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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.
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 finite procedure, written in a fixed symbolic vocabulary, governed by precise instructions, moving in discrete steps, 1, 2, 3, . . ., whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end." (boldface and italics in the original, p. xviii)
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
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.
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 ]
Every element of a graph dynamical system can be made stochastic in several ways. For example, in a sequential dynamical system the update sequence can be made stochastic. At each iteration step one may choose the update sequence w at random from a given distribution of update sequences with corresponding probabilities. The matching probability ...
SWTs are appropriate when the research focus is on the effectiveness of the treatment rather than on its mere existence. Overall, if the study is pragmatic (i.e. seeks primarily to implement a certain policy), logistical and other practical concerns are considered to be the best reasons to turn to a stepped wedge design. Also, if the treatment ...