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101
Analysis and Modeling of the Variations of Root Branching Density Within Individual Plants and Among Species
Published 2019-08-01“…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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102
Susceptibility in inhomogeneous random graphs
Published 2009“…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.…”
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103
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Published 2017-05-01“…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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104
An old approach to the giant component problem
Published 2012“…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.…”
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105
Asymptotic behaviour of gossip processes and small world networks
Published 2012“…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.…”
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106
Growth of uniform infinite causal triangulations
Published 2012“…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.…”
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107
The genealogy of branching brownian motion with absorption
Published 2013“…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. …”
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108
Spread-out percolation in R^d
Published 2005“…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.…”
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109
Classes of critical avalanche dynamics in complex networks
Published 2020-07-01“…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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110
A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions
Published 2004“…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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111
Contact tracing is an imperfect tool for controlling COVID-19 transmission and relies on population adherence
Published 2021“…We investigate potential pitfalls and areas for improvement by extending an existing branching process contact tracing model, adding diagnostic testing and refining parameter estimates. …”
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112
Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever
Published 2021-05-01“…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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113
Optimizing information processing in neuronal networks beyond critical states.
Published 2017-01-01“…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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114
Limit Theorems in Bellman–Harris Processes with Finites Second Moments
Published 2010-07-01“…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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115
The critical domain size of stochastic population models
Published 2016“…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. …”
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116
The time evolution of the large exponential and power population growth and their relation to the discrete linear birth-death process
Published 2022-05-01“…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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117
A stochastic epidemic model for the dynamics and control of maize streak disease
Published 2022-12-01“…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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118
Sequential mutations in exponentially growing populations.
Published 2023-07-01“…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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119
Uniqueness criteria for continuous-time Markov chains with general transition structures
Published 2005“…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. …”
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120
Hereditary tree growth and Lévy forests
Published 2018“…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. …”
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