Mines ParisTech

About: Mines ParisTech is a education organization based out in Paris, France. It is known for research contribution in the topics: Finite element method & Microstructure. The organization has 6564 authors who have published 11676 publications receiving 359898 citations. The organization is also known as: École nationale supérieure des mines de Paris & École des mines de Paris.

Flatness of Heavy Chain Systems

Abstract: In this paper the flatness [M. Fliess, J. Levine, P. Martin, and P. Rouchon, Internat. J. Control, 61 (1995), pp. 1327--1361, M. Fliess, J. Levine, P. Martin, and P. Rouchon, IEEE Trans. Automat. Control, 44 (1999), pp. 922--937] of heavy chain systems, i.e., trolleys carrying a fixed length heavy chain that may carry a load, is addressed in the partial derivatives equations framework. We parameterize the system trajectories by the trajectories of its free end and solve the motion planning problem, namely, steering from one state to another state. When considered as a finite set of small pendulums, these systems were shown to be flat [R. M. Murray, in Proceedings of the IFAC World Congress, San Francisco, CA, 1996, pp. 395--400]. Our study is an extension to the infinite dimensional case. Under small angle approximations, these heavy chain systems are described by a one-dimensional (1D) partial differential wave equation. Dealing with this infinite dimensional description, we show how to get the explicit parameterization of the chain trajectory using (distributed and punctual) advances and delays of its free end. This parameterization results from symbolic computations. Replacing the time derivative by the Laplace variable $s$ yields a second order differential equation in the spatial variable where s is a parameter. Its fundamental solution is, for each point considered along the chain, an entire function of s of exponential type. Moreover, for each, we show that, thanks to the Liouville transformation, this solution satisfies, modulo explicitly computable exponentials of s, the assumptions of the Paley--Wiener theorem. This solution is, in fact, the transfer function from the flat output (the position of the free end of the system) to the whole state of the system. Using an inverse Laplace transform, we end up with an explicit motion planning formula involving both distributed and punctual advances and delays operators.

Synthesis and characterization of a thiourea derivative of chitosan for platinum recovery

Abstract: Chitosan is effective at removing platinum from dilute solutions, but sorption properties are significantly affected by the presence of competitor anions, such as chloride and, especially, sulfate anions. Sorption capacities in such complex solutions are enhanced by grafting thiourea through glutaraldehyde linkage. The influence of the amount of glutaraldehyde and thiourea in the impregnation bath was investigated and optimized with special attention to the composition of the solution and the type of acid used for pH control. This modification involves a change in the sorption mechanism: While glutaraldehyde-crosslinked chitosan adsorbs platinum through an ion-exchange mechanism, the thiourea derivative of chitosan acts as a chelating resin, less sensitive to ionic strength and competitor anions. Platinum sorption is also less sensitive to pH, and increasing the sulfate anion concentration has a limited effect on platinum sorption in comparison with the crosslinked sorbent. Thiourea grafting seems to increase sorption kinetics, especially in solutions controlled with sulfuric acid. SEM–EDAX techniques as well as FTIR analyses were used to characterize chemical modifications of the sorbent. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 119–134, 2000

Graph-Driven Feature Extraction From Microarray Data Using Diffusion Kernels and Kernel CCA

Abstract: We present an algorithm to extract features from high-dimensional gene expression profiles, based on the knowledge of a graph which links together genes known to participate to successive reactions in metabolic pathways. Motivated by the intuition that biologically relevant features are likely to exhibit smoothness with respect to the graph topology, the algorithm involves encoding the graph and the set of expression profiles into kernel functions, and performing a generalized form of canonical correlation analysis in the corresponding reproducible kernel Hilbert spaces. Function prediction experiments for the genes of the yeast S. Cerevisiae validate this approach by showing a consistent increase in performance when a state-of-the-art classifier uses the vector of features instead of the original expression profile to predict the functional class of a gene.