A Contraction Theory Approach to Stochastic Incremental Stability

We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of stochastic nonlinear observers design and stochastic synchronization.Comment: 23 pages, 2 figure

Analysis of chronic rejection and obliterative arteriopathy: Possible contributions of donor antigen-presenting cells and lymphatic disruption

Sequential analysis of changes that lead to chronic rejection was undertaken in an animal model of chronic rejection and obliterative arteriopathy. Brown Norway rats are pretreated with a Lewis bone marrow infusion or a Lewis orthotopic liver allograft and a short course of immunosuppression. They are challenged 100 days later with a Lewis heterotopic heart graft without immunosuppression. The heart grafts in both groups undergo a transient acute rejection, but all rats are operationally tolerant; the heart grafts are accepted and remain beating for more than 100 days. Early arterial remodeling, marked by arterial bromodeoxyuridine incorporation, occurred in both groups between 5 and 30 days during the transient acute rejection. It coincided with the presence of interstitial (but not arterial intimal) inflammation and lymphatic disruption and resulted in mild intimal thickening. Significant arterial narrowing occurred only in the bone-marrow-pretreated rats between 60 and 100 days. It was associated with T lymphocyte and macrophage inflammation of the heart graft that accumulated in the endocardium and arterial intima and adventitia near draining lymphatics. There also was loss of passenger leukocytes from the heart graft, up-regulation of cytokine mRNA and major histocompatibility class II on the endothelium, and focal disruption of lymphatics. In contrast, long-surviving heart grafts from the Lewis orthotopic liver allograft pretreated group are near normal and freedom from chronic rejection in this group was associated with persistence of donor major histocompatibility class-II-positive hematolymphoid cells, including OX62+ donor dendritic cells. This study offers insights into two different aspects of chronic rejection: 1) possible mechanisms underlying the persistent immunological injury and 2) the association between immunological injury and the development of obliterative arteriopathy. Based on the findings, it is not unreasonable to raise the testable hypothesis that direct presentation of alloantigen by donor antigen-presenting cells is required for long-term, chronic-rejection-free allograft acceptance. In addition, chronic intermittent lymphatic disruption is implicated as a possible mechanism for the association between chronic interstitial allograft inflammation and the development of obliterative arteriopathy

Where neuroscience and dynamic system theory meet autonomous robotics: A contracting basal ganglia model for action selection

International audienceAction selection, the problem of choosing what to do next, is central to any autonomous agent architecture. We use here a multidisciplinary approach at the convergence of neuro-science, dynamical systems theory and autonomous robotics, in order to propose an efficient action selection mechanism based on a new model of the basal ganglia. We first describe new developments of contraction theory regarding locally projected dynamical systems. We exploit these results to design a stable computational model of the cortico-baso-thalamo-cortical loops. Based on recent anatomical data, we include usually neglected neu-ral projections, which participate in performing accurate selection. Finally, the efficiency of this model as an autonomous robot action selection mechanism is assessed in a standard survival task. The model exhibits valuable dithering avoidance and energy-saving properties , when compared with a simple if-then-else decision rule

One-loop flavor changing electromagnetic transitions

We discuss the effect of the external fermion masses in the flavor-changing radiative transitions of a heavy fermion (quark or lepton) to a lighter fermion at the one-loop level, and point out an often overlooked crucial difference in the sign of a charge factor between transitions of the down type $s\to d\gamma$ and the up type $c\to u\gamma$. We give formulas for the $F\to f\gamma$ effective vertex in various approximations and the exact formula for $t\to c\gamma$ and $\tau \to \mu \gamma$.Comment: LaTeX 16 pages + 4 postscript figures. Misprints corrected, some Comments adde

Neutrinos in 5D SO(10) Unification

We study neutrino physics in a 5D supersymmetric SO(10) GUT. We analyze several different choices for realizing the See-Saw mechanism. We find that the "natural" scale for the Majorana mass of right-handed neutrinos depends critically on whether the right-handed neutrinos are located in the bulk or localized on a brane. In the former case, the effective Majorana mass is "naturally" of order the compactification scale, about 10^{14} GeV. Note, this is the value necessary for obtaining a light tau neutrino mass approximately 10^{-2} eV which, within the context of hierarchical neutrino masses, is the right order of magnitude to explain atmospheric neutrino oscillations. On the other-hand when the right-handed neutrino is localized on the brane, the effective Majorana mass is typically larger than the compactification scale. Nevertheless with small parameters of order 1/10 - 1/30, an effective Majorana mass of order 10^{14} GeV can be accommodated. We also discuss the constraints on model building resulting from the different scenarios for locating the right-handed neutrinos.Comment: 24 page

BIOLOGICAL AMMONIA REMOVAL BY SUBMERGED AERATED FILTER FROM HANOI GROUND WATER

Joint Research on Environmental Science and Technology for the Eart