Discrete Space Wikipedia

Discrete space - Wikipedia.

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular, every singleton subset is ....


Discrete mathematics - Wikipedia.

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete ....


Discrete geometry - Wikipedia.

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. ... A sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, ....


State-space representation - Wikipedia.

In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of ....


Dynamical system - Wikipedia.

A dynamical system may be defined formally as a measure-preserving transformation of a measure space, the triplet (T, (X, ?, u), ?).Here, T is a monoid (usually the non-negative integers), X is a set, and (X, ?, u) is a probability space, meaning that ? is a sigma-algebra on X and u is a finite measure on (X, ?).A map ?: X -> X is said to be ?-measurable if and only if, for every ? ....


Discretization - Wikipedia.

Discretization of linear state space models . Discretization is also concerned with the transformation of continuous differential equations into discrete difference equations, suitable for numerical computing.. The following continuous-time state space model ? = + + () = + + ()where v and w are continuous zero-mean white noise sources with power spectral densities.


Discrete uniform distribution - Wikipedia.

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen"..


Continuous or discrete variable - Wikipedia.

Continuous variable. A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of values.. For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. The reason is that any range of real numbers between and with ,; is uncountable..


Random variable - Wikipedia.

Definition. A random variable is a measurable function: from a set of possible outcomes to a measurable space.The technical axiomatic definition requires to be a sample space of a probability triple (,,) (see the measure-theoretic definition).A random variable is often denoted by capital roman letters such as , , , .. The probability that takes on a value in a measurable set is ....


Pong - Wikipedia.

Pong was the first game developed by Atari. After producing Computer Space, Bushnell decided to form a company to produce more games by licensing ideas to other companies.The first contract was with Bally Manufacturing Corporation for a driving game. Soon after the founding, Bushnell hired Allan Alcorn because of his experience with electrical engineering and computer ....


Probability space - Wikipedia.

A probability space is a mathematical triplet (,,) that presents a model for a particular class of real-world situations. As with other models, its author ultimately defines which elements , , and will contain.. The sample space is the set of all possible outcomes. An outcome is the result of a single execution of the model. Outcomes may be states of nature, possibilities, experimental ....


Joint probability distribution - Wikipedia.

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual ....


Bayesian network - Wikipedia.

A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was ....


Extended Kalman filter - Wikipedia.

History. The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for linear system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are nonlinear, so attempts were made to ....


Group action - Wikipedia.

In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on ....


Priority queue - Wikipedia.

Using a sorting algorithm to make a priority queue. A sorting algorithm can also be used to implement a priority queue. Specifically, Thorup says: We present a general deterministic linear space reduction from priority queues to sorting implying that if we can sort up to n keys in S(n) time per key, then there is a priority queue supporting delete and insert in O(S(n)) time and find ....


Bandwidth (computing) - Wikipedia.

In computing, bandwidth is the maximum rate of data transfer across a given path. Bandwidth may be characterized as network bandwidth, data bandwidth, or digital bandwidth.. This definition of bandwidth is in contrast to the field of signal processing, wireless communications, modem data transmission, digital communications, and electronics, [citation needed] in which ....


Digital signal processing - Wikipedia.

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency..


Spinodal decomposition - Wikipedia.

Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no thermodynamic barrier to phase separation. As a result, phase separation via decomposition does not require the nucleation events resulting from thermodynamic fluctuations, which normally ....


Discrete element method - Wikipedia.

A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often ....


ベクトル空間 - Wikipedia.

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List of probability distributions - Wikipedia.

With finite support. The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 - p.; The Rademacher distribution, which takes value 1 with probability 1/2 and value -1 with probability 1/2.; The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same probability of ....