Analysis and Modeling of the Variations of Root Branching Density Within Individual Plants and Among Species by Loïc Pagès

“…Using measurements of inter-branch distance on various roots of the same species and our knowledge of the branching process, we defined a simple and generic model dedicated to the simulation of the observed variations. …”
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Susceptibility in inhomogeneous random graphs by Janson, S, Riordan, O

“…Here we relate the susceptibility of suitable random graphs to a quantity associated to the corresponding branching process, and study both quantities in various natural examples.…”

A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis by Linda J.S. Allen

“…Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30…”
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An old approach to the giant component problem by Bollobas, B, Riordan, O

“…In 1998, Molloy and Reed showed that, under suitable conditions, if a sequence of degree sequences converges to a probability distribution $D$, then the size of the largest component in corresponding $n$-vertex random graph is asymptotically $\rho(D)n$, where $\rho(D)$ is a constant defined by the solution to certain equations that can be interpreted as the survival probability of a branching process associated to $D$. There have been a number of papers strengthening this result in various ways; here we prove a strong form of the result (with exponential bounds on the probability of large deviations) under minimal conditions.…”

Asymptotic behaviour of gossip processes and small world networks by Barbour, A, Reinert, G

“…In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.…”

Growth of uniform infinite causal triangulations by Sisko, V, Yambartsev, A, Zohren, S

“…Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.…”

The genealogy of branching brownian motion with absorption by Berestycki, J, Berestycki, N, Schweinsberg, J

“…We show that the characteristic time scale for the evolution of this population is of order (logN)3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. …”

Spread-out percolation in R^d by Bollobas, B, Janson, S, Riordan, O

“…This is the simplest case of a `spread-out' percolation model studied by Penrose, who showed that, as $r\to\infty$, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the percolation threshold and the threshold for criticality of the naturally associated branching process approach one another. Here we show that this result follows immediately from of a general result of the authors on inhomogeneous random graphs.…”

Classes of critical avalanche dynamics in complex networks by Filippo Radicchi, Claudio Castellano, Alessandro Flammini, Miguel A. Muñoz, Daniele Notarmuzi

“…At asymptotically large scales instead—irrespective of the type of dynamics and of the topology of the underlying network—sizes and durations of avalanches are characterized by power-law distributions with the exponents of the standard mean-field critical branching process.…”
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A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions by Niyogi, Partha, Berwick, Robert C.

“…Although DNA is a presumably "organized system of signs" in Mandelbrot"s (1961) sense, and observation of statistical featurs of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's "gramar" and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an M-sided die or a finite-state branching process.…”
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Contact tracing is an imperfect tool for controlling COVID-19 transmission and relies on population adherence by Davis, E, Lucas, T, Borlase, A, Pollington, TM, Abbott, S, Ayabina, D, Crellen, T, Hellewell, J, Pi, L, Medley, G, Hollingsworth, T, Klepac, P

“…We investigate potential pitfalls and areas for improvement by extending an existing branching process contact tracing model, adding diagnostic testing and refining parameter estimates. …”

Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever by Glenn Lahodny Jr., Mona Zevika

“…This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. …”
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Optimizing information processing in neuronal networks beyond critical states. by Mariana Sacrini Ayres Ferraz, Hiago Lucas Cardeal Melo-Silva, Alexandre Hiroaki Kihara

“…Herein, we focused on how information entropy encoded in spatiotemporal activity patterns may vary in critical networks. We employed branching process based models to investigate how entropy can be embedded in spatiotemporal patterns. …”
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Limit Theorems in Bellman–Harris Processes with Finites Second Moments by Humberto Llinás Solano

“…In this article are studied different theorems limits in a critical Bellman-Harris branching process with a only type of particle and with finite second moments. …”
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The critical domain size of stochastic population models by Reimer, J, Bonsall, M, Maini, P

“…We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. …”

The time evolution of the large exponential and power population growth and their relation to the discrete linear birth-death process by E. A. Abdel-Rehim

“…The Feller exponential population growth is the continuous analogues of the classical branching process with fixed number of individuals. In this paper, I begin by proving that the discrete birth-death process, M/M/1 queue, could be mathematically modelled by the same Feller exponential growth equation via the Kolmogorov forward equation. …”
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A stochastic epidemic model for the dynamics and control of maize streak disease by Obiora Cornelius Collins, Kevin Jan Duffy

“…The probability of maize streak disease extinction or persistence is determined using the theory of a multi-type branching process. Using these results, the degrees to which these control measures are effective in reducing maize streak disease are considered. …”
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Sequential mutations in exponentially growing populations. by Michael D Nicholson, David Cheek, Tibor Antal

“…Here, within a multitype branching process framework, we consider a general mutational path where mutations may be advantageous, neutral or deleterious. …”
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Uniqueness criteria for continuous-time Markov chains with general transition structures by Chen, A, Pollett, P, Zhang, H, Cairns, B

“…We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. …”

Hereditary tree growth and Lévy forests by Duquesne, T, Winkel, M

“…We prove that the associated families of offspring distributions are completely characterised by the branching mechanism of a continuous-state branching process. We also prove that such growth processes converge to Lévy forests. …”