Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent

A study of the deep structure of the energy landscape of glassy polystyrene: the exponential distribution of the energy-barriers revealed by high-field Electron Spin Resonance spectroscopy

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field Electron Spin Resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). The exponential distribution of the energy-barriers for the rotational motion of the spin probe is unambigously evidenced at both 240K and 270K. The same shape for the distribution of the energy-barriers of PS was evidenced by the master curves provided by previous mechanical and light scattering studies. The breadth of the energy-barriers distribution of the spin probe is in the range of the estimates of the breadth of the PS energy-barriers distribution. The evidence that the deep structure of the energy landscape of PS exhibits the exponential shape of the energy-barriers distribution agrees with results from extreme-value statistics and the trap model by Bouchaud and coworkers.Comment: Final version in press as Letter to the Editor on J.Phys.:Condensed Matter. Changes in bol

Lectures on Gaussian approximations with Malliavin calculus

In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment. Shortly afterwards, Peccati and Tudor gave a multidimensional version of this characterization. Since the publication of these two beautiful papers, many improvements and developments on this theme have been considered. Among them is the work by Nualart and Ortiz-Latorre, giving a new proof only based on Malliavin calculus and the use of integration by parts on Wiener space. A second step is my joint paper "Stein's method on Wiener chaos" (written in collaboration with Peccati) in which, by bringing together Stein's method with Malliavin calculus, we have been able (among other things) to associate quantitative bounds to the Fourth Moment Theorem. It turns out that Stein's method and Malliavin calculus fit together admirably well. Their interaction has led to some remarkable new results involving central and non-central limit theorems for functionals of infinite-dimensional Gaussian fields. The current survey aims to introduce the main features of this recent theory. It originates from a series of lectures I delivered at the Coll\`ege de France between January and March 2012, within the framework of the annual prize of the Fondation des Sciences Math\'ematiques de Paris. It may be seen as a teaser for the book "Normal Approximations Using Malliavin Calculus: from Stein's Method to Universality" (jointly written with Peccati), in which the interested reader will find much more than in this short survey.Comment: 72 pages. To be published in the S\'eminaire de Probabilit\'es. Mild update: typos, referee comment

Lipids induce expression of serum-responsive transmembrane kinase EhTMKB1-9 in an early branching eukaryote Entamoeba histolytica

Mechanisms underlying the initiation of proliferative response are known only for a few organisms, and are not understood for the medically important organisms including Entamoeba histolytica. The trans membrane kinase EhTMKB1-9 of E. histolytica is one of the early indicators of proliferation and its' expression is regulated by serum, one of the components necessary for cellular proliferation in vitro. In this study we show that bovine serum albumin (BSA) can induce EhTMKB1-9 expression in place of serum, and that both follow the same mechanism. Both serum and BSA use the same promoter element and the activation process is initiated through a PI3 kinase-mediated pathway. We further show that BSA activates EhTMKB1-9 due to the lipids associated with it and that unsaturated fatty acids are responsible for activation. These results suggest that lipid molecules are ligand(s) for initiation of a signaling system that stimulates EhTMKB1-9 expression

Space Charge at Nanoscale: Probing Injection and Dynamic Phenomena Under Dark/Light Configurations by Using KPFM and C-AFM

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