Information dynamics: Temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text modified, to appear in Cent. Eur. J. Phy

Natural boundaries for the Smoluchowski equation and affiliated diffusion processes

The Schr\"{o}dinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994

On the use of State Predictors in Networked Control Systems

International audienceWithout pretending to be exhaustive, the aim of this chapter is to give an overview on the use of the state predictor in the context of time-delay systems, and more particularly for the stabilisation of networked control systems. We show that the stabilisation of a system through a deterministic network can be considered as the stabilisation of a time-delayed system with a delay of known dynamics. The predictor approach is proposed, along with some historical background on its application to time-delayed systems, to solve this problem. Some simulation results are also presented

No evidence for loss of short-wavelength sensitive cone photoreceptors in normal ageing of the primate retina

In old world primates including humans, cone photoreceptors are classified according to their maximal sensitivity at either short (S, blue), middle (M, green) or long (L, red) wavelengths. Colour discrimination studies show that the S-cone pathway is selectively affected by age and disease, and psychophysical models implicate their loss. Photoreceptors have high metabolic demand and are susceptible to age or disease-related losses in oxygen and nutrient supply. Hence 30% of rods are lost over life. While comparable losses are not seen in cones, S-cones comprise less than 10% of the cone population, so significant loss would be undetected in total counts. Here we examine young and aged primate retinae stained to distinguish S from M/L-cones. We show there is no age-related cone loss in either cone type and that S-cones are as regularly distributed in old as young primates. We propose that S-cone metabolism is less flexible than in their M/L counterparts, making them more susceptible to deficits in normal cellular function. Hypoxia is a feature of the ageing retina as extracellular debris accumulates between photoreceptors and their blood supply which likely impacts S-cone function. However, that these cells remain in the ageing retina suggests the potential for functional restoration

A Unified Framework for Signal Processing Applications

An overview of the computational issues; statistical, numerical, and algebraic properties, and new generalizations and applications of advances on TLS and EIV models. Experts from several disciplines prepared overview papers which were presented at the conference and are included in this book.https://nsuworks.nova.edu/gscis_facbooks/1025/thumbnail.jp

A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations

Recent results concerning cross Grammians for both SlSO and symmetric MIMO systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations