branching process


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branching process

[′branch·iŋ ′präs·əs]
(statistics)
A stochastic process in which the members of a population may have offspring and the lines of descent branch out as the new members are born.
References in periodicals archive ?
For each simplex S [subset or equal to] [S.sup.0] created by the branching process, this process gives a lower bound LB(S) for the optimal value v(S) of the following problem LMP(S),
Let Z(n) = ([Z.sub.1](n), ..., [Z.sub.p](n)), n = 0, 1, ..., be a p-type Galton-Watson branching process in a random environment.
Hence, there is inherent stochasticity caused by the finiteness of the number of lineages in applying the method, even if the branching and extinction events exactly follow the branching process model that leads to equation (5).
The first- and last-birth problems for a multitype age-dependent branching process. Advances in Appl.
This model can be understood from the discrete time binary Galton-Watson branching process.
Since, this decision tree technique is not efficacious and suffers from overfitting, a problem which gives distorted results from the training data at the latter stages of the branching process, the researchers moved on to random-forest technique that instead of calculating the outcome at every branch, calculates the outcome of random branches.
In this section, we also compute the stochastic threshold for disease extinction or invasion by applying the multitype Galton-Watson branching process. In Section 4, we show the relationship between reproductive number of the deterministic model and the thresholds for disease extinction of the stochastic version; we also illustrate our results using numerical simulations.
The Markov branching process (MBP) is the discrete-state Markov process ([Z.sub.t] : t [greater than or equal to] 0) on the state-space S = {0,1, ...} whose transition function F(t) = [[f.sub.ij](t)] is standard and satisfies the branching property,
Figure 10 shows the number of partial sets identified during the branching process normalized by the number of full sets in the entire system, with respect to the sum of the probabilities of the branches that reach a certain value.
The quasistationary limit of this process is the Yaglom limit of its associated branching process [39, 40] and is exactly geometric.
In our study, we use a branching process model to estimate the probability distribution of outbreak sizes resulting from the introduction of an Ebola case to a new country where the reproductive number R (i.e., expected number of transmissions per case) would likely be quickly, if not immediately, reduced to <1.
The branching process improves by using of polyfunctional monomer [19, 21, 22] and the materials known as iniferters such as Thiuram disulfides [23-25] and dithiocarbamates [26].