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Branching processes can be simulated for a range of problems. One specific use of simulated branching process is in the field of evolutionary biology. [5] [6] Phylogenetic trees, for example, can be simulated under several models, [7] helping to develop and validate estimation methods as well as supporting hypothesis testing.
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 ...
An example of branching random walk can be constructed where the branching process generates exactly two descendants for each element, a binary branching random walk. Given the initial condition that X ϵ = 0, we suppose that X 1 and X 2 are the two children of X ϵ .
Bernoulli schemes: discrete-time processes with N possible states; every stationary process in N outcomes is a Bernoulli scheme, and vice versa. Bessel process; Birth–death process; Branching process; Branching random walk; Brownian bridge; Brownian motion; Chinese restaurant process; CIR process; Continuous stochastic process; Cox process ...
Dendritic arborization, also known as dendritic branching, is a multi-step biological process by which neurons form new dendritic trees and branches to create new synapses. [1] Dendrites in many organisms assume different morphological patterns of branching.
A stochastic process with this semigroup is called a Brownian snake. We may again find a duality between this process and a branching process. Here the branching process will be a super-Brownian motion + with branching mechanism () =, started on a Dirac in 0.
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.
Another example is the branching process, [322] which models the growth of a population where each individual reproduces independently. The branching process is often used to describe population extinction or explosion, particularly in epidemiology, where it can model the spread of infectious diseases within a population.