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We present a model of the Hypothalamo-Adreno-Pituitary (HPA) system; our approach is hierarchical and biologically sound, reflecting the complexity of the real HPA system. The structure of the conceptual model is based on theoretical frameworks of biological complex systems and its implementation takes advantage of recent hybrid automata modelling and analysis tools, being modular and reflecting parameter and mechanisms uncertainties.

In this chapter, we present a method to infer the structure of the gene regulatory network that takes in account both the kinetic molecular interactions and the randomness of data. The dynamics of the gene expression level are fitted via a nonlinear stochastic differential equation (SDE) model. The drift term of the equation contains the transcription rate related to the architecture of the local regulatory network. The statistical analysis of data combines maximum likelihood principle with Akaike Information Criteria (AIC) through a forward selection Strategy to yield a set of specific regulators and their contribution. Tested with expression data concerning the cell cycle for S. Cerevisiae and embryogenesis for the D. melanogaster, this method provides a framework for the reverse engineering of various gene regulatory networks.

Protocadherins are transmembrane proteins exhibiting homophilic adhesive activities through their extracellular domain. Protocadherin 12 ( Pcdh12) is expressed in angiogenic endothelial cells, mesangial cells of kidney glomeruli, and glycogen cells of the mouse placenta. To get insight into the role of this protein in vivo, we analyzed PCDH12-deficient mice and investigated their placental phenotype. The mice were alive and fertile; however, placental and embryonic sizes were reduced compared with wild-type mice. We observed defects in placental layer segregation and a decreased vascularization of the labyrinth associated with a reduction in cell density in this layer. To understand the molecular events responsible for the phenotypic alterations observed in Pcdh12−/− placentas, we analyzed the expression profile of embryonic day 12.5 mutant placentas compared with wild-type placentas, using pangenomic chips: 2,289 genes exhibited statistically significant changes in expressed levels due to loss of PCDH12. Functional grouping of modified genes was obtained by GoMiner software. Gene clusters that contained most of the differentially expressed genes were those involved in tissue morphogenesis and development, angiogenesis, cell-matrix adhesion and migration, immune response, and chromatin remodeling. Our data show that loss of PCDH12 leads to morphological alterations of the placenta and to notable changes in its gene expression profile. Specific genes emerging from the microarray screen support the biological modifications observed in PCDH12-deficient placentas.

International audience; Protocadherins are transmembrane proteins exhibiting homophilic adhesive activities through their extracellular domain. Protocadherin 12 (Pcdh12) is expressed in angiogenic endothelial cells, mesangial cells of kidney glomeruli, and glycogen cells of the mouse placenta. To get insight into the role of this protein in vivo, we analyzed PCDH12-deficient mice and investigated their placental phenotype. The mice were alive and fertile; however, placental and embryonic sizes were reduced compared with wild-type mice. We observed defects in placental layer segregation and a decreased vascularization of the labyrinth associated with a reduction in cell density in this layer. To understand the molecular events responsible for the phenotypic alterations observed in Pcdh12(-/-) placentas, we analyzed the expression profile of embryonic day 12.5 mutant placentas compared with wild-type placentas, using pangenomic chips: 2,289 genes exhibited statistically significant changes in expressed levels due to loss of PCDH12. Functional grouping of modified genes was obtained by GoMiner software. Gene clusters that contained most of the differentially expressed genes were those involved in tissue morphogenesis and development, angiogenesis, cell-matrix adhesion and migration, immune response, and chromatin remodeling. Our data show that loss of PCDH12 leads to morphological alterations of the placenta and to notable changes in its gene expression profile. Specific genes emerging from the microarray screen support the biological modifications observed in PCDH12-deficient placentas.

Background This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.

We propose a method for estimating the number of clusters in data sets based only on the knowledge of the similarity measure between the data points to be clustered. The technique is inspired from spectral learning algorithms and Cramer multiplicity and is tested on synthetic and real data sets. This approach has the advantage to be computationally inexpensive while being an a priori method, independent from the clustering technique.

International audience

A method for computing the probability of symbol error for space-time trellis codes is developed by means of results from large deviation theory for quadratic Gaussian forms. The issue is that in order to build a space-time trellis code with small probability of error it is sufficient to find a metric for the Viterbi decoding algorithm for which there exists a Cramer’s rate function who minimizes a criterion on the transfer function of the trellis system. In particular, this approach gives a theoretical explanation for a simulation result of [2].

This paper contains one application of a method that allows one to produce likelihood ratios for realistic detection problems involving random signals of unknown laws, a method that requires that only the law of the input to the filter of the noise be available.

In the context of stochastic dependency of the noise and signal - as in the case of the reverberation noise - the classical methods of signal detection are not applicable. The paper presents a likelihood ratio detection method based on stochastic calculus. The novel aspects of the method are: the signal and the noise need not be stochastically independent and they both can be nonstationary and non-Gaussian. This method is applicable to the active sonar which is a reverberation limited system. Simulations related to the underwater propagation of the acoustic wave show a good performance of the detector at the receiver operating characteristic level. The likelihood ratio detection method can also be successfully applied in mobile communication for the channel dynamical allocation, as well as in radar applications.

We prove a central limit theorem for products of centered i.i.d. r.v.'s taking values on nilpotent, graded, simply connected Lie groups. The main tool is given by weak approximation results for SDEs.

Signal detection is one of the basic problems in statistical communication theory, and has many applications to contemporary technology, whether in engineering, medical science, or the environment. The most difficult problems are those involving random signals, and it is these types of signals that are found in applications to complex systems (the ocean, the atmosphere, the ecosystem). What is known of the subject at the present time is insufficient in that it suffers from mathematical restrictions which are difficult to justify in practice, is limited in the types of noises that can be accommodated, which do not cover the noises one meets in nature, and is based on algorithms whose behavior is not sufficiently understood. The broad aim of this thesis is to solve some of the problems that are open in that area of research. As detection of a non-Gaussian stochastic signal in additive and dependent Gaussian noise can be viewed as the canonical detection problem for active sonar in a reverberation-limited environment, and that this detection problem, except for a multiplicity restriction, is, mathematically, the problem nearest to a satisfactory solution, the first part of the thesis deals with the definition and the properties of a form of the Itô stochastic integral that must be tailored to remove the multiplicity restriction mentioned above. On the way some interesting connections with other forms of the stochastic integral are investigated. The second part of the thesis is devoted to the derivation of the likelihood ratio which acts as an universal detector, still within the framework of a stochastic signal in dependent Gaussian noise. The solution of the Gaussain noise problem is based on a representation of the noise and signal-plus-noise processes as superpositions of causal filters acting on noise and signal-plus-noise processes that are semimartingales, for the treatment of which stochastic calculus is the most efficient tool. The decomposition used is the Cramér-Hida decomposition which is particularly suited to the handling of Gaussian processes, though it is much more broadly valid. The last part of the thesis is a study of the possibility to extend the method that works for Gaussian noise to situations for which the noise is no longer Gaussian. A likelihood formula is obtained for noises that are non anti- cipative transformations of the sum of a Wiener process and an independent Poisson martingale.