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A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Q k for all k (from 0 to ∞).
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A finite-state machine can be used as a representation of a Markov chain. Assuming a sequence of independent and identically distributed input signals (for example, symbols from a binary alphabet chosen by coin tosses), if the machine is in state y at time n, then the probability that it moves to state x at time n + 1 depends only on the ...
English: Depiction of how DNA libraries created by random diversity-generation techniques sample the sequence space. The amino acid substituted into a given position is shown. Each dot or set of connected dots is one member of the library.
A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6] For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless ...
Genetic sequence in digital format. Once a nucleic acid sequence has been obtained from an organism, it is stored in silico in digital format. Digital genetic sequences may be stored in sequence databases, be analyzed (see Sequence analysis below), be digitally altered and be used as templates for creating new actual DNA using artificial gene ...
The sequence in which each of the phases occur may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of an absorbing Markov chain with one absorbing state. Each of the states of the Markov chain represents one of the phases.
A number of different Markov models of DNA sequence evolution have been proposed. [1] These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses.