Denumerable controlled Markov chains with average reward criterion: Sample path optimality

We consider discrete-time nonlinear controlled stochastic systems, modeled by controlled Makov chains with denumerable state space and compact action space. The corresponding stochastic control problem of maximizing average rewards in the long-run is studied. Departing from the most common position which usesexpected values of rewards, we focus on a sample path analysis of the stream of states/rewards. Under a Lyapunov function condition, we show that stationary policies obtained from the average reward optimality equation are not only average reward optimal, but indeed sample path average reward optimal, for almost all sample paths.Research supported by a U.S.-México Collaborative Research Program funded by the National Science Foundation under grant NSF-INT 9201430, and by CONACyT-MEXICO.Partially supported by the MAXTOR Foundation for applied Probability and Statistics, under grant No. 01-01-56/04-93.Research partially supported by the Engineering Foundation under grant RI-A-93-10, and by a grant from the AT&T Foundation.     

Solutions sous-analytiques globales de certaines équations d'Hamilton–Jacobi

In the 1980 Crandall and Lions introduced the concept of viscosity solution in order to get existence and/or unicity results for Hamilton–Jacobi equations. In this Note we focus on the Dirichlet problem for Hamilton–Jacobi equations stemming from calculus of variations, and assert that if the data are analytic then the viscosity solution is moreover subanalytic. We extend this result to generalized eikonal equations, stemming from sub-Riemannian geometry problems. To cite this article: E. Trélat, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Behaviour of (−Δ−k2−i0+)−1 outside fading obstacles,independant scattering hypothesis and applications

This paper deals with the behaviour of k‐outgoing solutions of ?Δu?k²u=f outside a fading soft obstacle. We extend an approach using the so‐called Lax–Phillips construction and the well‐known properties of the capacity of smooth obstacles. So, classical results are recovered in a straightforward manner. The previous approach enables us to consider the case of obstacles composed of many tiny spheres. Roughly speaking, we prove that the scattering amplitude is approximately the sum of the scattering amplitudes scattered by each isolated sphere, which is an alternative form of the first Born approximation. As a consequence, two inverse problems are solved. Copyright © 2003 John Wiley & Sons, Ltd.     

Actions moyennables et fonctions harmoniquesAmeanable actions and harmonic functions

We prove that the action of a countable discrete group on a locally compact invariant space of minimal harmonic functions is ameanable. To cite this article: P. Biane, E. Germain, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 355–358.     

Attenuation in trabecular bone: A comparison between numerical simulation and experimental results in human femur

Numerical simulations (finite-difference time domain) are compared to experimental results of ultrasound wave propagation through human trabecular bones. Three-dimensional high-resolution microcomputed tomography reconstructions served as input geometry for the simulation. The numerical simulation took into account scattering, but not absorption. Simulated and experimental values of the attenuation coefficients (alpha, dB/cm) and the normalized broadband ultrasound attenuation (nBUA, dB/cm/MHz) were measured and compared on a set of 28 samples. While experimental and simulated nBUA values were highly correlated (R(2)=0.83), and showed a similar dependence with bone volume fraction, the simulation correctly predicted experimental nBUA values only for low bone volume fraction (BV/TV). Attenuation coefficients were underestimated by the simulation. The absolute difference between experimental and simulated alpha values increased with both BV/TV and frequency. As a function of frequency, the relative difference between experimental and simulated alpha values decreased from 60% around 400 kHz to 30% around 1.2 MHz. Under the assumption that the observed discrepancy expresses the effect of the absorption, our results suggests that nBUA and its dependence on BV/TV can be mostly explained by scattering, and that the relative contribution of scattering to alpha increases with frequency, becoming predominant (>50 %) over absorption for frequencies above 600 kHz.     

A Bayesian approach to constrained single- and multi-objective optimization

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria—the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions—as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization.     

Redefining the transparency order

In this paper, we consider the multi-bit Differential Power Analysis (DPA) in the Hamming weight model. In this regard, we revisit the definition of Transparency Order (\(\mathsf {TO}\)) from the work of Prouff (FSE 2005) and find that the definition has certain limitations. Although this work has been quite well referred in the literature, surprisingly, these limitations remained unexplored for almost a decade. We analyse the definition from scratch, modify it and finally provide a definition with better insight that can theoretically capture DPA in Hamming weight model for hardware implementation with precharge logic. At the end, we confront the notion of (revised) transparency order with attack simulations in order to study to what extent the low transparency order of an s-box impacts the efficiency of a side channel attack against its processing. To the best of our knowledge, this is the first time that such a critical analysis is conducted (even considering the original notion of Prouff). It practically confirms that the transparency order is indeed related to the resistance of the s-box against side-channel attacks, but it also shows that it is not sufficient alone to directly achieve a satisfying level of security. Regarding this point, our conclusion is that the (revised) transparency order is a valuable criterion to consider when designing a cryptographic algorithm, and even if it does not preclude to also use classical countermeasures like masking or shuffling, it enables to improve their effectiveness.     

Control of surface chemistry, substrate stiffness, and cell function in a novel terpolymer methacrylate library

A focused library of methacrylate terpolymers was synthesized to explore the effects of varying surface chemistry and adhesive peptide ligands on cell function. The chemical diversity of methacrylate monomers enabled construction of a library of polymers in which one can systematically vary the chemical composition to achieve a wide range of contact angle, Young's modulus, and T(g) values. Furthermore, the materials were designed to allow surface immobilization of bioactive peptides. We then examined the effects of these material compositions on protein adsorption and cell attachment, proliferation, and differentiation. We observed that chemical composition of the polymers was an important determinant for NIH 3T3 cell attachment and proliferation, as well as human mesenchymal stem cell differentiation, and correlated directly with the ability of the polymers to adsorb proteins that mediate cell adhesion. Importantly, functionalization of the methacrylate terpolymer library with an adhesive GRGDS peptide normalized cellular responses. RGD-functionalized polymers uniformly exhibited robust attachment, proliferation, and differentiation irrespective of the underlying substrate chemistry. These studies provide a library-based approach to rapidly explore the biological functionality of biomaterials with a wide range of compositions and highlight the importance of cell and protein cell adhesion in predicting their performance.