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The Journal of Experimental and Theoretical Artificial Intelligence is a quarterly peer-reviewed scientific journal published by Taylor and Francis. It covers all aspects of artificial intelligence and was established in 1989. The editor-in-chief is Eric Dietrich (Binghamton University), the deputy editors-in-chief are...
Journal of Experimental and Theoretical Artificial Intelligence
0.823749
6,701
The use of radiometers to determine the temperature of objects and gasses by measuring radiation flux is called pyrometry. Handheld pyrometer devices are often marketed as infrared thermometers. Radiometry is important in astronomy, especially radio astronomy, and plays a significant role in Earth remote sensing. The m...
Spectral radiometric quantity
0.82374
6,702
In the figure to the right, the left circuit can be satisfied by setting both inputs to be 1, but the right circuit is unsatisfiable. CircuitSAT is closely related to Boolean satisfiability problem (SAT), and likewise, has been proven to be NP-complete. It is a prototypical NP-complete problem; the Cook–Levin theorem i...
Circuit satisfiability problem
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6,703
In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true. In other words, it asks whether the inputs to a given Boolean circuit...
Circuit satisfiability problem
0.823735
6,704
Physicists have pondered whether the fine-structure constant is in fact constant, or whether its value differs by location and over time. A varying α has been proposed as a way of solving problems in cosmology and astrophysics.String theory and other proposals for going beyond the Standard Model of particle physics hav...
Fine Structure Constant
0.823733
6,705
Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887,Arnold Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fi...
Fine Structure Constant
0.823732
6,706
You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out – without putting it in secretly! Conversely,...
Fine Structure Constant
0.823732
6,707
Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans.
Fine Structure Constant
0.823732
6,708
As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long fascinated physicists. Arthur Eddington argued that the value could be "obtained by pure deduction" and he related it to the Eddington number, his estimate of the number of protons i...
Fine Structure Constant
0.823732
6,709
A low voltage system used for telecommunications networking is not the same as a low voltage network. The information technology sector of electrical installations is used for computer networking, telephones, television, security systems, audio distribution, healthcare systems, robotics, and more. These services are ty...
Mechanical, electrical, and plumbing
0.823732
6,710
In countries of Asia such as Pakistan, China and Saudi Arabia the use of MEP is increasing in building construction projects due to extreme climates in summer and winter. For example, a plumber may select and install a commercial hot water system based on common practice and regulatory codes. A team of MEP engineers wi...
Mechanical, electrical, and plumbing
0.823732
6,711
For example, consider the following expression in which both variables are bound by logical quantifiers: ∀ y ∃ x ( x = y ) . {\displaystyle \forall y\,\exists x\,\left(x={\sqrt {y}}\right).} This expression evaluates to false if the domain of x {\displaystyle x} and y {\displaystyle y} is the real numbers, but true if ...
Bound variable
0.823724
6,712
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a...
Bound variable
0.823724
6,713
The Knowledge Machine is a concept of Seymour Papert, which is intended to enable children to explore any situation and engage them completely. Although Papert never clearly defined the Knowledge Machine, one interpretation is a virtual reality device that allows the user to slip into any situation and have a simulated...
Knowledge Machine
0.823718
6,714
Radio Science is a quarterly peer-reviewed scientific journal published by Wiley-Blackwell on behalf of the American Geophysical Union and co-sponsored by the International Union of Radio Science. It contains original scientific contributions on radio-frequency electromagnetic propagation and its applications (radio sc...
Radio Science
0.823713
6,715
He also introduced some basic notation (congruences) and devoted a section to computational matters, including primality tests. The last section of the Disquisitiones established a link between roots of unity and number theory: The theory of the division of the circle...which is treated in sec. 7 does not belong by its...
Elementary number theory
0.823711
6,716
In his old age, he was the first to prove Fermat's Last Theorem for n = 5 {\displaystyle n=5} (completing work by Peter Gustav Lejeune Dirichlet, and crediting both him and Sophie Germain). In his Disquisitiones Arithmeticae (1798), Carl Friedrich Gauss (1777–1855) proved the law of quadratic reciprocity and developed ...
Elementary number theory
0.823711
6,717
Joseph-Louis Lagrange (1736–1813) was the first to give full proofs of some of Fermat's and Euler's work and observations—for instance, the four-square theorem and the basic theory of the misnamed "Pell's equation" (for which an algorithmic solution was found by Fermat and his contemporaries, and also by Jayadeva and B...
Elementary number theory
0.823711
6,718
In some ways, the history of programming language theory predates even the development of programming languages themselves. The lambda calculus, developed by Alonzo Church and Stephen Cole Kleene in the 1930s, is considered by some to be the world's first programming language, even though it was intended to model compu...
Programming language research
0.823704
6,719
Type theory became applied as a discipline to programming languages, this application has led to tremendous advances in type theory over the years.1980sIn 1981, Gordon Plotkin publishes his paper on structured operational semantics. In 1988, Gilles Kahn published his paper on natural semantics. There emerged process ca...
Programming language research
0.823704
6,720
In 1969, William Alvin Howard observed that a "high-level" proof system, referred to as natural deduction, can be directly interpreted in its intuitionistic version as a typed variant of the model of computation known as lambda calculus. This became known as the Curry–Howard correspondence.1970sIn 1970, Dana Scott firs...
Programming language research
0.823704
6,721
Some other key events in the history of programming language theory since then: 1950sNoam Chomsky developed the Chomsky hierarchy in the field of linguistics, a discovery which has directly impacted programming language theory and other branches of computer science.1960sThe Simula language was developed by Ole-Johan Da...
Programming language research
0.823704
6,722
S–R compatibility is an important consideration in the field of human-computer interaction, and in software engineering. Programs are easier and more intuitive to use when the input of the user and the output of the program are S–R-compatible. This would also be an important consideration in the physical design of obje...
Stimulus–response compatibility
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6,723
For example, if the only expected effect of a medical test is to make one disease more likely than another, but the two diseases have the same treatment (or neither can be treated), then ri = 0 and the test is essentially without any benefit for the individual. Additional factors that influence a decision whether a med...
Post-test probabilities
0.823689
6,724
In the two most important implementations the neighborhood of generalization either varies with the training sample (CC1 network) or remains constant (CC4 network). These networks use unary coding for an effective representation of the data sets.This type of network was first proposed in a 1993 paper of Subhash Kak. Si...
Instantaneously trained neural networks
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6,725
Instantaneously trained neural networks are feedforward artificial neural networks that create a new hidden neuron node for each novel training sample. The weights to this hidden neuron separate out not only this training sample but others that are near it, thus providing generalization. This separation is done using t...
Instantaneously trained neural networks
0.823689
6,726
Small RNAs include several different classes of noncoding RNAs, depending on their sizes and functions: snRNA, snoRNA, scRNA, piRNA, miRNA, YRNA, tsRNA, rsRNA, and siRNA. Their functions go from RNAi (specific for endogenously expressed miRNA and exogenously derived siRNA), RNA processing and modification, gene silenci...
Small RNA sequencing
0.823687
6,727
Assuming that nature is described by a so-called Grand Unified Theory (GUT), the grand unification epoch began with a phase transition of this kind, when gravitation separated from the universal combined gauge force. This caused two forces to now exist: gravity, and an electrostrong interaction. There is no hard eviden...
Planck epoch
0.823686
6,728
It is not clear how this came about. Any explanation for this phenomenon must allow the Sakharov conditions related to baryogenesis to have been satisfied at some time after the end of cosmological inflation. Current particle physics suggests asymmetries under which these conditions would be met, but these asymmetries ...
Planck epoch
0.823686
6,729
Selection and amplification binding assay (SAAB) is a molecular biology technique typically used to find the DNA binding site for proteins. It was developed by T. Keith Blackwell and Harold M. Weintraub in 1990.
Selection and amplification binding assay
0.823683
6,730
(ii) Suppose the dual problem (D-SDP) is bounded above and strictly feasible (i.e., ∑ i = 1 m ( y 0 ) i A i ≺ C {\displaystyle \sum _{i=1}^{m}(y_{0})_{i}A_{i}\prec C} for some y 0 ∈ R m {\displaystyle y_{0}\in \mathbb {R} ^{m}} ). Then there is an optimal solution X ∗ {\displaystyle X^{*}} to (P-SDP) and the equality f...
Semidefinite program
0.823678
6,731
SDPs are in fact a special case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as SDPs, and via hierarchies of SDPs the solutions of polynomial optimization problems can be approximated. Semidefinite programming has been ...
Semidefinite program
0.823678
6,732
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semi...
Semidefinite program
0.823678
6,733
First-order methods for conic optimization avoid computing, storing and factorizing a large Hessian matrix and scale to much larger problems than interior point methods, at some cost in accuracy. A first-order method is implemented in the Splitting Cone Solver (SCS). Another first-order method is the alternating direct...
Semidefinite program
0.823678
6,734
There is also Bell's theorem: no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. While an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single counterexample. Such a counterexample would re...
Impossibility proof
0.823675
6,735
In natural science, impossibility assertions (like other assertions) come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underly...
Impossibility proof
0.823675
6,736
A problem that arose in the 16th century was creating a general formula using radicals to express the solution of any polynomial equation of fixed degree k, where k ≥ 5. In the 1820s, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) showed this to be impossible, using concepts such as solvable grou...
Impossibility proof
0.823675
6,737
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Proofs of im...
Impossibility proof
0.823675
6,738
To quote Nagel and Newman (p. 68), "Gödel's paper is difficult. Forty-six preliminary definitions, together with several important preliminary theorems, must be mastered before the main results are reached".
Impossibility proof
0.823675
6,739
Three famous questions of Greek geometry were how: to trisect any angle using a compass and a straightedge, to construct a cube with a volume twice the volume of a given cube, to construct a square equal in area to that of a given circle.For more than 2,000 years unsuccessful attempts were made to solve these problems;...
Impossibility proof
0.823675
6,740
It is unknown when, or by whom, the "theorem of Pythagoras" was discovered. The discovery can hardly have been made by Pythagoras himself, but it was certainly made in his school. Pythagoras lived about 570–490 BCE.
Impossibility proof
0.823675
6,741
The Gauss-Wantzel theorem showed in 1837 that constructing an equilateral n-gon is impossible for most values of n.
Impossibility proof
0.823675
6,742
Gödel's incompleteness theorems were other examples that uncovered fundamental limitations in the provability of formal systems.In computational complexity theory, techniques like relativization (the addition of an oracle) allow for "weak" proofs of impossibility, in that proofs techniques that are not affected by rela...
Impossibility proof
0.823675
6,743
It shows that it is impossible to express the square root of 2 as a ratio of two integers. Another consequential proof of impossibility was Ferdinand von Lindemann's proof in 1882, which showed that the problem of squaring the circle cannot be solved because the number π is transcendental (i.e., non-algebraic), and tha...
Impossibility proof
0.823675
6,744
Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility.
Impossibility proof
0.823675
6,745
The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves. If the viewing distance is large compared with the separation of the slits (the far field), the phase difference can be found using the geometry shown in the figure below right. The path difference ...
Double-slit experiment
0.823672
6,746
By definition, the depth of a local ring R {\displaystyle R} with a maximal ideal m {\displaystyle {\mathfrak {m}}} is its m {\displaystyle {\mathfrak {m}}} -depth as a module over itself. If R {\displaystyle R} is a Cohen-Macaulay local ring, then depth of R {\displaystyle R} is equal to the dimension of R {\displayst...
Depth (algebra)
0.823667
6,747
The other equation of state of an ideal gas must express Joule's second law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature, with U = U ( n , T ) {\displaystyle U=U(n,T)} . For the present purposes it is convenient to postulate an exemplary version of this law by writing: U ...
Ideal gases
0.823661
6,748
The dimensionless heat capacity at constant volume is generally defined by c ^ V = 1 n R T ( ∂ S ∂ T ) V = 1 n R ( ∂ U ∂ T ) V {\displaystyle {\hat {c}}_{V}={\frac {1}{nR}}T\left({\frac {\partial S}{\partial T}}\right)_{V}={\frac {1}{nR}}\left({\frac {\partial U}{\partial T}}\right)_{V}} where S is the entropy. This qu...
Ideal gases
0.823661
6,749
In quantum mechanics as formulated by Schrödinger, physical variables are represented by linear operators such as x {\displaystyle x} (meaning multiply by x {\displaystyle x} ), and d d x {\textstyle {\frac {d}{dx}}} . These two operators do not commute as may be seen by considering the effect of their compositions x d...
Commutative operation
0.823653
6,750
To tackle this issue some researchers use distribution of travel time instead of expected value of it so they find the probability distribution of total travelling time using different optimization methods such as dynamic programming and Dijkstra's algorithm . These methods use stochastic optimization, specifically sto...
Shortest-distance problems
0.823637
6,751
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest...
Shortest-distance problems
0.823637
6,752
In the context of continuous optimization, individual learning exists in the form of local heuristics or conventional exact enumerative methods. Examples of individual learning strategies include the hill climbing, Simplex method, Newton/Quasi-Newton method, interior point methods, conjugate gradient method, line searc...
Memetic algorithms
0.823629
6,753
A memetic algorithm (MA) in computer science and operations research, is an extension of the traditional genetic algorithm (GA) or more general evolutionary algorithm (EA). It may provide a sufficiently good solution to an optimization problem. It uses a suitable heuristic or local search technique to improve the quali...
Memetic algorithms
0.823629
6,754
where they state: There should be two "dual equivalent" field formulations of the same theory in which electric (Noether) and magnetic (topological) quantum numbers exchange roles. S-duality is now a basic ingredient in topological quantum field theories and string theories, especially since the 1990s with the advent o...
Electric-magnetic duality
0.823618
6,755
Personally, I would bet that this kind of anti-reductionist behaviour is true in any consistent synthesis of quantum mechanics and gravity.The first conclusion is that Dirac’s explanation of charge quantisation is triumphantly vindicated. At first sight it seemed as if the idea of unification provided an alternative ex...
Electric-magnetic duality
0.823618
6,756
The Montonen–Olive duality throws into question the idea that we can obtain a full theory of physics by reducing things into their "fundamental" parts. The philosophy of reductionism states that if we understand the "fundamental" or "elementary" parts of a system we can then deduce all the properties of the system as a...
Electric-magnetic duality
0.823618
6,757
SOAP (Short Oligonucleotide Analysis Package) is a suite of bioinformatics software tools from the BGI Bioinformatics department enabling the assembly, alignment, and analysis of next generation DNA sequencing data. It is particularly suited to short read sequencing data. All programs in the SOAP package may be used fr...
Short Oligonucleotide Analysis Package
0.823608
6,758
Conceptual model (computer science), a representation of entities and their relationships Mathematical model, a description of a system using mathematical concepts and language Economic model, a theoretical construct representing economic processes Statistical model, a mathematical model that usually specifies the rela...
Physical models
0.823598
6,759
Wind tunnel and water tunnel testing is often used for these design efforts. Instrumented physical models can also examine internal flows, for the design of ductwork systems, pollution control equipment, food processing machines, and mixing vessels. Transparent flow models are used in this case to observe the detailed ...
Physical models
0.823598
6,760
A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical representation of an object, person or system. The object being modelled may be small (e.g., an atom) or large (e.g., the Solar System) or life-size (e.g., a fashion m...
Physical models
0.823598
6,761
AECs are very general objects and one usually make some of the assumptions below when studying them: An AEC has joint embedding if any two model can be embedded inside a common model. An AEC has no maximal model if any model has a proper extension. An AEC K {\displaystyle K} has amalgamation if for any triple M 0 , M 1...
Abstract elementary class
0.823597
6,762
Shelah introduced AECs to provide a uniform framework in which to generalize first-order classification theory. Classification theory started with Morley's categoricity theorem, so it is natural to ask whether a similar result holds in AECs. This is Shelah's eventual categoricity conjecture. It states that there should...
Abstract elementary class
0.823597
6,763
The following are some important results about AECs. Except for the last, all results are due to Shelah. Shelah's Presentation Theorem: Any AEC K {\displaystyle K} is PC 2 LS ⁡ ( K ) {\displaystyle \operatorname {PC} _{2^{\operatorname {LS} (K)}}}: it is a reduct of a class of models of a first-order theory omitting at...
Abstract elementary class
0.823597
6,764
In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates the...
Digital circuit
0.823594
6,765
Mathematical theorems are known about combinations of relation properties, such as "A transitive relation is irreflexive if, and only if, it is asymmetric". Of particular importance are relations that satisfy certain combinations of properties. A partial order is a relation that is reflexive, antisymmetric, and transit...
Relation (mathematics)
0.823592
6,766
The Leibniz Institute for Solar Physics operates solar observing facilities for its own research and for the solar community in Germany and other countries. The institute's prime facilities are the German solar telescopes at the Teide Observatory of the Intituto des Astrofisica de Canarias on Tenerife, Spain, with Euro...
Leibniz Institute for Solar Physics
0.82359
6,767
The institute was founded in 1943 as the 'Fraunhofer Institute' by Karl-Otto Kiepenheuer. Kiepenheuer was director of the institute from 1943 until his death in 1975. The institute was renamed as the 'Kiepenheuer Institute for Solar Physics' to honour the founder of the institute and to enable the Fraunhofer Society to...
Leibniz Institute for Solar Physics
0.823589
6,768
The Leibniz Institute for Solar Physics (aka: KIS; German: Leibniz-Institut für Sonnenphysik), formerly known as Kiepenheuer Institute for Solar Physics (KIS) is a research institute located in Freiburg, Germany. As a member of the Leibniz Association, the institute conducts basic research in astronomy and astrophysics...
Leibniz Institute for Solar Physics
0.823589
6,769
The Leibniz Institute for Solar Physics (KIS) is a foundation under public law of the state of Baden-Württemberg and a member of the Leibniz Association. The organs of the Leibniz Institute for Solar Physics (KIS) are the Foundation Council, the Scientific Advisory Council and the Board of Directors. The institute is d...
Leibniz Institute for Solar Physics
0.823589
6,770
Classification has many applications. In some of these, it is employed as a data mining procedure, while in others more detailed statistical modeling is undertaken. Biological classification – The science of identifying, describing, defining and naming groups of biological organisms Biometric – Metrics related to human...
Algorithms for statistical classification
0.823589
6,771
Most algorithms describe an individual instance whose category is to be predicted using a feature vector of individual, measurable properties of the instance. Each property is termed a feature, also known in statistics as an explanatory variable (or independent variable, although features may or may not be statisticall...
Algorithms for statistical classification
0.823589
6,772
For example, the data constructor Leaf is logically a function Int -> Tree, meaning that giving an integer as an argument to Leaf produces a value of the type Tree. As Node takes two arguments of the type Tree itself, the datatype is recursive. Operations on algebraic data types can be defined by using pattern matching...
Algebraic data type
0.823589
6,773
In most languages that support algebraic data types, it is possible to define parametric types. Examples are given later in this article. Somewhat similar to a function, a data constructor is applied to arguments of an appropriate type, yielding an instance of the data type to which the type constructor belongs.
Algebraic data type
0.823589
6,774
One of the most common examples of an algebraic data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element x with a list xs to create a new list. Here is an example of how a singly linked list would be declared in Haskell: o...
Algebraic data type
0.823589
6,775
Many programming languages incorporate algebraic data types as a first class notion, including:
Algebraic data type
0.823589
6,776
Algebraic data types are highly suited to implementing abstract syntax. For example, the following algebraic data type describes a simple language representing numerical expressions: An element of such a data type would have a form such as Mult (Add (Number 4) (Minus (Number 0) (Number 1))) (Number 2). Writing an evalu...
Algebraic data type
0.823589
6,777
Some manufacturers of spherical roller bearings are SKF, Schaeffler, Timken Company, NSK Ltd., NTN Corporation and JTEKT.Since SKF introduced the spherical roller bearing in 1919, spherical roller bearings have purposefully been refined through the decades to improve carrying capacity and to reduce operational friction...
Spherical roller bearing
0.823579
6,778
In mathematics, the lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a quadric, Q known as the Klein quadric. If the underlying vector space of S is the 4-dimensional vector space V, then T has ...
Klein quadric
0.823571
6,779
Look for: Shortages, mistakes, inadequate verification of equipment causing delays and can be avoided by check tables, especially visual ones, and setup on an intermediary jig Inadequate or incomplete repairs to equipment causing rework and delays Optimization for least work as opposed to least delay Unheated molds whi...
Single-Minute Exchange of Die
0.823571
6,780
Representativeness explains systematic errors that people make when judging the probability of random events. For example, in a sequence of coin tosses, each of which comes up heads (H) or tails (T), people reliably tend to judge a clearly patterned sequence such as HHHTTT as less likely than a less patterned sequence ...
Heuristics in judgment and decision making
0.82357
6,781
Implementations of the Address programming language were used for nearly 20 years. A book about APL was published in Ukraine in 1963 and it was translated and published in France in 1974. The Address language affected not only the Soviet Union's and other socialist countries economical development, but information tech...
Address programming language
0.82357
6,782
Plasma Science and Technology is a scientific journal published by the Institute of Plasma Physics, Chinese Academy of Sciences (CAS) and the Chinese Society of Theoretical and Applied Mechanics, hosted by IOP Publishing. It publishes novel experimental and theoretical findings in all fields related to plasma physics. ...
Plasma Science and Technology
0.823569
6,783
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution. This is achieved by tradi...
Heuristic search
0.823567
6,784
ShāngMì 4 (SM4, 商密4) (formerly SMS4) is a block cipher used in the Chinese National Standard for Wireless LAN WAPI (WLAN Authentication and Privacy Infrastructure) and also used with Transport Layer Security.SM4 was a cipher proposed to for the IEEE 802.11i standard, but has so far been rejected. One of the reasons for...
SM4 algorithm
0.823564
6,785
Precision and recall can be interpreted as (estimated) conditional probabilities: Precision is given by P ( C = P | C ^ = P ) {\displaystyle \mathbb {P} (C=P|{\hat {C}}=P)} while recall is given by P ( C ^ = P | C = P ) {\displaystyle \mathbb {P} ({\hat {C}}=P|C=P)} , where C ^ {\displaystyle {\hat {C}}} is the predict...
Recall and precision
0.823564
6,786
M {\displaystyle \mathbb {M} } is of type 3 {\displaystyle {\bf {3}}} , or Boolean type, iff M {\displaystyle \mathbb {M} } is polynomially equivalent to a two-element Boolean algebra. M {\displaystyle \mathbb {M} } is of type 4 {\displaystyle {\bf {4}}} , or lattice type, iff M {\displaystyle \mathbb {M} } is polynomi...
Minimal algebra
0.823564
6,787
A polynomial of an algebra is a composition of its basic operations, 0 {\displaystyle 0} -ary operations and the projections. Two algebras are called polynomially equivalent if they have the same universe and precisely the same polynomial operations. A minimal algebra M {\displaystyle \mathbb {M} } falls into one of th...
Minimal algebra
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6,788
A minimal algebra is a finite algebra with more than one element, in which every non-constant unary polynomial is a permutation on its domain.
Minimal algebra
0.823564
6,789
Minimal algebra is an important concept in tame congruence theory, a theory that has been developed by Ralph McKenzie and David Hobby.
Minimal algebra
0.823564
6,790
More complicated situations are simulation of population genetics, or the behaviour of sub-atomic particles. Such simulation methods, often called stochastic methods, have many applications in computer simulation of real-world processes. Some more speculative projects, such as the Global Consciousness Project, monitor ...
Applications of randomness
0.823552
6,791
Public or third-party sources of random values, or random values computed from publicly observable phenomena (weather, sports game results, stock prices), are almost never cryptographically acceptable. Their use may be tempting, but in reality, they permit easier attacks than attacking the cryptography. Since most cryp...
Applications of randomness
0.823552
6,792
In any case, it is sometimes impossible to avoid the need for true (i.e., hardware-based) random number generators. Since a requirement in cryptography is high entropy, any published random sequence is a poor choice, as are such sequences as the digits in an irrational number such as the φ or even in transcendental num...
Applications of randomness
0.823552
6,793
A suitably motivated adversary could simply test them all; this is practical as of 2010, using readily available computers. Even if a linear congruential RNG is used with 1000-bit parameters, it is a simple exercise in linear algebra to recover the modulus m, and the constants a and b, where x' = ax +b (mod m), given o...
Applications of randomness
0.823552
6,794
A ubiquitous use of unpredictable random numbers is in cryptography, which underlies most of the schemes which attempt to provide security in modern communications (e.g., confidentiality, authentication, electronic commerce, etc.). For example, if a user wants to use an encryption algorithm, it is best that they select...
Applications of randomness
0.823552
6,795
Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized controlled trials helps scientists to test hypotheses, and random numbers or pseudorandom numbers help video games such as video poker. These uses have different levels of...
Applications of randomness
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Random numbers have uses in physics such as electronic noise studies, engineering, and operations research. Many methods of statistical analysis, such as the bootstrap method, require random numbers. Monte Carlo methods in physics and computer science require random numbers. Random numbers are often used in parapsychol...
Applications of randomness
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Many experiments in physics rely on a statistical analysis of their output. For example, an experiment might collect X-rays from an astronomical source and then analyze the result for periodic signals. Since random noise can be expected to appear to have faint periodic signals embedded in it, statistical analysis is re...
Applications of randomness
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A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in Schmidt's 1968 work and was subsequent...
Distributive homomorphism
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A number of algorithms and bioinformatics resources have been developed for refinement of sequence homology-based assignments of protein functions: InParanoid: Identifies eukaryotic orthologs by looking only at in-paralogs. CDD: Resource for the annotation of functional units in proteins. Its collection of domain model...
Metabolic pathway analysis
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