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We study the impact of having a non-spatial branching mechanism with infinite variance on some parameters (height, width and first hitting time) of an underlying Bienaymé-Galton-Watson branching process. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then… (More)

We derive some additional results on the Bienyamé-Galton-Watson branching process with θ−linear fractional branching mechanism, as studied in [16]. This includes: the explicit expression of the limit laws in both the sub-critical cases and the super-critical cases with finite mean, the long-run behavior of the population size in the critical case, limit… (More)

- Nicolas Grosjean, Thierry Huillet
- J. Applied Probability
- 2016

We define and analyze a coalescent process as a recursive boxfilling process whose genealogy is given by an ancestral time-reversed, timeinhomogeneous Bienyamé-Galton-Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated when the… (More)

- Nicolas Grosjean, Thierry Huillet, G. Rollet
- Theory in Biosciences
- 2016

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of… (More)

Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and nonoverlapping generations. Here we focus on similar problems in the context of the standard unconditional Bienaymé-Galton-Watson branching processes, either (sub)-critical or supercritical. Using an analytical tool, we… (More)

- Dana Khdr Sabir, Nicolas Grosjean, Elizabeth L Rylott, Neil C Bruce
- FEMS microbiology letters
- 2017

The xenobiotic hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) is a toxic explosive and environmental pollutant. This study examines three bacterial species that degrade RDX, using it as a sole source of nitrogen for growth. Although isolated from diverse geographical locations, the species contain near identical copies of genes encoding the RDX-metabolising… (More)

This paper is an attempt to formalize analytically the question raised in “World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?” Huffington Post, [7]. We start developing simple deterministic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both linear birth and… (More)

Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a… (More)

We study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then… (More)

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it… (More)