Constraint programmingConstraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found.
Constraint logic programmingConstraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is . In this clause, is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming. This clause states one condition under which the statement A(X,Y) holds: X+Y is greater than zero and both B(X) and C(Y) are true.
Rapid eye movement sleepRapid eye movement sleep (REM sleep or REMS) is a unique phase of sleep in humans, mammals and birds, characterized by random rapid movement of the eyes, accompanied by low muscle tone throughout the body, and the propensity of the sleeper to dream vividly. The REM phase is also known as paradoxical sleep (PS) and sometimes desynchronized sleep or dreamy sleep, because of physiological similarities to waking states including rapid, low-voltage desynchronized brain waves.
Constraint satisfaction problemConstraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families.
Multiple integralIn mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
Constraint satisfactionIn artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. A solution is therefore a set of values for the variables that satisfies all constraints—that is, a point in the feasible region. The techniques used in constraint satisfaction depend on the kind of constraints being considered.
Constraint (mathematics)In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. The following is a simple optimization problem: subject to and where denotes the vector (x1, x2). In this example, the first line defines the function to be minimized (called the objective function, loss function, or cost function).
General officerA general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry. In some usages the term "general officer" refers to a rank above colonel. The term general is used in two ways: as the generic title for all grades of general officer and as a specific rank. It originates in the 16th century, as a shortening of captain general, which rank was taken from Middle French capitaine général.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
IntegralIn mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.
Rapid eye movement sleep behavior disorderRapid eye movement sleep behavior disorder or REM behavior disorder (RBD) is a sleep disorder in which people act out their dreams. It involves abnormal behavior during the sleep phase with rapid eye movement (REM) sleep. The major feature of RBD is loss of muscle atonia (i.e., the loss of paralysis) during otherwise intact REM sleep (during which paralysis is not only normal but necessary). The loss of motor inhibition leads to sleep behaviors ranging from simple limb twitches to more complex integrated movements that can be violent or result in injury to either the individual or their bedmates.
CD-iThe Compact Disc-Interactive (CD-I, later CD-i) is a digital optical disc data storage format that was mostly developed and marketed by Dutch company Philips. It was created as an extension of CDDA and CD-ROM and specified in the Green Book specifications, co-developed by Philips and Sony, to combine audio, text and graphics. The two companies initially expected to impact the education/training, point of sale, and home entertainment industries, but CD-i eventually became best known for its video games.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
CD-ROMA CD-ROM (ˌsiːdiːˈrɒm, compact disc read-only memory) is a type of read-only memory consisting of a pre-pressed optical compact disc that contains data. Computers can read—but not write or erase—CD-ROMs. Some CDs, called enhanced CDs, hold both computer data and audio with the latter capable of being played on a CD player, while data (such as software or digital video) is only usable on a computer (such as ISO 9660 format PC CD-ROMs).
Brigadier generalBrigadier general or Brigade general is a military rank used in many countries. The rank is usually above a colonel, and below a major general or divisional general. When appointed to a field command, a brigadier general is typically in command of a brigade consisting of around 4,000 troops (four battalions). Brigadier general (Brig. Gen.) is a military rank used in many countries. It is the lowest ranking general officer in some countries, usually sitting between the ranks of colonel and major general.
Surface integralIn mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a surface as shown in the illustration.
Context-free languageIn formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language.
Colonel generalColonel general is a three- or four-star military rank used in some armies. It is particularly associated with Germany, where historically general officer ranks were one grade lower than in the Commonwealth and the United States, and Generaloberst was a rank above full General, but below Generalfeldmarschall. The rank of colonel general also exists in the armed forces organized along the lines of the Soviet model, where it is comparable to that of a lieutenant general in many NATO armed forces (rank code OF-8).
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Gaussian integralThe Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is Abraham de Moivre originally discovered this type of integral in 1733, while Gauss published the precise integral in 1809. The integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution.
