In: BMC Genomics, 2011, vol. 12, p. 181
Background: Multiplex experimental assays coupled to computational predictions are being increasingly employed for the simultaneous analysis of many specimens at the genome scale, which quickly generates very large amounts of data. However, inferring valuable biological information from the comparisons of very large genomic datasets still represents an enormous challenge.Results: As a study...
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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: The American Naturalist, 2010, vol. 176, no. 2, p. 170-177
Several stochastic models have tried to capture the architecture of food webs. This approach is interesting, but it is limited by the fact that different assumptions can yield similar results. To overcome this limitation, we develop a purely statistical approach. Body size in terms of an optimal ratio between prey and predator is used as explanatory variable. In 12 observed food webs, this model...
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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: Bulletin of Mathematical Biology, 2009, vol. 71, no. 6, p. 1394-1431
Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856–860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by...
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In: Bioinformatics, 2007, vol. 23, no. 23, p. 3185-3192
Motivation: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of...
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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: BMC Bioinformatics, 2007, vol. 8, p. 131
Background: PCR has the potential to detect and precisely quantify specific DNA sequences, but it is not yet often used as a fully quantitative method. A number of data collection and processing strategies have been described for the implementation of quantitative PCR. However, they can be experimentally cumbersome, their relative performances have not been evaluated systematically, and they...
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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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