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Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. (animated version)In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type ...
A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov.
Used to detect specific DNA sequence in DNA samples: Molecular biology: Test cross: Used to determine whether an individual is homozygous or heterozygous dominant: Genetics: Voltage clamp: Used to measure the ion currents through the membranes of excitable cells, such as neurons, while holding the membrane voltage at a set level. [16 ...
The Fisher–Yates shuffle is an algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and continually determines the next element in the shuffled sequence by randomly drawing an element from the list until no elements remain. [1]
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
Let G be a finite group and let S be a subset of G.A straight-line program of length m over S computing some g ∈ G is a sequence of expressions (w 1,...,w m) such that for each i, w i is a symbol for some element of S, or w i = (w j,-1) for some j < i, or w i = (w j,w k) for some j,k < i, such that w m takes upon the value g when evaluated in G in the obvious manner.