Concepts inA Markov chain approximation for the analysis of banyan networks
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes.
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Artificial neural network
An Artificial Neural Network (ANN), usually called neural network (NN), is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation.
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Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex functions. Analysis may be conventionally distinguished from geometry.
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Stochastic matrix
For a matrix whose elements are stochastic, see Random matrix In mathematics, a stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix) is a matrix used to describe the transitions of a Markov chain. It has found use in probability theory, statistics and linear algebra, as well as computer science.
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Stationary distribution
Stationary distribution may refer to: The limiting distribution in a Markov chain The marginal distribution of a stationary process or stationary time series The set of joint probability distributions of a stationary process or stationary time series In some fields of application, the term stable distribution is used for the equivalent of a stationary (marginal) distribution, although in probability and statistics the term has a rather different meaning: see stable distribution.
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Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero: The concept of steady state has relevance in many fields, in particular thermodynamics and economics. Steady state is a more general situation than dynamic equilibrium. If a system is in steady state, then the recently observed behavior of the system will continue into the future.
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Monte Carlo method
Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems. These methods are most suited to calculation by a computer and tend to be used when it is infeasible to compute an exact result with a deterministic algorithm. This method is also used to complement theoretical derivations.
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Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information. Where at least one process in one device is able to send/receive data to/from at least one process residing in a remote device, then the two devices are said to be in a network.
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