {\displaystyle f:\{0,1\}^{k}\to \{0,1\}^{m}} with m > 1 {\displaystyle m>1} is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography).There are 2 2 k {\displaystyle 2^{2^{k}}} different Boolean functions with k {\displaystyle k} arguments; equal to the number of different truth tables with 2 k {\displaystyle 2^{k}} entries. Every k {\displaystyle k} -ary Boolean function can be expressed as a propositional formula in k {\displaystyle k} variables x 1 , .


In software engineering, a management review is defined by the IEEE as: A systematic evaluation of a software acquisition, supply, development, operation, or maintenance process performed by or on behalf of management ...  to monitor progress, determine the status of plans and schedules, confirm requirements and their system allocation, or evaluate the effectiveness of management approaches used to achieve fitness for purpose. Management reviews support decisions about corrective actions, changes in the allocation of resources, or changes to the scope of the project. Management reviews are carried out by, or on behalf of, the management personnel having direct responsibility for the system. Management reviews identify consistency with and deviations from plans, or adequacies and inadequacies of management procedures.


When a process calls fork, it is deemed the parent process and the newly created process is its child. After the fork, both processes not only run the same program, but they resume execution as though both had called the system call. They can then inspect the call's return value to determine their status, child or parent, and act accordingly.


In order to implement 802.11i, one must first make sure both that the router/access point(s), as well as all client devices are indeed equipped to support the network encryption. If this is done, a server such as RADIUS, ADS, NDS, or LDAP needs to be integrated. This server can be a computer on the local network, an access point / router with integrated authentication server, or a remote server. AP's/routers with integrated authentication servers are often very expensive and specifically an option for commercial usage like hot spots.


In patient care, authorised users have the ability to override masking and access restrictions under emergency circumstances. If a patient is in a critical health state and treatment is urgently required, physicians are provided with the right to access all required information within the EHR. This mechanism is known as "breaking the glass." Any unmasking of a patient's EHR is audited, and a sufficient reason for access is generally required.


In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit over a simple power-law relationship (see references below). In the Laherrère/Deheuvels paper below, examples include galaxy sizes (ordered by luminosity), towns (in the USA, France, and world), spoken languages (by number of speakers) in the world, and oil fields in the world (by size). They also mention utility for this distribution in fitting seismic events (no example).


Social media influencers can be defined as "regular" individuals who have accrued a large number of followers across multiple social media platforms as a result of the content they post. For the most part, social media influencers focus their content on one subject area, like food or fashion. Social media influencers have become their own kind of "internet celebrities" and their followers value and trust their opinions.


There are several different ways to express reciprocity laws. The early reciprocity laws found in the 19th century were usually expressed in terms of a power residue symbol (p/q) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another prime, and gave a relation between (p/q) and (q/p). Hilbert reformulated the reciprocity laws as saying that a product over p of Hilbert symbols (a,b/p), taking values in roots of unity, is equal to 1. Artin's reformulated reciprocity law states that the Artin symbol from ideals (or ideles) to elements of a Galois group is trivial on a certain subgroup. Several more recent generalizations express reciprocity laws using cohomology of groups or representations of adelic groups or algebraic K-groups, and their relationship with the original quadratic reciprocity law can be hard to see.


In the context of algorithms that run over the very long term (servers, cloud...), the computer architecture evolves over time. However, it is preferable not to have to design a new algorithm each time. An extremely important parameter of a load balancing algorithm is therefore its ability to adapt to scalable hardware architecture. This is called the scalability of the algorithm.


Each guard for which the condition is true and the input channel is ready is successful. One of the successful alternatives is selected for execution. Example: ALT count1 < 100 & c1 ?


Recall the definition of SVD: S V D ( T ) = U Λ V T {\displaystyle \mathrm {SVD} ({\mathcal {T}})=U\Lambda V^{T}} It is the decomposition of the transformation, T {\displaystyle {\mathcal {T}}} , into a rotation in the source domain (i.e. the ellipsoid surface), V T {\displaystyle V^{T}} , a scaling along the basis, Λ {\displaystyle \Lambda } , and a subsequent second rotation, U {\displaystyle U} . For understanding distortion, the first rotation is irrelevant, as it rotates the axes of the circle but has no bearing on the final orientation of the ellipse. The next operation, represented by the diagonal singular value matrix, scales the circle along its axes, deforming it to an ellipse.


Through various implementations, the MPIC was included in PowerPC reference designs and some retail computers. IBM used a MPIC based on OpenPIC 1.0 in their RS/6000 F50 and one based on OpenPIC 1.2 in their RS/6000 S70. Both of these systems also used a dual 8259 on their PCI-ISA bridges.


In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition of functions. It transforms a function (which can be given via closed formulas or neural networks, fuzzy logic, etc.) into TP function form if such a transformation is possible. If an exact transformation is not possible, then the method determines a TP function that is an approximation of the given function. Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity.A free MATLAB implementation of the TP model transformation can be downloaded at  or an old version of the toolbox is available at MATLAB Central .


In the case where each N i {\displaystyle \textstyle {N}_{i}} is a Poisson point process, then the resulting process N {\displaystyle \textstyle {N}} is also a Poisson point process with mean intensity Λ = ∑ i = 1 ∞ Λ i . {\displaystyle \Lambda =\sum \limits _{i=1}^{\infty }\Lambda _{i}.}


In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the covariance may be considered optimal in some sense, this does not mean that the resulting discriminant obtained by substituting these values is optimal in any sense, even if the assumption of normally distributed classes is correct.


In the compilation of high-level programming languages, pathwidth arises in the problem of reordering sequences of straight-line code (that is, code with no control flow branches or loops) in such a way that all the values computed in the code can be placed in machine registers instead of having to be spilled into main memory. In this application, one represents the code to be compiled as a directed acyclic graph in which the nodes represent the input values to the code and the values computed by the operations within the code. An edge from node x to node y in this DAG represents the fact that value x is one of the inputs to operation y. A topological ordering of the vertices of this DAG represents a valid reordering of the code, and the number of registers needed to evaluate the code in a given ordering is given by the vertex separation number of the ordering.For any fixed number w of machine registers, it is possible to determine in linear time whether a piece of straight-line code can be reordered in such a way that it can be evaluated with at most w registers. For, if the vertex separation number of a topological ordering is at most w, the minimum vertex separation among all orderings can be no larger, so the undirected graph formed by ignoring the orientations of the DAG described above must have pathwidth at most w. It is possible to test whether this is the case, using the known fixed-parameter-tractable algorithms for pathwidth, and if so to find a path-decomposition for the undirected graph, in linear time given the assumption that w is a constant. Once a path decomposition has been found, a topological ordering of width w (if one exists) can be found using dynamic programming, again in linear time.


In much the same way as the IA is difficult to define, it can be utilised in a range of contexts by the information professional, from complying with freedom of information legislation to identifying any existing gaps, duplications, bottlenecks or other inefficiencies in information flows and to understand how existing channels can be used for knowledge transfer In 2007 Buchanan and Gibb developed upon their 1998 examination of the IA process by outlining a summary of its main objectives: To identify an organisation’s information resource To identify an organisation’s information needsFurthermore, Buchanan and Gibb went on to state that the IA also had to meet the following additional objectives: To identify the cost/benefits of information resources To identify the opportunities to use the information resources for strategic competitive advantage To integrate IT investment with strategic business initiatives To identify information flow and processes To develop an integrated information strategy and/or policy To create an awareness of the importance of Information Resource Management (IRM) To monitor/evaluate conformance to information related standards, legislations, policy and guidelines.


In statistical test theory, the notion of a statistical error is an integral part of hypothesis testing. The test goes about choosing about two competing propositions called null hypothesis, denoted by H0 and alternative hypothesis, denoted by H1. This is conceptually similar to the judgement in a court trial. The null hypothesis corresponds to the position of the defendant: just as he is presumed to be innocent until proven guilty, so is the null hypothesis presumed to be true until the data provide convincing evidence against it.


In mathematics, especially in the area of algebra known as group theory, the term Z-group refers to a number of distinct types of groups: in the study of finite groups, a Z-group is a finite group whose Sylow subgroups are all cyclic. in the study of infinite groups, a Z-group is a group which possesses a very general form of central series. in the study of ordered groups, a Z-group or Z {\displaystyle \mathbb {Z} } -group is a discretely ordered abelian group whose quotient over its minimal convex subgroup is divisible.


In planar directed graphs, the feedback arc set problem obeys a min-max theorem: the minimum size of a feedback arc set equals the maximum number of edge-disjoint directed cycles that can be found in the graph. This is not true for some other graphs; for instance the first illustration shows a directed version of the non-planar graph K 3 , 3 {\displaystyle K_{3,3}} in which the minimum size of a feedback arc set is two, while the maximum number of edge-disjoint directed cycles is only one. Every tournament graph has a Hamiltonian path, and the Hamiltonian paths correspond one-for-one with minimal feedback arc sets, disjoint from the corresponding path. The Hamiltonian path for a feedback arc set is found by reversing its arcs and finding a topological order of the resulting acyclic tournament.


{\displaystyle =efg.} The relation above shows that /ef equals the number g of prime factors of p in OL. By the orbit-stabilizer formula this number is also equal to |G|/|DPj| for every j, where DPj, the decomposition group of Pj, is the subgroup of elements of G sending a given Pj to itself.


In principle, exact recovery can be solved in its feasible range using maximum likelihood, but this amounts to solving a constrained or regularized cut problem such as minimum bisection that is typically NP-complete. Hence, no known efficient algorithms will correctly compute the maximum-likelihood estimate in the worst case. However, a wide variety of algorithms perform well in the average case, and many high-probability performance guarantees have been proven for algorithms in both the partial and exact recovery settings. Successful algorithms include spectral clustering of the vertices, semidefinite programming, forms of belief propagation, and community detection among others.


The USPA protocol for training students is called the "Integrated Student Program" (ISP). The ISP is separated into categories, each with targeted learning objectives that must be met before the student progresses to the next level. Static Line, AFF, and Tandem Progression all follow the same categories, but use different methods to train within each category.


In the above example, each vertex of H has exactly 2 preimages in C. Hence C is a 2-fold cover or a double cover of H. For any graph G, it is possible to construct the bipartite double cover of G, which is a bipartite graph and a double cover of G. The bipartite double cover of G is the tensor product of graphs G × K2: If G is already bipartite, its bipartite double cover consists of two disjoint copies of G. A graph may have many different double covers other than the bipartite double cover.


In processor mode cores are on and executing code from the system memory and programmed I/O (inputs and outputs) through the system which is connected to the system board FPGA. Loading memory and configuring the processor for bootstrapping (sustaining after the initial load) is currently done by software running on the SCC's management console that's embedded in the chip.


{\displaystyle (\phi ,\psi )\cdot f=\psi ^{-1}\circ f\circ \phi .} Under this action we see that the map germs f , g: ( M , x ) → ( N , y ) {\displaystyle f,g:(M,x)\to (N,y)} are A {\displaystyle {\mathcal {A}}} -equivalent if, and only if, g {\displaystyle g} lies in the orbit of f {\displaystyle f} , i.e. g ∈ orb G ( f ) {\displaystyle g\in {\mbox{orb}}_{G}(f)} (or vice versa). A map germ is called stable if its orbit under the action of G := diff ( M x ) × diff ( N y ) {\displaystyle G:={\mbox{diff}}(M_{x})\times {\mbox{diff}}(N_{y})} is open relative to the Whitney topology.


Call this number Ω R ( s 1 ) {\displaystyle \;\Omega _{R}(s_{1})} . By assumption, the combined system (of the system we are interested in and the reservoir) is isolated, so all microstates are equally probable. Therefore, for instance, if Ω R ( s 1 ) = 2 Ω R ( s 2 ) {\displaystyle \;\Omega _{R}(s_{1})=2\;\Omega _{R}(s_{2})} , we can conclude that our system is twice as likely to be in state s 1 {\displaystyle \;s_{1}} than s 2 {\displaystyle \;s_{2}} .


For many distributions, the kernel can be written in closed form, but not the normalization constant. An example is the normal distribution. Its probability density function is p ( x | μ , σ 2 ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 {\displaystyle p(x|\mu ,\sigma ^{2})={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}} and the associated kernel is p ( x | μ , σ 2 ) ∝ e − ( x − μ ) 2 2 σ 2 {\displaystyle p(x|\mu ,\sigma ^{2})\propto e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}} Note that the factor in front of the exponential has been omitted, even though it contains the parameter σ 2 {\displaystyle \sigma ^{2}} , because it is not a function of the domain variable x {\displaystyle x} .


These evaluations are then transferred to the linguistic feature. An observer's attention may be drawn to a target as a result of certain general features of that target. These features include: General object attributes – vivid colors, object's proximity to observer Difference between object attribute and its immediate environment.


In regression analysis, plotting is a more natural way to view the overall trend of the whole data. The mean of the distance from each point to the predicted regression model can be calculated, and shown as the mean squared error. The squaring is critical to reduce the complexity with negative signs. To minimize MSE, the model could be more accurate, which would mean the model is closer to actual data.


First, define a modified greedy algorithm, that selects the set S i {\displaystyle S_{i}} that has the best ratio of weighted uncovered elements to cost. Second, among covers of cardinality 1 , 2 , . .


The longer, e.g. a sentence (measured in terms of the number of clauses) the shorter the clauses (measured in terms of the number of words), or: the longer a word (in syllables or morphs) the shorter the syllables or words in sounds). Law of diversification: If linguistic categories such as parts-of-speech or inflectional endings appear in various forms it can be shown that the frequencies of their occurrences in texts are controlled by laws. Martin's law: This law concerns lexical chains which are obtained by looking up the definition of a word in a dictionary, then looking up the definition of the definition just obtained etc. Finally, all these definitions form a hierarchy of more and more general meanings, whereby the number of definitions decreases with increasing generality.


The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proved numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.


This yields one scalar equation for x 1 {\displaystyle x_{1}}: As such, we find: The implementation in Dev-C++ without preserving the coefficient vectors: In both cases the auxiliary systems to be solved are genuinely tri-diagonal, so the overall computational complexity of solving system A x = d {\displaystyle Ax=d} remains linear with the respect to the dimension of the system n {\displaystyle n} , that is O ( n ) {\displaystyle O(n)} arithmetic operations. In other situations, the system of equations may be block tridiagonal (see block matrix), with smaller submatrices arranged as the individual elements in the above matrix system (e.g., the 2D Poisson problem). Simplified forms of Gaussian elimination have been developed for these situations.The textbook Numerical Mathematics by Quarteroni, Sacco and Saleri, lists a modified version of the algorithm which avoids some of the divisions (using instead multiplications), which is beneficial on some computer architectures. Parallel tridiagonal solvers have been published for many vector and parallel architectures, including GPUsFor an extensive treatment of parallel tridiagonal and block tridiagonal solvers see


In telecommunication, the term can be defined as: The ability to provide services to and accept services from other systems, and to use the services exchanged to enable them to operate effectively together. ITU-T provides standards for international telecommunications. The condition achieved among communications-electronics systems or items of communications-electronics equipment when information or services can be exchanged directly and satisfactorily between them and/or their users. The degree of interoperability should be defined when referring to specific cases.In two-way radio, interoperability is composed of three dimensions: compatible communications paths (compatible frequencies, equipment and signaling), radio system coverage or adequate signal strength, and; scalable capacity.


In numerical computation, pseudocode often consists of mathematical notation, typically from set and matrix theory, mixed with the control structures of a conventional programming language, and perhaps also natural language descriptions. This is a compact and often informal notation that can be understood by a wide range of mathematically trained people, and is frequently used as a way to describe mathematical algorithms. For example, the sum operator (capital-sigma notation) or the product operator (capital-pi notation) may represent a for-loop and a selection structure in one expression: Return ∑ k ∈ S x k {\displaystyle \sum _{k\in S}x_{k}} Normally non-ASCII typesetting is used for the mathematical equations, for example by means of markup languages, such as TeX or MathML, or proprietary formula editors. Mathematical style pseudocode is sometimes referred to as pidgin code, for example pidgin ALGOL (the origin of the concept), pidgin Fortran, pidgin BASIC, pidgin Pascal, pidgin C, and pidgin Lisp.


In the analysis of algorithms on graphs, the distinction between a graph and its complement is an important one, because a sparse graph (one with a small number of edges compared to the number of pairs of vertices) will in general not have a sparse complement, and so an algorithm that takes time proportional to the number of edges on a given graph may take a much larger amount of time if the same algorithm is run on an explicit representation of the complement graph. Therefore, researchers have studied algorithms that perform standard graph computations on the complement of an input graph, using an implicit graph representation that does not require the explicit construction of the complement graph. In particular, it is possible to simulate either depth-first search or breadth-first search on the complement graph, in an amount of time that is linear in the size of the given graph, even when the complement graph may have a much larger size. It is also possible to use these simulations to compute other properties concerning the connectivity of the complement graph. == References ==


In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete.


In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special number field sieve is efficient for integers of the form re ± s, where r and s are small (for instance Mersenne numbers). Heuristically, its complexity for factoring an integer n {\displaystyle n} is of the form: exp  ( ( 1 + o ( 1 ) ) ( 32 9 log  n ) 1 / 3 ( log  log  n ) 2 / 3 ) = L n  {\displaystyle \exp \left(\left(1+o(1)\right)\left({\tfrac {32}{9}}\log n\right)^{1/3}\left(\log \log n\right)^{2/3}\right)=L_{n}\left} in O and L-notations. The SNFS has been used extensively by NFSNet (a volunteer distributed computing effort), NFS@Home and others to factorise numbers of the Cunningham project; for some time the records for integer factorization have been numbers factored by SNFS.


In penetration testing, black-box testing refers to a method where an ethical hacker has no knowledge of the system being attacked. The goal of a black-box penetration test is to simulate an external hacking or cyber warfare attack.


In the concept hierarchy derivation step, the OL system tries to arrange the extracted concepts in a taxonomic structure. This is mostly achieved with unsupervised hierarchical clustering methods. Because the result of such methods is often noisy, a supervision step, e.g., user evaluation, is added.


First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts, several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the "usual" topological cohomology theories such as singular cohomology.


In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become an active area in group theory.


In telecommunications and computer networking, connection-oriented communication is a communication protocol where a communication session or a semi-permanent connection is established before any useful data can be transferred. The established connection ensures that data is delivered in the correct order to the upper communication layer. The alternative is called connectionless communication, such as the datagram mode communication used by Internet Protocol (IP) and User Datagram Protocol, where data may be delivered out of order, since different network packets are routed independently and may be delivered over different paths. Connection-oriented communication may be implemented with a circuit switched connection, or a packet-mode virtual circuit connection.


In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian). It is especially useful for sums of independent random variables, such as sums of Bernoulli random variables.The bound is commonly named after Herman Chernoff who described the method in a 1952 paper, though Chernoff himself attributed it to Herman Rubin. In 1938 Harald Cramér had published an almost identical concept now known as Cramér's theorem.


ALGOL's key ideas were continued, producing ALGOL 68: syntax and semantics became even more orthogonal, with anonymous routines, a recursive typing system with higher-order functions, etc.; not only the context-free part, but the full language syntax and semantics were defined formally, in terms of Van Wijngaarden grammar, a formalism designed specifically for this purpose.ALGOL 68's many little-used language features (for example, concurrent and parallel blocks) and its complex system of syntactic shortcuts and automatic type coercions made it unpopular with implementers and gained it a reputation of being difficult. Niklaus Wirth actually walked out of the design committee to create the simpler Pascal language. Some notable languages that were developed in this period include:


There were also around 188 million AXE lines in place or on order in 117 countries. Telecom and chip companies worked in the 1990s to provide Internet access over mobile telephones. Early versions such as Wireless Application Protocol (WAP) used packet data over the existing GSM network, in a form known as GPRS (General Packet Radio Service), but these services, known as 2.5G, were fairly rudimentary and did not achieve much mass-market success.The International Telecommunication Union (ITU) had prepared the specifications for a 3G mobile service that included several technologies.


In the absence of empirical algorithmics, analyzing the complexity of an algorithm can involve various theoretical methods applicable to various situations in which the algorithm may be used. Memory and cache considerations are often significant factors to be considered in the theoretical choice of a complex algorithm, or the approach to its optimization, for a given purpose. Performance profiling is a dynamic program analysis technique typically used for finding and analyzing bottlenecks in an entire application's code or for analyzing an entire application to identify poorly performing code. A profiler can reveal the code most relevant to an application's performance issues.A profiler may help to determine when to choose one algorithm over another in a particular situation.


The morphisms take one from one object to another, and form a dependent family of types, thus morphisms might be typed g: A → B {\displaystyle g:A\rightarrow B} , h: B → C {\displaystyle h:B\rightarrow C} , say. Composition is then a total function: ∘: ( B → C ) → ( A → B ) → A → C {\displaystyle \circ :(B\rightarrow C)\rightarrow (A\rightarrow B)\rightarrow A\rightarrow C} , so that h ∘ g: A → C {\displaystyle h\circ g:A\rightarrow C} . Special cases include: Setoids: sets that come with an equivalence relation, G-sets: sets equipped with an action of a group G {\displaystyle G} .Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt semigroups.


There is no undisputed winner by only looking at the pairwise differences here. Now the strongest paths have to be identified. To help visualize the strongest paths, the set of pairwise preferences is depicted in the diagram on the right in the form of a directed graph.


This is related to the rearrangement of the elements of S in which each element s is replaced by the corresponding f(s). For example, the permutation (3, 1, 2) mentioned above is described by the function α {\displaystyle \alpha } defined as α ( 1 ) = 3 , α ( 2 ) = 1 , α ( 3 ) = 2 {\displaystyle \alpha (1)=3,\quad \alpha (2)=1,\quad \alpha (3)=2} .The collection of all permutations of a set form a group called the symmetric group of the set. The group operation is the composition (performing two given rearrangements in succession), which results in another rearrangement.


In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board. For example, the Chebyshev distance between f6 and e2 equals 4.


In the case of a wholly textual search, the first step in classifying web pages is to find an ‘index item’ that might relate expressly to the ‘search term.’ In the past, search engines began with a small list of URLs as a so-called seed list, fetched the content, and parsed the links on those pages for relevant information, which subsequently provided new links. The process was highly cyclical and continued until enough pages were found for the searcher's use. These days, a continuous crawl method is employed as opposed to an incidental discovery based on a seed list.


In the early 1950s, Alick Glennie developed Autocode, possibly the first compiled programming language, at the University of Manchester. In 1954, a second iteration of the language, known as the "Mark 1 Autocode," was developed for the Mark 1 by R. A. Brooker. Brooker, with the University of Manchester, also developed an autocode for the Ferranti Mercury in the 1950s.


If the other developers check out the new code without being aware of the problem, their work may grind to a halt while they wait for the problem to be fixed (or try to fix it themselves, which can be even more problematic, if multiple developers attempt to fix the issue at the same time). This naturally can result in a significant loss of productivity. Neutral builds are important for software development processes running at high loads with short schedules (see extreme programming, startup). Not having them means that any build that needs to be created for the software quality assurance department will use code that may be in the middle of major modifications, and which is therefore best left out of a build intended for independent validation – particularly a build being evaluated for possible release.


In mathematics, the Cramér–Wold theorem in measure theory states that a Borel probability measure on R k {\displaystyle \mathbb {R} ^{k}} is uniquely determined by the totality of its one-dimensional projections. It is used as a method for proving joint convergence results. The theorem is named after Harald Cramér and Herman Ole Andreas Wold. Let X n = ( X n 1 , … , X n k ) {\displaystyle {X}_{n}=(X_{n1},\dots ,X_{nk})} and X = ( X 1 , … , X k ) {\displaystyle \;{X}=(X_{1},\dots ,X_{k})} be random vectors of dimension k. Then X n {\displaystyle {X}_{n}} converges in distribution to X {\displaystyle {X}} if and only if: ∑ i = 1 k t i X n i → n → ∞ D ∑ i = 1 k t i X i . {\displaystyle \sum _{i=1}^{k}t_{i}X_{ni}{\overset {D}{\underset {n\rightarrow \infty }{\rightarrow }}}\sum _{i=1}^{k}t_{i}X_{i}.} for each ( t 1 , … , t k ) ∈ R k {\displaystyle (t_{1},\dots ,t_{k})\in \mathbb {R} ^{k}} , that is, if every fixed linear combination of the coordinates of X n {\displaystyle {X}_{n}} converges in distribution to the correspondent linear combination of coordinates of X {\displaystyle {X}} .If X n {\displaystyle {X}_{n}} takes values in R + k {\displaystyle \mathbb {R} _{+}^{k}} , then the statement is also true with ( t 1 , … , t k ) ∈ R + k {\displaystyle (t_{1},\dots ,t_{k})\in \mathbb {R} _{+}^{k}} .


In the context of rental harmony (envy-free division of rooms and rent), the following results are known. Unanimous envy-freeness (called strong envy-freeness in the paper) may not exist when the cost-sharing policy is equal or proportional, but always exists with free cost-sharing policy. Moreover, a unanimously-envy-free allocation with free cost-sharing that maximizes the total rent can be found in polynomial time. With ad-hoc groups, unanimous envy-freeness exists even with equal cost-sharing policy. Average envy-freeness (called aggregate envy-freeness in the paper) always exists when the cost-sharing policy is equal or proportional or free.


Private (optional) – indicates that the function procedure is accessible only to other procedures in the module where it is declared. Friend (optional) – used only in a class module. Indicates that the Function procedure is visible throughout the project, but not visible to a controller of an instance of an object.


The soundness property provides the initial reason for counting a logical system as desirable. The completeness property means that every validity (truth) is provable. Together they imply that all and only validities are provable.


In mathematics, given a field F {\displaystyle \mathbb {F} } , nonnegative integers m , n {\displaystyle m,n} , and a matrix A ∈ F m × n {\displaystyle A\in \mathbb {F} ^{m\times n}} , a rank decomposition or rank factorization of A is a factorization of A of the form A = CF, where C ∈ F m × r {\displaystyle C\in \mathbb {F} ^{m\times r}} and F ∈ F r × n {\displaystyle F\in \mathbb {F} ^{r\times n}} , where r = rank  A {\displaystyle r=\operatorname {rank} A} is the rank of A {\displaystyle A} .


In the decision-making process, when faced with uncertainty, a subject can make two possible errors: type I or type II. A type I error is a false positive, thinking that an effect is there, when it is not. For example, acting on a fire alarm that turns out to be false. When someone infers sexual interest, where there is none, then a false-positive error has occurred.


In parallel programming, the code is divided into threads. The read-write conflicting variables are split between threads and each thread has a copy of them. Data structures like linked lists, trees, hash tables etc. have data variables that are linked and cannot be split between threads and hence implementing parallelism is very difficult. To improve the efficiency of implementing data structures multiple operations like insertion, deletion, search need to be executed in parallel.


Durrett and Steif (1993) and Steif (1994) show that for large radii there is a critical value θ c {\displaystyle \theta _{c}} such that if θ > θ c {\displaystyle \theta >\theta _{c}} most individuals never change, and for θ ∈ ( 1 / 2 , θ c ) {\displaystyle \theta \in (1/2,\theta _{c})} in the limit most sites agree. (Both of these results assume the probability of ξ 0 ( x ) = 1 {\displaystyle \xi _{0}(x)=1} is one half.) This process has a natural generalization to more dimensions, some results for this are discussed in Durrett and Steif (1993).


Following a failure, the failover mechanism is tested to ensure that data is not lost or corrupted and that any agreed service levels are maintained (e.g., function availability or response times). Type or extent of recovery is specified in the requirement specifications.


Complex craters have uplifted centers, and they have typically broad flat shallow crater floors, and terraced walls. At the largest sizes, one or more exterior or interior rings may appear, and the structure may be labeled an impact basin rather than an impact crater. Complex-crater morphology on rocky planets appears to follow a regular sequence with increasing size: small complex craters with a central topographic peak are called central peak craters, for example Tycho; intermediate-sized craters, in which the central peak is replaced by a ring of peaks, are called peak-ring craters, for example Schrödinger; and the largest craters contain multiple concentric topographic rings, and are called multi-ringed basins, for example Orientale. On icy (as opposed to rocky) bodies, other morphological forms appear that may have central pits rather than central peaks, and at the largest sizes may contain many concentric rings. Valhalla on Callisto is an example of this type.


If the significance level, alpha (α), is 0.05, and only reject the null hypothesis if the p-value is less than or equal to 0.05, then the hypothesis test will indeed have a significance level (maximal type 1 error rate) of 0.05. As Neyman wrote: “The error that a practising statistician would consider the more important to avoid (which is a subjective judgment) is called the error of the first kind. The first demand of the mathematical theory is to deduce such test criteria as would ensure that the probability of committing an error of the first kind would equal (or approximately equal, or not exceed) a preassigned number α, such as α = 0.05 or 0.01, etc. This number is called the level of significance”; Neyman 1976, p.


Small farmers in Colombia grow a much wider range of cultivars than large commercial plantations. A study of these cultivars showed that they could be placed into at least three groups based on their characteristics: dessert bananas, non-plantain cooking bananas, and plantains, although there were overlaps between dessert and cooking bananas.In Southeast Asia—the center of diversity for bananas, both wild and cultivated—the distinction between "bananas" and "plantains" does not work, according to Valmayor et al. Many bananas are used both raw and cooked. There are starchy cooking bananas which are smaller than those eaten raw.


It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution). It is related to the Gompertz distribution: when its density is first reflected about the origin and then restricted to the positive half line, a Gompertz function is obtained.


In radio, for example, a very narrow band will carry Morse code, a broader band will carry speech, and a still broader band will carry music without losing the high audio frequencies required for realistic sound reproduction. This broad band is often divided into channels or "frequency bins" using passband techniques to allow frequency-division multiplexing instead of sending a higher-quality signal. In data communications, a 56k modem will transmit a data rate of 56 kilobits per second (kbit/s) over a 4-kilohertz-wide telephone line (narrowband or voiceband).


H D ( x , R ) {\displaystyle H_{D}(x,R)} is a good measure for local complexity. Entropy only measures the statistic of the local attribute. It does not measure the spatial arrangement of the local attribute.


Formal theories of grammar seek to define the different elements of language and describe the way they relate to each other as systems of formal rules or operations, while functional theories seek to define the functions performed by language and then relate them to the linguistic elements that carry them out. The framework of cognitive linguistics interprets language in terms of the concepts (which are sometimes universal, and sometimes specific to a particular language) which underlie its forms. Cognitive linguistics is primarily concerned with how the mind creates meaning through language.


Examples of this include the failure to account for measurement error, or the failure to adequately control experiments for any parameters being measured. Fabrication can also occur in the context of undergraduate or graduate studies wherein a student fabricates a laboratory or homework assignment. Such cheating, when discovered, is usually handled within the institution, and does not become a scandal within the larger academic community (as cheating by students seldom has any academic significance).


In mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle \mathbb {S} ^{1}} , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C × {\displaystyle \mathbb {C} ^{\times }} , the multiplicative group of all nonzero complex numbers. Since C × {\displaystyle \mathbb {C} ^{\times }} is abelian, it follows that T {\displaystyle \mathbb {T} } is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized by the angle measure θ {\displaystyle \theta }: This is the exponential map for the circle group.


In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. A quasigroup with an identity element is called a loop.