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Nguyen T.T.,FEMTO ST Institute | Lenczner M.,FEMTO ST Institute | Brassart M.,Laboratoire Of Mathematiques Of Besancon
Lecture Notes in Computational Science and Engineering | Year: 2015

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary conditions of the homogenized equation. Numerical simulations are reported. © Springer International Publishing Switzerland 2015. Source

Henriques J.,Laboratoire Of Mathematiques Of Besancon | Pazart L.,Besancon University Hospital Center | Pazart L.,Ea 481 Laboratoire Of Neurosciences Of Besancon | Grigoryeva L.,Laboratoire Of Mathematiques Of Besancon | And 12 more authors.
PLoS ONE | Year: 2016

To measure the level of residual cognitive function in patients with disorders of consciousness, the use of electrophysiological and neuroimaging protocols of increasing complexity is recommended. This work presents an EEG-based method capable of assessing at an individual level the integrity of the auditory cortex at the bedside of patients and can be seen as the first cortical stage of this hierarchical approach. The method is based on two features: first, the possibility of automatically detecting the presence of a N100 wave and second, in showing evidence of frequency processing in the auditory cortex with a machine learning based classification of the EEG signals associated with different frequencies and auditory stimulation modalities. In the control group of twelve healthy volunteers, cortical frequency processing was clearly demonstrated. EEG recordings from two patients with disorders of consciousness showed evidence of partially preserved cortical processing in the first patient and none in the second patient. From these results, it appears that the classification method presented here reliably detects signal differences in the encoding of frequencies and is a useful tool in the evaluation of the integrity of the auditory cortex. Even though the classification method presented in this work was designed for patients with disorders of consciousness, it can also be applied to other pathological populations. © 2016 Henriques et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Source

Boussaid N.,Laboratoire Of Mathematiques Of Besancon | Caponigro M.,French National Conservatory of Arts and Crafts | Chambrion T.,University of Lorraine | Chambrion T.,French National Center for Scientific Research | Chambrion T.,French Institute for Research in Computer Science and Automation
SIAM Conference on Control and Its Applications 2015 | Year: 2015

This note presents a positive approximate controllability result for a bilinear quantum system modeling a chemical bond. The main difficulties are due to the presence of a continuous spectrum part for the uncontrolled Hamiltonian (modeled by a Morse potential) and the unboundedness of the interaction potential (dipolar interaction). The proof is based on averaging technique and spectral analysis. Source

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