Dendriform-Tree Setting for Fully Non-commutative Fliess Operators

This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in quantum control. In particular, a description of such Fliess operators is provided using planar binary trees. Sufficient conditions for convergence of the defining series are also given

Interconnections of Nonlinear Systems Driven by L₂-ITÔ Stochastic Processes

Fliess operators have been an object of study in connection with nonlinear systems acting on deterministic inputs since the early 1970\u27s. They describe a broad class of nonlinear input-output maps using a type of functional series expansion, but in most applications, a system\u27s inputs have noise components. In such circumstances, new mathematical machinery is needed to properly describe the input-output map via the Chen-Fliess algebraic formalism. In this dissertation, a class of L2-Itô stochastic processes is introduced specifically for this purpose. Then, an extension of the Fliess operator theory is presented and sufficient conditions are given under which these operators are convergent in the mean-square sense. Next, three types of system interconnections are considered in this context: the parallel, product and cascade connections. This is done by first introducing the notion of a formal Fliess operator driven by a formal stochastic process. Then the generating series induced by each interconnection is derived. Finally, sufficient conditions are given under which the generating series of each composite system is convergent. This allows one to determine when an interconnection of Fliess operators driven by a class of L2-Itô stochastic processes is well-defined

Les lymphocytes du tissu adipeux humain : caractérisation et rôles

L'obésité est associée à un état inflammatoire systémique de bas niveau et à une production excessive de cytokines pro-inflammatoires dans le tissu adipeux (TA). La principale source de ces cytokines est le macrophage qui a été décrit pour s'accumuler dans le TA au cours de l'obésité. Ces travaux de thèse ont pour but de caractériser et d'analyser le rôle potentiel des partenaires immunitaires des macrophages, les lymphocytes dans le TA. Nos travaux montrent que le nombre de lymphocytes présents dans le TA humain augmente avec l'indice de masse corporelle (IMC) des patients ainsi qu'avec la localisation viscérale du TA. Les lymphocytes du TA humain sont majoritairement des cellules TCD3+, CD4+ et CD8+, effecteurs et mémoires. Nos études sur les milieux conditionnés par les lymphocytes CD3+ isolés du TA ont permis de démontrer que les lymphocytes ont un effet anti-adipogénique sur les cellules progénitrices. Sur les adipocytes matures, ils inhibent l'effet de l'insuline sur l'expression des enzymes de la lipogenèse. Les modèles animaux montrent une cinétique complexe de trafic des cellules immunes dans le TA au cours du développement de l'obésité et une accumulation forte de cellules natural killer et de macrophages dans le TA de souris immunodéficientes. L'ensemble de ce travail a permis de caractériser les populations lymphocytaires présentes dans le TA humain et de montrer que leurs productions peuvent moduler le métabolisme mais également la différenciation adipocytaire humaine. Les résultats obtenus sur les modèles murins suggèrent que les lymphocytes du TA pourraient exercer un rôle protecteur en limitant le développement d'une réaction inflammatoire innée excessiveObesity is associated to a low level systemic inflammatory state and to an excessive production of pro-inflammatory cytokines in adipose tissue. These cytokines are mainly produced by macrophages, previously described to accumulate in adipose tissue (AT) during obesity. My PhD work has been focussed on characterizing and analyzing the potential role of lymphocytes, immune partners of macrophages. Our results show that the number of lymphocytes presents in AT increases with the body mass index (BMI) and with the visceral AT location. Human AT lymphocytes are mainly effector and memory CD3+ CD4+ and CD3+ CD8+ T cells. A study on AT CD3+ lymphocyte-conditioned media allowed us to demonstrate an anti-adipogenic effect of lymphocytes on AT progenitor cells. In addition, these media inhibit the insulin-mediated effect on the expression of lipogenic enzymes from mature adipocytes. Murine models show a complex traffic of immune cells in adipose tissues during the onset of obesity and a marked accumulation of natural killer cells and macrophages in AT from immunodeficient mice. All these results allowed us to characterize the lymphocyte populations of the human AT and to demonstrate that their productions can modulate both the metabolism and the adipocyte differentiation. The data obtained on murine models suggest that adipose tissue lymphocytes could have a protective role limiting the development of an excessive innate inflammatory reactio