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

The ChromaTest, a digital color contrast sensitivity analyzer, for diabetic maculopathy: a pilot study

BACKGROUND: To assess the ability of the Chromatest in investigating diabetic maculopathy. METHOD: Patients with Type 2 diabetes and no concurrent ocular pathology or previous laser photocoagulation were recruited. Visual acuities were assessed followed by colour contrast sensitivity testing of each eye using Chromatest. Dilated fundoscopy with slit lamp biomicroscopy with 78 D lens was then performed to confirm the stage of diabetic retinopathy according to the Early Treatment Diabetic Retinopathy Study. RESULTS: 150 eyes in 150 patients were recruited into this study. 35 eyes with no previous laser photocoagulation were shown to have clinically significant macular oedema (CSMO) and 115 eyes with untreated non-proliferative diabetic retinopathy (NPDR) on fundus biomicroscopy. Statistical significant difference was found between CSMO and NPDR eyes for protan colour contrast threshold (p = 0.01). Statistical significance was found between CSMO and NPDR eyes for tritan colour contrast threshold (p = 0.0002). Sensitivity and specificity for screening of CSMO using pass-fail criterion for age matched TCCT results achieved 71% (95% confidence interval: 53-85%) and 70% (95% confidence interval: 60-78%), respectively. However, threshold levels were derived using the same data set for both training and testing the effectiveness since this was the first study of NPDR using the Chromatest CONCLUSION: The ChromaTest is a simple, cheap, easy to use, and quick test for colour contrast sensitivity. This study did not achieve results to justify use of the Chromatest for screening, but it reinforced the changes seen in tritan colour vision in diabetic retinopathy

Revealed preference tests for collective household behavior

This chapter contains a state of the art of revealed preference tests for consistency of observed household behavior with Pareto efficiency. These tests are entirely nonparametric, since they do not require any assumptions regarding the parametric form of individual preferences or the intrahousehold bargaining process. We start with a discussion of some tests that are based on Chiappori’s (Econometrica, 56, 63–89, 1988) seminal labor supply model with egoistic preferences and observed individual leisure. We then present revealed preference conditions for Browning and Chiappori’s (Econometrica, 66, 1241–1278, 1998) collective consumption model with general individual preferences (including public goods and externalities) and only aggregate household consumption observed. Finally, we deal with a test for special cases of the general model, one that is based on integer programming