In: SIAM Journal on Applied Mathematics, 2019, vol. 79, no. 4, p. 1173–1196
We investigate a broad family of stochastically modeled reaction networks by looking at their stationary distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first explicitly give product-form stationary distributions for a class of mostly non-weakly-reversible autocatalytic reaction networks of arbitrary deficiency. We provide...
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In: Bulletin of Mathematical Biology, 2019, vol. 81, no. 5, p. 1461–1478
Here, we present a theoretical investigation with potential insights on developmental mechanisms. Three biological factors, consisting of two diffusing factors and a cell- autonomous immobile transcription factor are combined with different feedback mechanisms. This results in four different situations or fur patterns. Two of them reproduce classical Turing patterns: (1) regularly spaced...
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In: Advances in Applied Probability, 2011, vol. 43, no. 2, p. 375-398
Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait t ∈ T in environment e ∈ E is given by some (fixed) distribution...
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In: Nucleic Acid Research, 2011, vol. 39, no. 15, p. e104
Gene transfer and expression in eukaryotes is often limited by a number of stably maintained gene copies and by epigenetic silencing effects. Silencing may be limited by the use of epigenetic regulatory sequences such as matrix attachment regions (MAR). Here, we show that successive transfections of MAR-containing vectors allow a synergistic increase of transgene expression. This finding is...
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In: Random Structures & Algorithms, 2010, vol. 37, no. 1, p. 67–84
Polygon spaces such as $ M_{\ell} = \{ (u_{1,\ldots,} u_{n})\; \epsilon \; S^{1}\times \ldots S^{1}, \sum \nolimits^{n}_{i=1}\;l_{i}u_{i} = 0 \}/SO(2) $, or the three-dimensional analogs Nℓ play an important rle in geometry and topology, and are also of interest in robotics where the li model the lengths of robot arms. When n is large, one can assume that each li is a positive real valued...
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In: Insurance: Mathematics and Economics, 2009, vol. 45, no. 3, p. 374-381
In the classical risk model, we prove the weak convergence of a sequence of empirical finite-time ruin probabilities. In an earlier paper (see Loisel et al., (2008)), we proved an equivalent result in the special case where the initial reserve is zero, and checked that numerically the general case seems to be true. In this paper, we prove the general case (with a nonnegative initial reserve),...
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In: Insurance: Mathematics and Economics, 2008, vol. 42, no. 2, p. 746-762
We consider the classical risk model and carry out a sensitivity and robustness analysis of finite-time ruin probabilities. We provide algorithms to compute the related influence functions. We also prove the weak convergence of a sequence of empirical finite-time ruin probabilities starting from zero initial reserve toward a Gaussian random variable. We define the concepts of reliable finite-time...
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In: Journal of Mathematical Biology, 2007, vol. 55, no. 2, p. 249-269
Organisms are known to adapt to regularly varying environments. However, in most cases, the fluctuations of the environment are irregular and stochastic, alternating between favorable and unfavorable regimes, so that cells must cope with an uncertain future. A possible response is population diversification. We assume here that the cell population is divided into two groups, corresponding to...
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In: Journal of Multivariate Analysis, 2005, vol. 93, p. 180-197
This paper proposes a unified treatment of maximum likelihood estimates of angular Gaussian and multivariate Cauchy distributions in both the real and the complex case. The complex case is relevant in shape analysis. We describe in full generality the set of maxima of the corresponding log-likelihood functions with respect to an arbitrary probability measure. Our tools are the convexity of...
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