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Predicting correlation coefficients for Monte Carlo eigenvalue simulations with multitype branching process

Annals of Nuclear Energy, 2018
© 2017 Elsevier Ltd This paper provides a prediction method of the generation-to-generation correlations as observed when solving large scale eigenvalue problems such as full core nuclear reactor simulations.
Jilang Miao, Benoit Forget, Kord Smith   +2 more
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Multitype Branching Processes

1985
The concepts and results of Chapter 2 are readily extended to aggregates of more than one particle type. Our interest lies in the aggregation behavior of f-valent antigen and bivalent antibody. Processes involving more than two types, [for example, f-valent antigen in solution with either a mixture of bivalent antibody and Fab fragments (univalent ...
Catherine A. Macken, Alan S. Perelson
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On Multitype Branching Processes in a Random Environment

Journal of Mathematical Sciences, 2002
For a critical multitype Galton-Watson process in an i.i.d. random environment the probability of extinction at time \(T\) is shown to be of order \(T^{-3/2}\) as \(T\to\infty\). This generalizes a result of \textit{V. A. Vatutin} and the author [Discrete Math. Appl. 7, No. 5, 469-496 (1997); translation from Diskretn. Mat. 9, No. 4, 100-126 (1997; Zbl
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Multitype Branching Processes and Some Queueing Systems

Journal of Mathematical Sciences, 2002
The authors derive limit theorems for multitype Galton-Watson branching processes with immigration at zero in the near critical case and apply them to obtain heavy traffic limit theorems in polling systems with gated service and exhaustive service.
Vatutin, V. A., Dyakonova, E. E.
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Inclusive Fitness from Multitype Branching Processes

Bulletin of Mathematical Biology, 2010
I use multitype branching processes to study genetic models for the evolution of social behaviour, i.e. behaviours that, when acted out, affect the success of the actor's neighbours. Here, I suppose an individual bearing a mutant copy of a gene influences the reproductive success of a neighbour by altering its own competitive ability.
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Multitype Contact Branching Processes

1995
Connections exist between n-type contact branching processes and deterministic models for spatial epidemics. Let the position of the furthest individual in a contact branching process from position 0 at time t in a given direction be denoted by U(t). Define \(y_i(s,t) = P[U(t) > s| \ \textup{one} \ \textup{type} \ i \ \textup dividual \ \textup{at} \ \
J. Radcliffe, L. Rass
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A Multitype Branching Process Model

1988
The model we develop is one of the simplest nontrivial models of cell growth in culture. We assume that there are three general classes of cells, which we label stem cells (S), macrophage progenitors (M), and end cells (E). Discrimination among the classes is on the basis of function of the member cells since typically the cell types cannot be ...
Catherine A. Macken, Alan S. Perelson
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Stationary measures for multitype branching processes

Journal of Applied Probability, 1975
The multitype Galton-Watson process is considered both with and without immigration. Proofs are given for the existence of invariant measures and their uniqueness is examined by functional equation methods. Theorem 2.1 proves the uniqueness, under certain conditions, of solutions of a multidimensional Schröder equation.
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Multitype infinite-allele branching processes in continuous time

Journal of Applied Probability, 2017
AbstractWe introduce extensions to an infinite-allele branching process that allows for multiple types to exist alongside labels. We consider a Markov branching process and general branching process under different assumptions, and show asymptotic results about the growth of the labels as well as the frequency spectrum.
Thomas O. McDonald, Marek Kimmel
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A note on the multitype Markov branching process

Journal of Applied Probability, 1989
We consider a supercritical, p-dimensional Markov branching process (MBP). Based on the finite and the infinite lines of descent of particles of this p-dimensional MBP, we construct an associated 2p-dimensional process. We show that such a process is a 2p-dimensional, supercritical MBP.
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