Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

Micro-capteur à fort gradient de température pour des mesures de frottement pariétal et de direction de l'écoulement

International audienceWe present an efficient and high-sensitive thermal micro-sensor for near wall flow parametersmeasurements. By combining substrate-free wire structure and mechanical support using siliconoxide micro-bridges, the sensor achieves a high temperature gradient, with wires reaching 1 mmlong for only 3 µm wide over a 20 µm deep cavity. Elaborated to reach a compromise solutionbetween conventional hot-films and hot-wire sensors, the sensor presents a high sensitivity to thewall shear stress and to the flow direction. The sensor can be mounted flush to the wall for research studies such as turbulence and near wall shear flow analysis, and for technical applications, such as flow control and separation detection. The fabrication process is CMOS-compatible and allows on-chip integration. The present letter describes the sensor elaboration, design, and micro-fabrication, then the electrical and thermal characterizations, and finally the calibration experiments in a turbulent boundary layer wind tunnel

Mise en oeuvre de capteurs RF-MEMS acoustiques pour l’industrie 4.0

Cette étude propose la conception complète d’un système de suivi à distance des sollicitations mécaniques dans les machines électriques afin de répondre aux problématiques de l’industrie 4.0 et de la maintenance prédictive. Elle s’appuie sur la conception, la fabrication et la caractérisation de MEMS acoustiques hautes fréquences (bande ISM à 433MHz) intégrés à un banc de test et comparés aux performances de jauges de déformation commerciales