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The most common formulation of a branching process is that of the Galton–Watson process.Let Z n denote the state in period n (often interpreted as the size of generation n), and let X n,i be a random variable denoting the number of direct successors of member i in period n, where X n,i are independent and identically distributed random variables over all n ∈{ 0, 1, 2, ...} and i ∈ {1 ...
The Galton–Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names. [ 1 ] [ 2 ] The process models family names as patrilineal (passed from father to son), while offspring are randomly either male or female, and names become extinct if the family name line dies ...
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed ...
In probability theory, a branching random walk is a stochastic process that generalizes both the concept of a random walk and of a branching process.At every generation (a point of discrete time), a branching random walk's value is a set of elements that are located in some linear space, such as the real line.
A version of this process, with the critical probability , has been studied as a model for speciation, where it is known as the critical branching process. In this process, each species has an exponentially distributed lifetime, and over the course of its lifetime produces child species at a rate equal to the lifetime. When a child is produced ...
The following is the skeleton of a generic branch and bound algorithm for minimizing an arbitrary objective function f. [3] To obtain an actual algorithm from this, one requires a bounding function bound, that computes lower bounds of f on nodes of the search tree, as well as a problem-specific branching rule.
Last time, I mused a bit on the concept of linearity versus openness in gaming. Today, I'd like to continue that line of thought, with a look at narrative paths in game design.
Figure 1: Example of 4-stage pipeline. The colored boxes represent instructions independent of each other. Two-way branching is usually implemented with a conditional jump instruction. A conditional jump can either be "taken" and jump to a different place in program memory, or it can be "not taken" and continue execution immediately after the ...