8,808 research outputs found
Stability of the stochastic heat equation in
We consider the white-noise driven stochastic heat equation on
with Lipschitz-continuous drift and diffusion
coefficients and . We derive an inequality for the
-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 , 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 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
Notes on Contraction Theory
These notes derive a number of technical results on nonlinear contraction
theory, a comparatively recent tool for system stability analysis. In
particular, they provide new results on the preservation of contraction through
system combinations, a property of interest in modelling biological systems
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 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
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