Stability of the stochastic heat equation in L1([0,1])L^1([0,1])

We consider the white-noise driven stochastic heat equation on $[0,\infty)\times[0,1]$ with Lipschitz-continuous drift and diffusion coefficients $b$ and $\sigma$. We derive an inequality for the $L^1([0,1])$-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some {\it a priori} estimates on solutions. This allows us to prove the strong existence and (partial) uniqueness of weak solutions when the initial condition belongs only to $L^1([0,1])$, and the stability of the solution with respect to this initial condition. We also obtain, under some conditions, some results concerning the large time behavior of solutions: uniqueness of the possible invariant distribution and asymptotic confluence of solutions

Contraction analysis of nonlinear random dynamical systems

In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of contraction (almost sure contraction and contraction in mean square) which allow to master the evolution of a stochastic system in two manners. The first one guarantees eventual exponential convergence of the system for almost all draws, whereas the other guarantees the exponential convergence in $L_2$ of to a unique trajectory. We then illustrate the relative simplicity of this extension by analyzing usual deterministic properties in the presence of noise. Specifically, we analyze stochastic gradient descent, impact of noise on oscillators synchronization and extensions of combination properties of contracting systems to the stochastic case. This is a first step towards combining the interesting and simplifying properties of contracting systems with the probabilistic approach.Comment: No. RR-8368 (2013

He-like ions as practical astrophysical plasma diagnostics: From stellar coronae to active galactic nuclei

We review X-ray plasma diagnostics based on the line ratios of He-like ions. Triplet/singlet line intensities can be used to determine electronic temperature and density, and were first developed for the study of the solar corona. Since the launches of the X-ray satellites Chandra and XMM-Newton, these diagnostics have been extended and used (from CV to Si XIII) for a wide variety of astrophysical plasmas such as stellar coronae, supernova remnants, solar system objects, active galactic nuclei, and X-ray binaries. Moreover, the intensities of He-like ions can be used to determine the ionization process(es) at work, as well as the distance between the X-ray plasma and the UV emission source for example in hot stars. In the near future thanks to the next generation of X-ray satellites (e.g., Astro-H and IXO), higher-Z He-like lines (e.g., iron) will be resolved, allowing plasmas with higher temperatures and densities to be probed. Moreover, the so-called satellite lines that are formed closed to parent He-like lines, will provide additional valuable diagnostics to determine electronic temperature, ionic fraction, departure from ionization equilibrium and/or from Maxwellian electron distribution.Comment: 36 pages, 16 figures. Invited Review talk at the "High-resolution X-ray spectroscopy: past, present, and future" conference, Utrecht, March 15-17 2010. Accepted for publication in Space Science Reviews (2010); the final publication is available at http://www.springerlink.co

Chaotic iterations versus Spread-spectrum: chaos and stego security

A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of chaos-security is clarified, by presenting a novel data hiding scheme that is twice stego and chaos-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative chaos-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme

Postural destabilization induced by trunk extensor muscles fatigue is suppressed by use of a plantar pressure-based electro-tactile biofeedback

Separate studies have reported that postural control during quiet standing could be (1) impaired with muscle fatigue localized at the lower back, and (2) improved through the use of plantar pressure-based electro-tactile biofeedback, under normal neuromuscular state. The aim of this experiment was to investigate whether this biofeedback could reduce postural destabilization induced by trunk extensor muscles. Ten healthy adults were asked to stand as immobile as possible in four experimental conditions: (1) no fatigue/no biofeedback, (2) no fatigue/biofeedback, (3) fatigue/no biofeedback and (4) fatigue/biofeedback. Muscular fatigue was achieved by performing trunk repetitive extensions until maximal exhaustion. The underlying principle of the biofeedback consisted of providing supplementary information related to foot sole pressure distribution through electro-tactile stimulation of the tongue. Centre of foot pressure (CoP) displacements were recorded using a force platform. Results showed (1) increased CoP displacements along the antero-posterior axis in the fatigue than no fatigue condition in the absence of biofeedback and (2) no significant difference between the no fatigue and fatigue conditions in the presence of biofeedback. This suggests that subjects were able to efficiently integrate an artificial plantar pressure information delivered through electro-tactile stimulation of the tongue that allowed them to suppress the destabilizing effect induced by trunk extensor muscles fatigue

Lyapunov exponent evaluation of a digital watermarking scheme proven to be secure

In our previous researches, a new digital watermarking scheme based on chaotic iterations has been introduced. This scheme was both stego-secure and topologically secure. The stego-security is to face an attacker in the "watermark only attack" category, whereas the topological security concerns other categories of attacks. Its Lyapunov exponent is evaluated here, to quantify the chaos generated by this scheme. Keywords : Lyapunov exponent; Information hiding; Security; Chaotic iterations; Digital Watermarking.Comment: 10 page

Universality of thermally assisted magnetic domain wall motion under spin torque

Thermally assisted motion of magnetic domain wall under spin torque is studied theoretically. It is shown that the wall velocity $v$ depends exponentially on the spin current, \Is, below the threshold value, in the same way as in a thermally activated motion driven by a force. A novel property of the spin torque driven case at low temperature is that the linear term in spin current is universal, i.e., \ln v \sim \frac{\pi\hbar}{2e}(\Is/\kB T). This behavior, which is independent of pinning and material constants, could be used to confirm experimentally the spin torque as the driving mechanism

Bulking II: Classifications of Cellular Automata

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools allowing to classify cellular automata