In the diagrams, P is used for N’s parent, G for the grandparent, and U will denote N’s uncle. The diagrams show the parent node P as the left child of its parent G even though it is possible for P to be on either side. The sample code covers both possibilities by means of the side variable dir. N is the insertion node, but as the operation proceeds also other nodes may become current (see case I2).


This made it harder to interface other processors. Upgrading to a more powerful processor would subtly change the timings, and timing restraints were not always tightly specified. Nor were electrical parameters and physical dimensions.


In reality, initial exponential growth is often not sustained forever. After some period, it will be slowed by external or environmental factors. For example, population growth may reach an upper limit due to resource limitations. In 1845, the Belgian mathematician Pierre François Verhulst first proposed a mathematical model of growth like this, called the "logistic growth".


The total time for his algorithm is O(m log m). For planar graphs with maximum degree Δ ≥ 7, the optimal number of colors is again exactly Δ. With the stronger assumption that Δ ≥ 9, it is possible to find an optimal edge coloring in linear time (Cole & Kowalik 2008). For d-regular graphs which are pseudo-random in the sense that their adjacency matrix has second largest eigenvalue (in absolute value) at most d1−ε, d is the optimal number of colors (Ferber & Jain 2020).


The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits. Later, beginning with RSA-576, binary digits are counted instead. An exception to this is RSA-617, which was created before the change in the numbering scheme. The numbers are listed in increasing order below.


In most cases, ELM is used as a single hidden layer feedforward network (SLFN) including but not limited to sigmoid networks, RBF networks, threshold networks, fuzzy inference networks, complex neural networks, wavelet networks, Fourier transform, Laplacian transform, etc. Due to its different learning algorithm implementations for regression, classification, sparse coding, compression, feature learning and clustering, multi ELMs have been used to form multi hidden layer networks, deep learning or hierarchical networks.A hidden node in ELM is a computational element, which need not be considered as classical neuron. A hidden node in ELM can be classical artificial neurons, basis functions, or a subnetwork formed by some hidden nodes.


Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else.


Factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P; this is a matrix formulation of Gaussian elimination.


In mathematics, if A {\displaystyle A} is a subset of B , {\displaystyle B,} then the inclusion map (also inclusion function, insertion, or canonical injection) is the function ι {\displaystyle \iota } that sends each element x {\displaystyle x} of A {\displaystyle A} to x , {\displaystyle x,} treated as an element of B: {\displaystyle B:} A "hooked arrow" (U+21AA ↪ RIGHTWARDS ARROW WITH HOOK) is sometimes used in place of the function arrow above to denote an inclusion map; thus: (However, some authors use this hooked arrow for any embedding.) This and other analogous injective functions from substructures are sometimes called natural injections. Given any morphism f {\displaystyle f} between objects X {\displaystyle X} and Y {\displaystyle Y} , if there is an inclusion map into the domain ι: A → X , {\displaystyle \iota :A\to X,} then one can form the restriction f ι {\displaystyle f\,\iota } of f . {\displaystyle f.} In many instances, one can also construct a canonical inclusion into the codomain R → Y {\displaystyle R\to Y} known as the range of f . {\displaystyle f.}


In the 2005 Star Trek: Enterprise episode "The Aenar", it was used in the Aenar city.


One downside to the RISC design was that the programs that run on them tend to be larger. This is because compilers must generate longer sequences of the simpler instructions to perform the same results. Since these instructions must be loaded from memory anyway, the larger code offsets some of the RISC design's fast memory handling.


In psycholinguistics, semantic processing is the stage of language processing that occurs after one hears a word and encodes its meaning: the mind relates the word to other words with similar meanings. Once a word is perceived, it is placed in a context mentally that allows for a deeper processing. Therefore, semantic processing produces memory traces that last longer than those produced by shallow processing, since shallow processing produces fragile memory traces that decay rapidly. Semantic processing is the deepest level of processing and it requires the listener to think about the meaning of the cue.


2(2). In computer science terms, programming in the large can refer to programming code that represents the high-level state transition logic of a system. This logic encodes information such as when to wait for messages, when to send messages, when to compensate for failed non-ACID transactions, etc. A language that was designed to explicitly support programming in the large is BPEL.


Conversely, a group of participants can atomically broadcast messages by achieving consensus regarding the first message to be received, followed by achieving consensus on the next message, and so forth until all the messages have been received. Thus, atomic broadcast reduces to consensus.


In the Northeast Caucasian languages, such as Tsez, the dative also takes the functions of the lative case in marking the direction of an action. By some linguists, they are still regarded as two separate cases in those languages, although the suffixes are exactly the same for both cases. Other linguists list them separately only for the purpose of separating syntactic cases from locative cases. An example with the ditransitive verb "show" (literally: "make see") is given below: The dative/lative is also used to indicate possession, as in the example below, because there is no such verb as "to have".


In the early days of computing, CPU time was expensive, and peripherals were very slow. When the computer ran a program that needed access to a peripheral, the central processing unit (CPU) would have to stop executing program instructions while the peripheral processed the data. This was usually very inefficient. The first computer using a multiprogramming system was the British Leo III owned by J. Lyons and Co.


These scores, based on a normal curve, are known as "scaled" scores. Because of their grounding in this model, scaled MAT scores of 500-600 are extremely rare, as they would be more than four standard deviations above the norm of 400.


The order of a hypergraph ( X , E ) {\displaystyle (X,E)} is the number of vertices in X {\displaystyle X} . The size of the hypergraph is the number of edges in E {\displaystyle E} . The order of an edge e = ( D , C ) {\displaystyle e=(D,C)} in a directed hypergraph is | e | = ( | D | , | C | ) {\displaystyle |e|=(|D|,|C|)}: that is, the number of vertices in its tail followed by the number of vertices in its head.


The new networks have higher download speeds, with a peak speed of 10 gigabits per second (Gbit/s) when there is only one user in the network. 5G has higher bandwidth to deliver faster speeds than 4G and can thus connect more different devices, improving the quality of Internet services in crowded areas. Due to the increased bandwidth, it is expected the 5G networks will increasingly be used as general internet service providers (ISPs), competing with existing ISPs such as cable internet, and also will make possible new applications in internet-of-things (IoT) and machine-to-machine areas. Cellphones with 4G capability alone are not able to use the 5G networks.


Then, the distances between consecutive occurrences of the strings are likely to be multiples of the length of the keyword. Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances. The reason this test works is that if a repeated string occurs in the plaintext, and the distance between corresponding characters is a multiple of the keyword length, the keyword letters will line up in the same way with both occurrences of the string.


Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection.


Read before write, read after read and write before write ordering is still preserved in this model. The processor consistency model is similar to the PRAM consistency model with a stronger condition that defines all writes to the same memory location must be seen in the same sequential order by all other processes. Processor consistency is weaker than sequential consistency but stronger than the PRAM consistency model.


By Bézout's identity, there are r and s such that r n + s a = 1. {\displaystyle rn+sa=1.} Multiply both sides by b: r n b + s a b = b . {\displaystyle rnb+sab=b.} The first term on the left is divisible by n, and the second term is divisible by ab, which by hypothesis is divisible by n. Therefore their sum, b, is also divisible by n.


In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement (via projective measurements) in the case of cluster states.


Concurrent schedules often induce rapid alternation between the keys. To prevent this, a "changeover delay" is commonly introduced: each schedule is inactivated for a brief period after the subject switches to it.


Ng5 f5 11. g3 Nh6 12. Bd3 Nf7 13. Bxf5?


In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Z n {\displaystyle \mathbb {Z} ^{n}} , is the lattice in the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. Z n {\displaystyle \mathbb {Z} ^{n}} is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice.


Stack machines can work around the memory delay by either having a deep out-of-order execution pipeline covering many instructions at once, or more likely, they can permute the stack such that they can work on other workloads while the load completes, or they can interlace the execution of different program threads, as in the Unisys A9 system. Today's increasingly parallel computational loads suggests, however, this might not be the disadvantage it's been made out to be in the past. Stack machines can omit the operand fetching stage of a register machine. For example, in the Java Optimized Processor (JOP) microprocessor the top 2 operands of stack directly enter a data forwarding circuit that is faster than the register file.


In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Principal Component or PC), plane (for two PCs) or hyper-plane (for more than two PCs). For each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper-plane (calculated as the residual standard deviation) is used to determine a critical distance for classification. This critical distance is based on the F-distribution and is usually calculated using 95% or 99% confidence intervals.


The contraction generated by the cooling supposedly produced the high pressure required to transform graphite into diamond. Moissan published his work in a series of articles in the 1890s.Many other scientists tried to replicate his experiments. Sir William Crookes claimed success in 1909.


In attributive sentences (see below), as well as agreement in person and number between the subject and the verb, there is also agreement of gender and number between the subject and the head of the attribute when it is a noun or an adjective. In Catalan there are four main types of sentence: Predicative sentences, consisting of a subject, a verb and some complements. En Jordi va collir tres roses per a la Núria (Jordi picked three roses for Núria).


It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid.


A variant of this problem gives the total number of travelers available, and asks for the maximum distance that can be reached. In the cars across the desert problem, the starting base has unlimited units of fuel. Each car can carry at most 1 unit of supplies at any time, and can travel 1 unit of distance on 1 unit of fuel.


Sometimes schools do half-day in-service days in which students are dismissed early, rather than full-day holidays. Unplanned interruptions in schooling (such as weather events like heavy snow) can extend the school year on occasion. Such calendar extensions, as well as the initial cancellations, are decided by each local administration and announced to the parents in as timely manner as possible.


To show that a system S is required to prove a theorem T, two proofs are required. The first proof shows T is provable from S; this is an ordinary mathematical proof along with a justification that it can be carried out in the system S. The second proof, known as a reversal, shows that T itself implies S; this proof is carried out in the base system. The reversal establishes that no axiom system S′ that extends the base system can be weaker than S while still proving T.


In order to say something about the security properties of the above explained XTR encryption scheme, first it is important to check the security of the XTR group, which means how hard it is to solve the Discrete Logarithm problem there. The next part will then state the equivalency between the Discrete Logarithm problem in the XTR group and the XTR version of the discrete logarithm problem, using only the traces of elements.


In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description.


In practice this becomes computationally onerous as k {\displaystyle ~k~} and N {\displaystyle ~N~} increase so it is probably only worth using exact tests for small samples. For larger samples, asymptotic approximations are accurate enough and easier to calculate. One of these approximations is the likelihood ratio.


In the case of server consolidation, many small physical servers can be replaced by one larger physical server to decrease the need for more (costly) hardware resources such as CPUs, and hard drives. Although hardware is consolidated in virtual environments, typically OSs are not. Instead, each OS running on a physical server is converted to a distinct OS running inside a virtual machine.


In mathematics, the Thue–Morse sequence or Prouhet–Thue–Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. The full sequence begins: 01101001100101101001011001101001.... The sequence is named after Axel Thue and Marston Morse.


In statistics, qualitative comparative analysis (QCA) is a data analysis based on set theory to examine the relationship of conditions to outcome. QCA describes the relationship in terms of necessary conditions and sufficient conditions. The technique was originally developed by Charles Ragin in 1987 to study data sets that are too small for linear regression analysis but large for cross-case analysis.


Below is the example that compares SPARQL and SQL queries for medications that treats "TB of vertebra". SELECT ?medication WHERE { ?diagnosis a example:Diagnosis . ?diagnosis example:name “TB of vertebra” . ?medication example:canTreat ?diagnosis . } SELECT DRUG.medID FROM DIAGNOSIS, DRUG, DRUG_DIAGNOSIS WHERE DIAGNOSIS.diagnosisID=DRUG_DIAGNOSIS.diagnosisID AND DRUG.medID=DRUG_DIAGNOSIS.medID AND DIAGNOSIS.name=”TB of vertebra”


The reason is that if V {\displaystyle V} is an F {\displaystyle F} -vector space and q: V → F {\displaystyle q:V\to F} is a quadratic form and v {\displaystyle v} is an element of V {\displaystyle V} such that q ( v ) = a ∈ F × {\displaystyle q(v)=a\in F^{\times }} , then for all u ∈ F × {\displaystyle u\in F^{\times }} , q ( u v ) = a u 2 {\displaystyle q(uv)=au^{2}} and thus it is sometimes more convenient to talk about the square classes which the quadratic form represents. Every element of the square class group is an involution. It follows that, if the number of square classes of a field is finite, it must be a power of two. == References ==


In Greek, for example, the imperfective sometimes adds the notion of "try to do something" (the so-called conative imperfect); hence, the same verb, in the imperfective (present or imperfect) and aorist, respectively, is used to convey look and see, search and find, listen and hear. (For example, ἠκούομεν (ēkouomen, "we listened") vs. ἠκούσαμεν (ēkousamen, "we heard").) Spanish has similar pairs for certain verbs, such as (imperfect and preterite, respectively) sabía ("I knew") vs. supe ("I found out"), podía ("I was able to") vs. pude ("I succeeded (in doing something)"), quería ("I wanted to") vs. quise ("I tried to"), and no quería ("I did not want to") vs. no quise ("I refused (to do something)"). Such differences are often highly language-specific.


In some communication systems, a receiver can achieve character synchronization from an undifferentiated bit stream, or start-of-header synchronization from a byte stream, without the overhead of an explicit syncword. For example, the FSK441 protocol achieves character synchronization by synchronizing on any "space" characters in the message—in effect, every "space" character in the message does double duty as a syncword. For example, CRC-based framing achieves character and start-of-header synchronization. In a self-synchronizing code, every character is, in effect, a syncword, and can be used to achieve character synchronization in an undifferentiated bit stream.


In the age of advanced mobile devices, there is some disadvantage in using phonewords. Devices with physical keyboards such as BlackBerry and some other smartphones do not have the apportioned letters on the keys used for dialing, so one is unable to do alphabetic dialing without some other cross-reference to the actual phone number. This can be overcome by phonewords also being accompanied by the actual numeric phone number, allowing users of such smartphones to dial using the numeric phone number. However, devices which have virtual keyboards, including iOS and Android devices, will translate phoneword phone numbers in webpages and SMS messages to their proper digits within a hyperlink leading to that device's phone app, and their keypads show the appropriate local mapping of letters within their virtual dialpad.


In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution.


In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria. Fluid limits were first introduced by Thomas G. Kurtz publishing a law of large numbers and central limit theorem for Markov chains. It is known that a queueing network can be stable, but have an unstable fluid limit. == References ==


In the context of machine learning, the exploration-exploitation tradeoff is often encountered in reinforcement learning, a type of machine learning that involves training agents to make decisions based on feedback from the environment. The agent must decide whether to exploit the current best-known policy or explore new policies to improve its performance. Various algorithms have been developed to address this challenge, such as epsilon-greedy, Thompson sampling, and the upper confidence bound. == References ==


In practice, the main application of the Peano kernel theorem is to bound the error of an approximation that is exact for all f ∈ P ν {\displaystyle f\in \mathbb {P} _{\nu }} . The theorem above follows from the Taylor polynomial for f {\displaystyle f} with integral remainder: f ( x ) = f ( a ) + ( x − a ) f ′ ( a ) + ( x − a ) 2 2 f ″ ( a ) + ⋯ ⋯ + ( x − a ) ν ν ! f ( ν ) ( a ) + 1 ν ! ∫ a x ( x − θ ) ν f ( ν + 1 ) ( θ ) d θ , {\displaystyle {\begin{aligned}f(x)=f(a)+{}&(x-a)f'(a)+{\frac {(x-a)^{2}}{2}}f''(a)+\cdots \\&\cdots +{\frac {(x-a)^{\nu }}{\nu ! }}f^{(\nu )}(a)+{\frac {1}{\nu ! }}\int _{a}^{x}(x-\theta )^{\nu }f^{(\nu +1)}(\theta )\,d\theta ,\end{aligned}}} defining L ( f ) {\displaystyle L(f)} as the error of the approximation, using the linearity of L {\displaystyle L} together with exactness for f ∈ P ν {\displaystyle f\in \mathbb {P} _{\nu }} to annihilate all but the final term on the right-hand side, and using the ( ⋅ ) + {\displaystyle (\cdot )_{+}} notation to remove the x {\displaystyle x} -dependence from the integral limits.


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 called exact if the image of each homomorphism is equal to the kernel of the next: i m ( f k ) = k e r ( f k + 1 ) . {\displaystyle \mathrm {im} (f_{k})=\mathrm {ker} (f_{k+1}).\!} Note that the sequence of groups and homomorphisms may be either finite or infinite.


In the field of topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy).


In several fields, especially computing, deprecation is the discouragement of use of some terminology, feature, design, or practice, typically because it has been superseded or is no longer considered efficient or safe, without completely removing it or prohibiting its use. Typically, deprecated materials are not completely removed to ensure legacy compatibility or back up practice in case new methods are not functional in an odd scenario. It can also imply that a feature, design, or practice will be removed or discontinued entirely in the future.


The most computationally expensive component of the best predictor formula is inverting the covariance matrix Σ {\displaystyle \mathbf {\Sigma } } , which has cubic complexity O ( n 3 ) {\displaystyle {\mathcal {O}}(n^{3})} . Similarly, evaluating likelihood involves both calculating Σ − 1 {\displaystyle \mathbf {\Sigma } ^{-1}} and the determinant det ( Σ ) {\displaystyle \det(\mathbf {\Sigma } )} which has the same cubic complexity. Gaussian process approximations can often be expressed in terms of assumptions on y {\displaystyle y} under which log  ℓ ( y ) {\displaystyle \log \ell (\mathbf {y} )} and μ y ∗ {\displaystyle \mathbf {\mu } _{\mathbf {y} }^{*}} can be calculated with much lower complexity. Since these assumptions are generally not believed to reflect reality, the likelihood and the best predictor obtained in this way are not exact, but they are meant to be close to their original values.


In non-smooth method, unilateral interactions between bodies are fundamentally modelled by the Signorini condition for non-penetration, and impact laws are used to define the impact process. The Signorini condition can be expressed as the complementarity problem: g ≥ 0 , λ ≥ 0 , λ ⊥ g {\displaystyle g\geq 0,\quad \lambda \geq 0,\quad \lambda \perp g} , where g {\displaystyle g} denotes the distance between two bodies and λ {\displaystyle \lambda } denotes the contact force generated by the unilateral constraints, as shown in the figure below. Moreover, in terms of the concept of proximal point of convex theory, the Signorini condition can be equivalently expressed as: λ = p r o j R + ( λ − ρ g ) {\displaystyle \lambda ={\rm {proj}}_{\mathbb {R} ^{+}}(\lambda -\rho g)} , where ρ > 0 {\displaystyle \rho >0} denotes an auxiliary parameter, and p r o j C ( x ) {\displaystyle {\rm {proj}}_{\bf {C}}(x)} represents the proximal point in the set C {\displaystyle C} to the variable x {\displaystyle x} , defined as: p r o j C ( x ) = a r g m i n y ∈ C ‖ y − x ‖ {\displaystyle {\rm {proj}}_{\bf {C}}(x)={\rm {argmin}}_{y\in C}\|y-x\|} . Both the expressions above represent the dynamic behaviour of unilateral constraints: on the one hand, when the normal distance g N {\displaystyle g_{\rm {N}}} is above zero, the contact is open, which means that there is no contact force between bodies, λ = 0 {\displaystyle \lambda =0} ; on the other hand, when the normal distance g N {\displaystyle g_{\rm {N}}} is equal to zero, the contact is closed, resulting in λ ≥ 0 {\displaystyle \lambda \geq 0} .


If the participant makes a mistake, the experimenter prompts them to start again. The threat of negative evaluation is the social stressor.


The choice of loss function here gives rise to several well-known learning algorithms such as regularized least squares and support vector machines. A purely online model in this category would learn based on just the new input ( x t + 1 , y t + 1 ) {\displaystyle (x_{t+1},y_{t+1})} , the current best predictor f t {\displaystyle f_{t}} and some extra stored information (which is usually expected to have storage requirements independent of training data size). For many formulations, for example nonlinear kernel methods, true online learning is not possible, though a form of hybrid online learning with recursive algorithms can be used where f t + 1 {\displaystyle f_{t+1}} is permitted to depend on f t {\displaystyle f_{t}} and all previous data points ( x 1 , y 1 ) , … , ( x t , y t ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{t},y_{t})} .


Designed by PLP Architecture, the development has 546 rooms with most units grouped into "twodios" – two en-suite bedrooms that share a small kitchenette. There are also some private suites. The units sizes range from 9.2 square metres (99 sq ft) for an ensuite rooms with a 5.8 square metres (62 sq ft) shared kitchenette, to 12 square metres (130 sq ft) for a shared ensuite and 16.5 square metres (178 sq ft) shared ensuite with kitchenette. Each floor features one larger kitchen with a dining table, which is shared between 30 and 70 residents, and themed communal living spaces such as a games room, a cinema, a 'disco-launderette', a hidden garden and a spa. A restaurant, gym and co-working spaces are located in the lower floors of the building.


In mathematics, the generalized taxicab number Taxicab(k, j, n) is the smallest number — if it exists — that can be expressed as the sum of j kth positive powers in n different ways. For k = 3 and j = 2, they coincide with taxicab number. T a x i c a b ( 1 , 2 , 2 ) = 4 = 1 + 3 = 2 + 2. {\displaystyle \mathrm {Taxicab} (1,2,2)=4=1+3=2+2.}


The UNIVAC 1232 was a military version of the 490. The UNIVAC 492 is similar to the UNIVAC 490, but with extended memory to 64K 30-bit words. The UNIVAC 494 was a 30-bit word machine and successor to the UNIVAC 490/492 with faster CPU and 131K (later 262K) core memory.


In support vector machines (SVMs), the formulating the primal problem of SVMs as the dual problem can be used to implement Kernel trick, but the latter has higher time complexity in the historical cases.


In mathematics, specifically additive number theory, Romanov's theorem is a mathematical theorem proved by Nikolai Pavlovich Romanov. It states that given a fixed base b, the set of numbers that are the sum of a prime and a positive integer power of b has a positive lower asymptotic density.


In remote sensing, "ground truth" refers to information collected at the imaged location. Ground truth allows image data to be related to real features and materials on the ground. The collection of ground truth data enables calibration of remote-sensing data, and aids in the interpretation and analysis of what is being sensed. Examples include cartography, meteorology, analysis of aerial photographs, satellite imagery and other techniques in which data are gathered at a distance.


In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.


In the context of business process integration (see figure), data modeling complements business process modeling, and ultimately results in database generation.The process of designing a database involves producing the previously described three types of schemas - conceptual, logical, and physical. The database design documented in these schemas are converted through a Data Definition Language, which can then be used to generate a database. A fully attributed data model contains detailed attributes (descriptions) for every entity within it. The term "database design" can describe many different parts of the design of an overall database system.


Simon Tatham's contribution, based on Duff's device, is a notable example of the genre, and is the basis for Protothreads and similar implementations. In addition to Duff's objections, Tatham's own comments provide a frank evaluation of the limitations of this approach: "As far as I know, this is the worst piece of C hackery ever seen in serious production code." The main shortcomings of this approximation are that, in not maintaining a separate stack frame for each coroutine, local variables are not preserved across yields from the function, it is not possible to have multiple entries to the function, and control can only be yielded from the top-level routine.


In mathematics, one can define a product of group subsets in a natural way. If S and T are subsets of a group G, then their product is the subset of G defined by S T = { s t: s ∈ S and t ∈ T } . {\displaystyle ST=\{st:s\in S{\text{ and }}t\in T\}.} The subsets S and T need not be subgroups for this product to be well defined.


In optimization, a self-concordant function is a function f: R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } for which | f ‴ ( x ) | ≤ 2 f ″ ( x ) 3 / 2 {\displaystyle |f'''(x)|\leq 2f''(x)^{3/2}} or, equivalently, a function f: R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } that, wherever f ″ ( x ) > 0 {\displaystyle f''(x)>0} , satisfies | d d x 1 f ″ ( x ) | ≤ 1 {\displaystyle \left|{\frac {d}{dx}}{\frac {1}{\sqrt {f''(x)}}}\right|\leq 1} and which satisfies f ‴ ( x ) = 0 {\displaystyle f'''(x)=0} elsewhere. More generally, a multivariate function f ( x ): R n → R {\displaystyle f(x):\mathbb {R} ^{n}\rightarrow \mathbb {R} } is self-concordant if d d α ∇ 2 f ( x + α y ) | α = 0 ⪯ 2 y T ∇ 2 f ( x ) y ∇ 2 f ( x ) {\displaystyle \left. {\frac {d}{d\alpha }}\nabla ^{2}f(x+\alpha y)\right|_{\alpha =0}\preceq 2{\sqrt {y^{T}\nabla ^{2}f(x)\,y}}\,\nabla ^{2}f(x)} or, equivalently, if its restriction to any arbitrary line is self-concordant.


In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables.


While we cannot do this by simply rearranging the quantifiers, we show that it is yet enough to prove the theorem for sentences of that form. Finally we prove the theorem for sentences of that form. This is done by first noting that a sentence such as B = ∀x1∀x2...∀xk ∃y1∃y2...∃ym φ(x1...xk, y1...ym) is either refutable (its negation is always true) or satisfiable, i.e. there is some model in which it holds (it might even be always true, i.e. a tautology); this model is simply assigning truth values to the subpropositions from which B is built.


In the IBM System/370 models with virtual storage (DAT) and 24-bit addresses, control register 0 specifies a segment size of either 64 KiB or 1 MiB and a page size of either 2 KiB or 4 KiB; control register 1 contains a Segment Table Designator (STD), which specifies the length and real address of the segment table. Each segment table entry contains a page table location, a page table length and an invalid bit. IBM later expanded the address size to 31 bits and added two bits to the segment table entries: Segment-protection bit Segment is read-only Common-segment bit The segment is shared between address spaces; this bit is set to optimize TLB useEach of IBM's DAT implementations includes a translation cache, which IBM called a Translation Lookaside Buffer (TLB).


In the 19th century new developments such as the discovery of photography, Rowland's invention of the concave diffraction grating, and Schumann's works on discovery of vacuum ultraviolet (fluorite for prisms and lenses, low-gelatin photographic plates and absorption of UV in air below 185 nm) made advance to shorter wavelengths very fast. At the same time Dewar observed series in alkali spectra, Hartley found constant wave-number differences, Balmer discovered a relation connecting wavelengths in the visible hydrogen spectrum, and finally Rydberg derived a formula for wave-numbers of spectral series. Meanwhile, the substantial summary of past experiments performed by Maxwell (1873), resulted in his equations of electromagnetic waves.


One says also a is prime to b or a is coprime with b. The numbers 8 and 9 are coprime, despite the fact that neither considered individually is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition.


In the early 1970s, Diffie worked with Martin Hellman to develop the fundamental ideas of dual-key, or public key, cryptography. They published their results in 1976—solving one of the fundamental problems of cryptography, key distribution—and essentially broke the monopoly that had previously existed where government entities controlled cryptographic technology and the terms on which other individuals could have access to it. "From the moment Diffie and Hellman published their findings..., the National Security Agency's crypto monopoly was effectively terminated. ... Every company, every citizen now had routine access to the sorts of cryptographic technology that not many years ago ranked alongside the atom bomb as a source of power." The solution has become known as Diffie–Hellman key exchange.


This bias is especially prevalent in group settings where one thinks the collective opinion of their own group matches that of the larger population. Since the members of a group reach a consensus and rarely encounter those who dispute it, they tend to believe that everybody thinks the same way. The false-consensus effect is not restricted to cases where people believe that their values are shared by the majority, but it still manifests as an overestimate of the extent of their belief.Additionally, when confronted with evidence that a consensus does not exist, people often assume that those who do not agree with them are defective in some way.


For example, following a known software design structure, such as client and broker, can help in designing a well-built structure with a solid foundation. Furthermore, if the software is to be modified in the future, it is even more important that it follows a logical foundation of separation between the client and server. This is because if a programmer comes in and cannot clearly understand the dynamics of the program, they may end up adding or changing something that can add a security flaw. Even with the best design, this is always a possibility, but the better the standardization of the design, the less chance there is of this occurring.


Thus, print carries the individuating power of the phonetic alphabet much further than manuscript culture could ever do. Print is the technology of individualism.


If the affected program is running with special privileges, or accepts data from untrusted network hosts (e.g. a webserver) then the bug is a potential security vulnerability. If the stack buffer is filled with data supplied from an untrusted user then that user can corrupt the stack in such a way as to inject executable code into the running program and take control of the process. This is one of the oldest and more reliable methods for attackers to gain unauthorized access to a computer.


In mathematics, rational reconstruction is a method that allows one to recover a rational number from its value modulo a sufficiently large integer.


A continuum of complex morphology of language may be adopted. The three models of morphology stem from attempts to analyze languages that more or less match different categories in this typology. The item-and-arrangement approach fits very naturally with agglutinative languages.


In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and The generators are as independent as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in every Boolean algebra no matter which elements are chosen.


For the Bluetooth Low Energy stack, according to Bluetooth 4.0 a special set of profiles applies. A host Operating System can expose a basic set of profiles (namely OBEX, HID and Audio Sink) and manufacturers can add additional profiles to its driver and stack to enhance what their Bluetooth device can do. Devices such as mobile phones can expose additional profiles by installing appropriate apps.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 57, 157, 457, and 1457 are the patterns related to Braille pattern dots-34, since the two additional dots of kantenji patterns 034, 347, and 0347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In software development and product management, a user story is an informal, natural language description of features of a software system. They are written from the perspective of an end user or user of a system, and may be recorded on index cards, Post-it notes, or digitally in project management software. Depending on the project, user stories may be written by different stakeholders like client, user, manager, or development team. User stories are a type of boundary object. They facilitate sensemaking and communication; and may help software teams document their understanding of the system and its context.


In signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient or autocovariance function.


In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5/6 = 1/2 + 1/3. As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the Liber Abaci of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction.


In these scenarios, modularity is an abstraction of the 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice. In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary elements x and a (for a ≤ b).


{\displaystyle \operatorname {disc} ({\mathcal {H}}):=\min _{\chi :V\rightarrow \{-1,+1\}}\operatorname {disc} ({\mathcal {H}},\chi ).} These notions as well as the term 'discrepancy' seem to have appeared for the first time in a paper of Beck.


In the counter-electronic codebook mode, the Cascaded Cipher uses full strength AES-128 in counter mode to generate a secure key stream and supplies this key-stream to a reduced round Serpent in electronic codebook mode to encrypt each plaintext block. To increase performance, each inner key stream block is reused several times to encrypt multiple blocks.


And here, Kant says, we are liable to error in two ways. The first type of error consists in trying to attract students into being moral by providing them examples in which morality and self-love coincide. The second type of error consists in trying to emotionally arouse the students about morality by providing examples of extraordinary moral heroism, above what morality normally requires.


In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.


In mathematics, the Babenko–Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be ‖ F ‖ q , p = sup f ∈ L p ( R n ) ‖ F f ‖ q ‖ f ‖ p , where 1 < p ≤ 2 , and 1 p + 1 q = 1. {\displaystyle \|{\mathcal {F}}\|_{q,p}=\sup _{f\in L^{p}(\mathbb {R} ^{n})}{\frac {\|{\mathcal {F}}f\|_{q}}{\|f\|_{p}}},{\text{ where }}1


In stage two, testers will recruit test subjects across a broad spectrum of abilities. For example, in one study, experienced users showed no problem using any design, from the first to the last, while naive users and self-identified power users both failed repeatedly. Later on, as the design smooths out, users should be recruited from the target population.


Petersburg paradox.In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing is proportional to the population. This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a logarithmic scale for the growth axis.


The command will be applied to all unit codes sent. It is also possible to send a message with no unit codes, just a house code and a command code. This will apply to the command to the last group of units codes previously sent.


In the category of graphs, the product is the tensor product of graphs. In the category of relations, the product is given by the disjoint union. (This may come as a bit of a surprise given that the category of sets is a subcategory of the category of relations.)


In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion. It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case.


This raises the question of how to implement this randomized allocation in practice? One cannot just randomize for each object separately, since this may result in allocations in which some people get many objects while other people get no objects.


The modern formulation of the conjecture relates arithmetic data associated with an elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K (Wiles 2006). The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof.


In object-oriented jargon, abstract datatypes are called classes. However, a class is only a definition; no memory is allocated. When memory is allocated to a class, it's called an object.Object-oriented imperative languages developed by combining the need for classes and the need for safe functional programming.


The Seidel matrix of G is also the adjacency matrix of a signed complete graph KG in which the edges of G are negative and the edges not in G are positive. It is also the adjacency matrix of the two-graph associated with G and KG. The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs.


These would be rendered at the same width as the other single-byte characters, making them half-width kana characters rather than normally proportioned kana. Although the JIS X 0201 standard itself did not specify half-width display for katakana, this became the visually distinguishing feature in Shift JIS between the single-byte JIS X 0201 and double-byte JIS X 0208 katakana. Some IBM code pages used a similar treatment for Korean jamo, based on the N-byte Hangul code and its EBCDIC translation.


In the United Kingdom, the Data Protection Acts and later the Freedom of Information Act 2000 gave patients or their representatives the right to a copy of their record, except where information breaches confidentiality (e.g., information from another family member or where a patient has asked for information not to be disclosed to third parties) or would be harmful to the patient's wellbeing (e.g., some psychiatric assessments). Also, the legislation gives patients the right to check for any errors in their record and insist that amendments be made if required.


The sole aim of the design was to eliminate the mains transformer. The lower cost of transformerless designs remained popular with manufacturers long after DC power distribution had disappeared.


In telecommunication, a coded set is a set of elements onto which another set of elements has been mapped according to a code. Examples of coded sets include the list of names of airports that is mapped onto a set of corresponding three-letter representations of airport names, the list of classes of emission that is mapped onto a set of corresponding standard symbols, and the names of the months of the year mapped onto a set of two-digit decimal numbers. This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.


In the first section, Christian interweaves discussions of the history of artificial intelligence research, particularly the machine learning approach of artificial neural networks such as the Perceptron and AlexNet, with examples of how AI systems can have unintended behavior. He tells the story of Julia Angwin, a journalist whose ProPublica investigation of the COMPAS algorithm, a tool for predicting recidivism among criminal defendants, led to widespread criticism of its accuracy and bias towards certain demographics. One of AI's main alignment challenges is its black box nature (inputs and outputs are identifiable but the transformation process in between is undetermined). The lack of transparency makes it difficult to know where the system is going right and where it is going wrong.


, x 1 , y i − 1 , y i − 2 , . . .


In programming, a docstring is a string literal specified in source code that is used, like a comment, to document a specific segment of code. Unlike conventional source code comments, or even specifically formatted comments like docblocks, docstrings are not stripped from the source tree when it is parsed and are retained throughout the runtime of the program. This allows the programmer to inspect these comments at run time, for instance as an interactive help system, or as metadata. Languages that support docstrings include Python, Lisp, Elixir, Clojure, Gherkin, Julia and Haskell.


(1964–1977). By the early 2010s videotelephony and videophones had become commonplace and unremarkable in various forms of media, in part due to their real and ubiquitous presence in common electronic devices and laptop computers.


It depends on the models, which one to use and requires experience to choose the right one. In most cases, the goal is to estimate the state sequence from the measurements. In other cases, one can use the description to estimate the parameters of a noise process for example.


In mathematics the symmetrization methods are algorithms of transforming a set A ⊂ R n {\displaystyle A\subset \mathbb {R} ^{n}} to a ball B ⊂ R n {\displaystyle B\subset \mathbb {R} ^{n}} with equal volume vol  ( B ) = vol  ( A ) {\displaystyle \operatorname {vol} (B)=\operatorname {vol} (A)} and centered at the origin. B is called the symmetrized version of A, usually denoted A ∗ {\displaystyle A^{*}} . These algorithms show up in solving the classical isoperimetric inequality problem, which asks: Given all two-dimensional shapes of a given area, which of them has the minimal perimeter (for details see Isoperimetric inequality). The conjectured answer was the disk and Steiner in 1838 showed this to be true using the Steiner symmetrization method (described below).


In matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint paths in a directed graph. The concept of a gammoid was introduced and shown to be a matroid by Hazel Perfect (1968), based on considerations related to Menger's theorem characterizing the obstacles to the existence of systems of disjoint paths. Gammoids were given their name by Pym (1969) and studied in more detail by Mason (1972).


In the following the Ranked pairs winner for the first group of voters is determined. The results would be tabulated as follows:  indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption  indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column captionThe sorted list of victories would be: Result: B > C and A > B are locked in first (and C > A can't be locked in after that), so the full ranking is A > B > C. Thus, A is elected Ranked pairs winner by the first group of voters.


In parallel computing, folded cube graphs have been studied as a potential network topology, as an alternative to the hypercube. Compared to a hypercube, a folded cube with the same number of nodes has nearly the same vertex degree but only half the diameter. Efficient distributed algorithms (relative to those for a hypercube) are known for broadcasting information in a folded cube.


It is a tool that postal management uses to redistribute and eliminate overtime costs, based on consultation with the carrier about his/her estimated workload for the day and mail volume projections from the DOIS (Delivery Operations Information System) computer program. Routes are adjusted and/or eliminated based on information (length, time, and overall workload) also controlled by this program, consultations with the carrier assigned to the route, and a current PS Form 3999 (street observation by a postal supervisor to determine accurate times spent on actual delivery of mail). Rural carriers are under a form of salary called "evaluated hours", usually with overtime built into their pay.


In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement. An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on. Experimental uncertainty estimates are needed to assess the confidence in the results. A related field is design of experiments.


In fact, subjects actually named predictable words faster than they did unpredictable words. Whittlesea was able to conclude from this study that subjects misattributed their fast responses for highly predictable words as an indication that they had previously experienced the word whereas in fact that was incorrect. As a result, the fluency of processing caused the subjects to misinterpret their quickness as a case of familiarity.


In mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures.


In most tabletop role-playing games, die rolls required by the system are given in the form AdX. A and X are variables, separated by the letter d, which stands for die or dice. The letter d is most commonly lower-case, but some forms of notation use upper-case D (non-English texts can use the equivalent form of the first letter of the given language's word for "dice", but also often use the English "d"). A is the number of dice to be rolled (usually omitted if 1).


In number theory, Sylvester's sequence is an integer sequence in which each term is the product of the previous terms, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence A000058 in the OEIS).Sylvester's sequence is named after James Joseph Sylvester, who first investigated it in 1880. Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions. The recurrence by which it is defined allows the numbers in the sequence to be factored more easily than other numbers of the same magnitude, but, due to the rapid growth of the sequence, complete prime factorizations are known only for a few of its terms. Values derived from this sequence have also been used to construct finite Egyptian fraction representations of 1, Sasakian Einstein manifolds, and hard instances for online algorithms.


In mid-2001, the Xeon brand was introduced ("Pentium" was dropped from the name). The initial variant that used the new NetBurst microarchitecture, "Foster", was slightly different from the desktop Pentium 4 ("Willamette"). It was a decent chip for workstations, but for server applications it was almost always outperformed by the older Cascades cores with a 2 MB L2 cache and AMD's Athlon MP. Combined with the need to use expensive Rambus Dynamic RAM, the Foster's sales were somewhat unimpressive.


In practice, the easiest way to find an optimal BFS is to use the simplex algorithm. It keeps, at each point of its execution, a "current basis" B (a subset of m out of n variables), a "current BFS", and a "current tableau". The tableau is a representation of the linear program where the basic variables are expressed in terms of the non-basic ones:: 65 where x B {\displaystyle x_{B}} is the vector of m basic variables, x N {\displaystyle x_{N}} is the vector of n non-basic variables, and z {\displaystyle z} is the maximization objective. Since non-basic variables equal 0, the current BFS is p {\displaystyle p} , and the current maximization objective is z 0 {\displaystyle z_{0}} .


Division by a power of 2 is often written as a right-shift, not for optimization as might be assumed, but because the floor of negative results is required. Assuming such shifts are "premature optimization" and replacing them with division can break software.Many programming languages (including C, C++, C#, Java, PHP, R, and Python) provide standard functions for floor and ceiling, usually called floor and ceil, or less commonly ceiling. The language APL uses ⌊x for floor.


The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation A*A = AA* is diagonalizable. The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces. The left and right singular vectors in the singular value decomposition of a normal matrix A = U Σ V ∗ {\displaystyle \mathbf {A} =\mathbf {U} {\boldsymbol {\Sigma }}\mathbf {V} ^{*}} differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values.


Compound or "query-based" operations on groups of identifiers, based on the namespaces in which they are declared, are rendered unwieldy or unfeasible. In languages with restricted identifier length, the use of prefixes limits the number of characters that can be used to identify what the function does. This is a particular problem for packages originally written in FORTRAN 77, which offered only 6 characters per identifier.


Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if R {\displaystyle R} is a square matrix representing a rotation (rotation matrix) and v {\displaystyle \mathbf {v} } is a column vector describing the position of a point in space, the product R v {\displaystyle R\mathbf {v} } yields another column vector describing the position of that point after that rotation. If v {\displaystyle \mathbf {v} } is a row vector, the same transformation can be obtained using v R T {\displaystyle \mathbf {v} R^{\mathsf {T}}} , where R T {\displaystyle R^{\mathsf {T}}} is the transpose of R {\displaystyle R} .


Examples are "sales department", "procurement department", etc. It is represented as an ellipse with a vertical line.Information, material, or resource object In the event-driven process chain, the information, material, or resource objects portray objects in the real world, for example business objects, entities, etc., which can be input data serving as the basis for a function, or output data produced by a function. Examples are "material", "order", etc. In the EPC graph such an object is represented as rectangle.Logical connector In the event-driven process chain the logical relationships between elements in the control flow, that is, events and functions are described by logical connectors. With the help of logical connectors it is possible to split the control flow from one flow to two or more flows and to synchronize the control flow from two or more flows to one flow.Logical relationshipsThere are three kinds of logical relationships defined in event-driven process chains:Branch/Merge: Branch and merge correspond to making decision of which path to choose among several control flows.


In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln  2 , {\displaystyle \ln 2,} and exponential and sine functions. It was proved in 1968 by mathematician and computer scientist Daniel Richardson of the University of Bath. Specifically, the class of expressions for which the theorem holds is that generated by rational numbers, the number π, the number ln 2, the variable x, the operations of addition, subtraction, multiplication, composition, and the sin, exp, and abs functions. For some classes of expressions (generated by other primitives than in Richardson's theorem) there exist algorithms that can determine whether an expression is zero.


In some cases, it is easy to calculate t(G) directly: If G is itself a tree, then t(G) = 1. When G is the cycle graph Cn with n vertices, then t(G) = n. For a complete graph with n vertices, Cayley's formula gives the number of spanning trees as nn − 2. If G is the complete bipartite graph K p , q {\displaystyle K_{p,q}} ,then t ( G ) = p q − 1 q p − 1 {\displaystyle t(G)=p^{q-1}q^{p-1}} . For the n-dimensional hypercube graph Q n {\displaystyle Q_{n}} , the number of spanning trees is t ( G ) = 2 2 n − n − 1 ∏ k = 2 n k ( n k ) {\displaystyle t(G)=2^{2^{n}-n-1}\prod _{k=2}^{n}k^{n \choose k}} .


In mathematics, the Paley–Zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moments. The inequality was proved by Raymond Paley and Antoni Zygmund. Theorem: If Z ≥ 0 is a random variable with finite variance, and if 0 ≤ θ ≤ 1 {\displaystyle 0\leq \theta \leq 1} , then P  ( Z > θ E   ) ≥ ( 1 − θ ) 2 E   2 E   . {\displaystyle \operatorname {P} (Z>\theta \operatorname {E} )\geq (1-\theta )^{2}{\frac {\operatorname {E} ^{2}}{\operatorname {E} }}.}


It is very difficult to support new peers joining part-way through a game. Each peer must communicate with all other peers, limiting the number of connected players. Each peer must wait for every other peer's message before simulating the next "network frame", resulting in all players experiencing the same latency as the player with the worst connection.


When n = 2 r {\displaystyle n=2r} there are other equally-large families, but for larger values of n {\displaystyle n} only the families constructed in this way can be largest. The Erdős–Ko–Rado theorem can also be described in terms of hypergraphs or independent sets in Kneser graphs. Several analogous theorems apply to other kinds of mathematical object than sets, including linear subspaces, permutations, and strings. They again describe the largest possible intersecting families as being formed by choosing an element and forming the family of all objects that contain the chosen element.


}}\right)\\\\&{}=\lambda e^{-\lambda t}-e^{-\lambda t}\sum _{u=1}^{x-1}\left({\frac {\lambda ^{u}t^{u-1}}{(u-1)! }}-{\frac {\lambda ^{u+1}t^{u}}{u! }}\right)\end{aligned}}} The sum telescopes, leaving f ( t ) = λ x t x − 1 e − λ t ( x − 1 ) ! . {\displaystyle f(t)={\frac {\lambda ^{x}t^{x-1}e^{-\lambda t}}{(x-1)!}}.}


A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In this theory an equivalent representation of field is a field particle, for instance a boson.


So, 30 Z {\displaystyle 30\mathbb {Z} } is a semiprime ideal of the integers (because 30 = 2 × 3 × 5, with no repeated prime factors), but 12 Z {\displaystyle 12\mathbb {Z} \,} is not (because 12 = 22 × 3, with a repeated prime factor). The class of semiprime rings includes semiprimitive rings, prime rings and reduced rings. Most definitions and assertions in this article appear in (Lam 1999) and (Lam 2001).


In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime power or twice a prime power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.


In the Unicode standard, the symbol £ is called POUND SIGN, and the symbol ₤ is the LIRA SIGN. These have respective code points: U+00A3 £ POUND SIGN (£ · inherited from Latin-1) U+20A4 ₤ LIRA SIGNUnicode notes that the "lira sign" is not widely used and was added due to both it and the pound sign being available on HP printers.The encoding of the £ symbol in position xA3 (16310) was first standardised by ISO Latin-1 (an "extended ASCII") in 1985. Position xA3 was used by the Digital Equipment Corporation VT220 terminal, Mac OS Roman, Amstrad CPC, Amiga, and Acorn Archimedes. Many early computers (limited to a 7-bit, 128-position character set) used a variant of ASCII with one of the less-frequently used characters replaced by the £.


In netstalking, there are two general methods for finding unusual information: a deli-search and a net-random. Deli-search, or "deliberated search", is a targeted search for objects of interest whose characteristics are already known. This method usually uses the language of search queries and web archives, with which one can view old or deleted versions of these pages. Net-random searches for hidden and unknown information through the process of trial and error.


The b {\displaystyle b} on the right-hand side can also be written as b 1 {\displaystyle b^{1}} , giving b r + r = b 1 {\displaystyle b^{r+r}=b^{1}} . Equating the exponents on both sides, we have r + r = 1 {\displaystyle r+r=1} .


In the age of information, the amount of the written material we encounter each day is simply beyond our processing capacity. Topic models can help to organize and offer insights for us to understand large collections of unstructured text bodies. Originally developed as a text-mining tool, topic models have been used to detect instructive structures in data such as genetic information, images, and networks. They also have applications in other fields such as bioinformatics and computer vision.


If the components of the gradient of a function f {\displaystyle f} , ( ∇ f ) i {\displaystyle (\nabla f)^{i}} , are expressed in terms of a given basis, e i {\displaystyle \mathbf {e} _{i}} , then these components will in fact still vary oppositely to that of the basis vectors, as can be seen by observing (using the Einstein summation convention): where δ j i {\displaystyle \delta _{j}^{i}} is the kronecker delta symbol, and ( T ) k i {\displaystyle (T)_{k}^{i}} represents the components of some transformation matrix corresponding to the transformation T {\displaystyle T} . As can be seen, whatever transformation acts on the basis vectors, the inverse transformation must act on the components. A third concept related to covariance and contravariance is invariance.


In mathematics, the free matroid over a given ground-set E is the matroid in which the independent sets are all subsets of E. It is a special case of a uniform matroid. The unique basis of this matroid is the ground-set itself, E. Among matroids on E, the free matroid on E has the most independent sets, the highest rank, and the fewest circuits.


In the United Kingdom, mobile phone network providers are not obliged to provide unlocking, even after the end of the contract. Ofcom, UK's telecom regulator, allowed 3 UK to sell a mobile phone with the SIM card permanently superglued to the phone. Most operators offer some form of unlocking service, depending on the state of the contract and the model of phone, but usually for a charge. The full Oftel 2002 SIM-lock position paper specifies that there is no SIM-locking law in the UK; the regulator wants only "consumer awareness".


Following is another example: TABLE 1 The join dependencies of the table are {medic name, occupation}, {medic name, practice in years} and {medic name, type}. Hence we could see that such table is 2NF (due to the appearance of transitive dependency). The following tables try to bring it to 6NF: TABLE 2.1 TABLE 2.2 TABLE 2.3 TABLE 2.4


In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way.


In simple cases, the user can compute the path delay between elements manually. If the design is more than a dozen or so elements this is impractical. For example, the time delay along a path from the output of a D-Flip Flop, through combinatorial logic gates, then into the next D-Flip Flop input must satisfy (be less than) the time period between synchronizing clock pulses to the two flip flops. When the delay through the elements is greater than the clock cycle time, the elements are said to be on the critical path.


In recent years the model formulating approach of considering a "typical user" in cellular (or other) networks has been used considerably. This is, however, just a first approach which allows one to characterize only the spectral efficiency (or information rate) of the network. In other words, this approach captures the best possible service that can be given to a single user who does not need to share wireless network resources with other users. Models beyond the typical user approach have been proposed with the aim of analyzing QoS metrics of a population of users, and not just a single user.


Over a perfect field of non-zero characteristic p, this quotient is the product of the a i {\displaystyle a_{i}} such that i is not a multiple of p. Further GCD computations and exact divisions allow computing the square-free factorization (see square-free factorization over a finite field). In characteristic zero, a better algorithm is known, Yun's algorithm, which is described below. Its computational complexity is, at most, twice that of the GCD computation of the input polynomial and its derivative. More precisely, if T n {\displaystyle T_{n}} is the time needed to compute the GCD of two polynomials of degree n {\displaystyle n} and the quotient of these polynomial by the GCD, then 2 T n {\displaystyle 2T_{n}} is an upper bound for the time needed to compute the square free decomposition. There are also known algorithms for the computation of the square-free decomposition of multivariate polynomials, that proceed generally by considering a multivariate polynomial as a univariate polynomial with polynomial coefficients, and applying recursively a univariate algorithm.


However, the size of each table does not change, so both table and directory now have only 512 entries. Because this allows only one half of the entries of the original scheme, an extra level of hierarchy has been added, so CR3 now points physically to a Page Directory Pointer Table, a short table containing four pointers to page directories. Supporting 64 bit addresses in the page-table is a significant change as this enables two changes to the processor addressing.


In mathematics, especially homotopy theory, the mapping cone is a construction C f {\displaystyle C_{f}} of topology, analogous to a quotient space. It is also called the homotopy cofiber, and also notated C f {\displaystyle Cf} . Its dual, a fibration, is called the mapping fibre. The mapping cone can be understood to be a mapping cylinder M f {\displaystyle Mf} , with one end of the cylinder collapsed to a point. Thus, mapping cones are frequently applied in the homotopy theory of pointed spaces.


In the field of Information theory Shannon entropy is defined to quantify the complexity of a distribution p as p log  p {\displaystyle p\log p\,} . Therefore, higher entropy means p is more complex hence more unpredictable. To measure the complexity of an image region { x , R } {\displaystyle \{x,R\}} around point x {\displaystyle x} with shape R {\displaystyle R} , a descriptor D {\displaystyle D} that takes on values d 1 , … , d r {\displaystyle {d_{1},\dots ,d_{r}}} (e.g., in an 8 bit grey level image, D would range from 0 to 255 for each pixel) is defined so that P D ( d i , x , R ) {\displaystyle P_{D}(d_{i},x,R)} , the probability of descriptor value d i {\displaystyle d_{i}} occurs in region { x , R } {\displaystyle \{x,R\}} can be computed. Further, the entropy of image region R x {\displaystyle R_{x}} can compute as H D ( x , R ) = − ∑ i ∈ ( 1 … r ) P D ( d i , x , R ) log  P D ( d i , x , R ) .


In physics, it is conventional to denote a Lorentz transformation Λ ∈ SO +  ( 1 , 3 ) {\displaystyle \Lambda \in \operatorname {SO} ^{+}(1,3)} as Λ μ ν , {\displaystyle {\Lambda ^{\mu }}_{\nu }~,} thus showing the matrix with spacetime indexes μ , ν = 0 , 1 , 2 , 3. {\displaystyle \mu ,\nu =0,1,2,3.} A four-vector can be created from the Pauli matrices in two different ways: as σ μ = ( I , σ → ) {\displaystyle \sigma ^{\mu }=(I,{\vec {\sigma }})} and as σ ¯ μ = ( I , − σ → ) .


In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional or planar space.


In number theory, a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that a m ≡ 1 ( mod n ) {\displaystyle a^{m}\equiv 1{\pmod {n}}} holds for every integer a coprime to n. In algebraic terms, λ(n) is the exponent of the multiplicative group of integers modulo n. The Carmichael function is named after the American mathematician Robert Carmichael who defined it in 1910. It is also known as Carmichael's λ function, the reduced totient function, and the least universal exponent function. The following table compares the first 36 values of λ(n) (sequence A002322 in the OEIS) with Euler's totient function φ (in bold if they are different; the ns such that they are different are listed in OEIS: A033949).


The most prominent of these models has been the Penn Discourse Treebank (PDTB). PDTB is focusing on the annotation of discourse cues (discourse markers, discourse connectives), which are assigned an internal argument (to which the discourse marker is attached), an external argument (target or attachment point of the relation) and a sense (discourse relation). Both arguments are defined as the smallest string that expresses the meaning of the utterances to be connected.


It was an upgrade path for users who had outgrown the IBM System/3. It ran Cobol-74, RPG2, Fortran, and Assembler. The instruction set of the 90/xx series was implemented in microcode and was loaded into control storage as part of the boot up process, before loading the operating system.Shortly after the 90/30 was introduced, Sperry Univac introduced the 90/25 which was the same basic hardware, however had an option for a smaller 80 column card reader and was a bit slower.


A common variant on the RISC design employs the Harvard architecture, versus Von Neumann architecture or stored program architecture common to most other designs. In a Harvard Architecture machine, the program and data occupy separate memory devices and can be accessed simultaneously. In Von Neumann machines, the data and programs are mixed in one memory device, requiring sequential accessing which produces the so-called Von Neumann bottleneck.


In these examples, the ranks are assigned to values in ascending order. (In some other cases, descending ranks are used.) Ranks are related to the indexed list of order statistics, which consists of the original dataset rearranged into ascending order.


In order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. An example would be where one is given one positive x2 tile, three positive x tiles, and two positive unit tiles. The student forms the rectangle by having the x2 tile in the upper right corner, then one has two x tiles on the right side of the x2 tile, one x tile underneath the x2 tile, and two unit tiles are in the bottom right corner.


In order to bound the time complexity of the algorithm, we must analyze the number of push and relabel operations which occur within the main loop. The numbers of relabel, saturating push and nonsaturating push operations are analyzed separately. In the algorithm, the relabel operation can be performed at most (2| V | − 1)(| V | − 2) < 2| V |2 times. This is because the labeling 𝓁(u) value for any node u can never decrease, and the maximum label value is at most 2| V | − 1 for all nodes.


And edges connect different types of nodes (i.e. actors to movies) if they have a relationship (actors in a movie). Initially the network was found to have a small-world property. Afterwards, it was discovered that it exhibits a scale-free (power-law) behavior.The parlor game of Six Degrees of Kevin Bacon involves finding paths in this network from specified actors to Kevin Bacon.


In terms of integer operations, the PRISM architecture was similar to the MIPS designs. Of the 32-bits in the instructions, the 6 highest and 5 lowest bits were the instruction, leaving the other 21 bits of the word for encoding either a constant or register locations. Sixty-four 32-bit registers were included, as opposed to thirty-two in the MIPS, but usage was otherwise similar. PRISM and MIPS both lack the register windows that were a hallmark of the other major RISC design, Berkeley RISC.


In the domain of computer vision, efforts have been made to model the mechanism of human attention, especially the bottom-up intentional mechanism and its semantic significance in classification of video contents. Both spatial attention and temporal attention have been incorporated in such classification efforts. Generally speaking, there are two kinds of models to mimic the bottom-up salience mechanism in static images.


In terms of components, let A = A i d x i , {\displaystyle A=A_{i}dx^{i},} where d x i {\displaystyle dx^{i}} is the standard one-form coordinate bases on the cotangent bundle T*M. Inserting into the above, and expanding, one obtains (using the summation convention): F = 1 2 ( ∂ A j ∂ x i − ∂ A i ∂ x j +  ) d x i ∧ d x j . {\displaystyle F={\frac {1}{2}}\left({\frac {\partial A_{j}}{\partial x^{i}}}-{\frac {\partial A_{i}}{\partial x^{j}}}+\right)dx^{i}\wedge dx^{j}.} Keep in mind that for an n-dimensional vector space, each A i {\displaystyle A_{i}} is an n×n matrix, the indices of which have been suppressed, whereas the indices i and j run over 1,...,m, with m being the dimension of the underlying manifold. Both of these indices can be made simultaneously manifest, as shown in the next section. The notation presented here is that which is commonly used in physics; for example, it can be immediately recognizable as the gluon field strength tensor. For the abelian case, n=1, and the vector bundle is one-dimensional; the commutator vanishes, and the above can then be recognized as the electromagnetic tensor in more or less standard physics notation.


However, they are only assumed identical or nearly identical in musical set theory. Sets are said to be inversionally symmetrical if they map onto themselves under inversion. The pitch that the sets must be inverted around is said to be the axis of symmetry (or center).


Find k ∈ Z {\displaystyle k\in \mathbb {Z} } such that p = r + k ⋅ q {\displaystyle p=r+k\cdot q} is a P {\displaystyle P} -bit prime with p ≡ 2 mod 3 {\displaystyle p\equiv 2\ {\text{mod}}\ 3} .Correctness of Algorithm A:It remains to check that q ∣ p 2 − p + 1 {\displaystyle q\mid p^{2}-p+1} because all the other necessary properties are obviously satisfied per definition of p {\displaystyle p} and q {\displaystyle q} . We easily see that p 2 − p + 1 = r 2 + 2 r k q + k 2 q 2 − r − k q + 1 = r 2 − r + 1 + q ( 2 r k + k 2 q − k ) = q ( 1 + 2 r k + k 2 q − k ) {\displaystyle p^{2}-p+1=r^{2}+2rkq+k^{2}q^{2}-r-kq+1=r^{2}-r+1+q(2rk+k^{2}q-k)=q(1+2rk+k^{2}q-k)} which implies that q ∣ p 2 − p + 1 {\displaystyle q\mid p^{2}-p+1} .Algorithm A is very fast and can be used to find primes p {\displaystyle p} that satisfy a degree-two polynomial with small coefficients. Such p {\displaystyle p} lead to fast arithmetic operations in G F ( p ) {\displaystyle GF(p)} .


In the background there is an update stream that runs a series of insert/delete operations (one pair for each query user). The choice of the number of users is at the discretion of the test sponsor. The throughput metric is computed as the total amount of work (S×17), converted to hours from seconds (3600 seconds per hour), scaled by the database volume (SF) and divided by the total elapsed time (Ts) required between the first query starting and the last query or update function completing. Therefore, the complete formulation is: Q t h D = S × 17 × 3600 T s × S F {\displaystyle {\mathit {QthD}}={\frac {S\times 17\times 3600}{T_{s}}}\times {\mathit {SF}}} == References ==


To generate this distribution experimentally, we have to repeat the experiment until it happens to give n balls. If we want to fix the value of n prior to the experiment then we have to take the balls one by one until we have n balls. The balls are therefore no longer independent.


In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution is used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t-distribution, or light (in comparison with the normal distribution). Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are also used in robust statistics to evaluate proposed multivariate-statistical procedures.


In the Hermite polynomial Hen(x) of variance 1, the absolute value of the coefficient of xk is the number of (unordered) partitions of an n-element set into k singletons and n − k/2 (unordered) pairs. Equivalently, it is the number of involutions of an n-element set with precisely k fixed points, or in other words, the number of matchings in the complete graph on n vertices that leave k vertices uncovered (indeed, the Hermite polynomials are the matching polynomials of these graphs). The sum of the absolute values of the coefficients gives the total number of partitions into singletons and pairs, the so-called telephone numbers 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496,... (sequence A000085 in the OEIS).This combinatorial interpretation can be related to complete exponential Bell polynomials as where xi = 0 for all i > 2. These numbers may also be expressed as a special value of the Hermite polynomials:


While classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an ontology. Metaclasses are supported in the ontology language OWL and the data-modeling vocabulary RDFS. Metaclasses are often modeled by setting them as the object of claims involving rdf:type and rdfs:subClassOf—built-in properties commonly referred to as instance of and subclass of.


In the United Kingdom, the term "back-to-back agreement" refers to an NDA entered into with a third party who legitimately receives confidential information, putting them under similar non-disclosure obligations as the initial party granted the information. Case law in a 2013 Court of Appeal decision (Dorchester Project Management v BNP Paribas) confirmed that a confidentiality agreement will be interpreted as a contract subject to the rules of contractual interpretation which generally apply in the English courts.NDAs are often used as a condition of a financial settlement in an attempt to silence whistleblowing employees from making public the misdeeds of their former employers. There is law, the Public Interest Disclosure Act 1998, which allows "protected disclosure" despite the existence of an NDA, although employers sometimes intimidate the former employee into silence despite this.


In the fields of computational linguistics and applied linguistics, a morphological dictionary is a linguistic resource that contains correspondences between surface form and lexical forms of words. Surface forms of words are those found in natural language text. The corresponding lexical form of a surface form is the lemma followed by grammatical information (for example the part of speech, gender and number).


Store: Data-collection or some sort of material. Flow: Movement of data or material in the process. External Entity: External to the modeled system, but interacts with it.Now, with these symbols, a process can be represented as a network of these symbols. This decomposed process is a DFD, data flow diagram. In Dynamic Enterprise Modeling a division is made in the Control model, Function Model, Process model and Organizational model.


With object-oriented programming the memory objects are often stored dynamically on the heap but modern operating systems use address space layout randomization (ASLR). Therefore, the only way to modify such memory in a reproducible manner is to get information from inside the game process. This requires reverse engineering methods like API hooking of malloc() and free(), code injection or searching for static access pointers.


This problem has initialized a significant effort in developing automated detection methods for misinformation on social media platforms.Social media platforms allow for easy spread of misinformation. The specific reasons why misinformation spreads through social media so easily remain unknown. A 2018 study of Twitter determined that, compared to accurate information, false information spread significantly faster, further, deeper, and more broadly.


In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL(H) are homotopic to a constant, for the norm topology on operators. A significant corollary, also referred to as Kuiper's theorem, is that this group is weakly contractible, ie. all its homotopy groups are trivial. This result has important uses in topological K-theory.


In network science, the strength notated as si of a node i is defined as si = Σjwij, where wij is the weight of the link between i and j. In order to apply the disparity filter algorithm without overlooking nodes with low strength, a normalized weight pij is defined as pij = wij/si. In the null model, the normalized weights of a certain node with degree k is generated like this: k − 1 pins are randomly assigned between the interval 0 and 1. The interval is then divided into k subintervals. The length of the subinterval represents the normalized weight of each link in the null model. Consecutively, and based on the null model, we can derive that the normalized weight distribution of a node with degree k follows ρ ( x ) d x = ( k − 1 ) ( 1 − x ) k − 2 d x {\displaystyle \rho (x)\,dx=(k-1)(1-x)^{k-2}\,dx} .


In the case where a parametrized family has a location parameter, a slightly different definition is often used as follows. If we denote the location parameter by m {\displaystyle m} , and the scale parameter by s {\displaystyle s} , then we require that F ( x ; s , m , θ ) = F ( ( x − m ) / s ; 1 , 0 , θ ) {\displaystyle F(x;s,m,\theta )=F((x-m)/s;1,0,\theta )} where F ( x , s , m , θ ) {\displaystyle F(x,s,m,\theta )} is the cmd for the parametrized family. This modification is necessary in order for the standard deviation of a non-central Gaussian to be a scale parameter, since otherwise the mean would change when we rescale x {\displaystyle x} . However, this alternative definition is not consistently used.


In the examination of individual scripts, the study of writing systems has developed along partially independent lines. Thus, the terminology employed differs somewhat from field to field.


Some terminals and editing programs could not deal with double-byte characters starting at odd columns, only even ones (some could not even put double-byte and single-byte characters in the same line). So the DBCS sets generally included Roman characters and digits also, for use alongside the CJK characters in the same line. On the other hand, early Japanese computing used a single-byte code page called JIS X 0201 for katakana.


In software engineering, these activities are known as software maintenance (cf. ISO/IEC 9126). Closely related concepts in the software engineering domain are evolvability, modifiability, technical debt, and code smells. The maintainability index is calculated with certain formulae from lines-of-code measures, McCabe measures and Halstead complexity measures. The measurement and tracking of maintainability are intended to help reduce or reverse a system's tendency toward "code entropy" or degraded integrity, and to indicate when it becomes cheaper and/or less risky to rewrite the code than it is to change it.


In proof theory, the semantic tableau (; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics (Girle 2000).


An algorithm is a formal procedure in which each step is clearly defined. It guarantees success if applied correctly. The long multiplication usually taught in school is an example of an algorithm for solving the problem of multiplying big numbers.


In mathematics, a ranked partially ordered set or ranked poset may be either: a graded poset, or a poset with the property that for every element x, all maximal chains among those with x as greatest element have the same finite length, or a poset in which all maximal chains have the same finite length.The second definition differs from the first in that it requires all minimal elements to have the same rank; for posets with a least element, however, the two requirements are equivalent. The third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank. Richard P. Stanley defines a graded poset of length n as one in which all maximal chains have length n. == References ==


Many other shock-related changes take place within both impactor and target as the shock wave passes through, and some of these changes can be used as diagnostic tools to determine whether particular geological features were produced by impact cratering.As the shock wave decays, the shocked region decompresses towards more usual pressures and densities. The damage produced by the shock wave raises the temperature of the material. In all but the smallest impacts this increase in temperature is sufficient to melt the impactor, and in larger impacts to vaporize most of it and to melt large volumes of the target. As well as being heated, the target near the impact is accelerated by the shock wave, and it continues moving away from the impact behind the decaying shock wave.


In occupational health and safety, a tagging system is a system of recording and displaying the status of a machine or equipment, enabling staff to view whether it is in working order. It is a product of industry-specific legislation which sets safety standards for a particular piece of equipment, involving inspection, record-keeping, and repair. This sets standardized umbrella terms for equipment and machinery (e.g. machinery, scaffolding, forklift, cherry picker) to be deemed 'safe to use'.


In some circumstances, the "pre-" in preadaptation can be interpreted as applying, for non-teleological reasons, prior to the adaptation itself, creating a meaning for the term that is distinct from exaptation. For example, future environments (say, hotter or drier ones), may resemble those already encountered by a population at one of its current spatial or temporal margins. This is not actual foresight, but rather the luck of having adapted to a climate which later becomes more prominent. Cryptic genetic variation may have the most strongly deleterious mutations purged from it, leaving an increased chance of useful adaptations, but this represents selection acting on current genomes with consequences for the future, rather than foresight. Function may not always come before form: developed structures could change or alter the primary functions they were intended for due to some structural or historical cause.


{\displaystyle n=1,2,...} , to converge to a minimum, provided such a minimum exists and p n {\displaystyle \mathbf {p} _{n}} is selected appropriately in each step. For gradient descent, p n {\displaystyle \mathbf {p} _{n}} is selected as − ∇ f ( x n ) {\displaystyle -\nabla f(\mathbf {x} _{n})} . The value of α j {\displaystyle \alpha _{j}} for the j {\displaystyle j} that fulfills the Armijo–Goldstein condition depends on x {\displaystyle \mathbf {x} } and p {\displaystyle \mathbf {p} } , and is thus denoted below by α ( x , p ) {\displaystyle \alpha (\mathbf {x} ,\mathbf {p} )} .


A page table maps virtual memory to physical memory. There may be a single page table, a page table for each process, a page table for each segment, or a hierarchy of page tables, depending on the architecture and the OS. The page tables are usually invisible to the process.


In subjective testing, implicit learning occurs when participants who show above chance performance have no knowledge of their judgements. Subjects who are theorized to have no knowledge of their judgements generally are convinced that their judgements are guesses and will have an accuracy rate that has little correlation with their ratings of confidence they assigned to each of their judgements. In artificial grammar learning and sequence learning participants showed higher than chance performance. These participants were convinced that they were only making assumptions and had no real knowledge of the subject. Results usually showed that in reality, they had gained implicit knowledge throughout the experiment.