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Honeine P.,CNRS Risk Management Science and Technology | Richard C.,University of Nice Sophia Antipolis
IEEE Signal Processing Magazine

Kernel machines have gained considerable popularity during the last 15 years, making a breakthrough in nonlinear signal processing and machine learning, thanks to extraordinary advances. This increased interest is undoubtedly driven by the practical goal of being able to easily develop efficient nonlinear algorithms. The key principle behind this, known as the kernel trick, exploits the fact that a great number of data-processing techniques do not explicitly depend on the data itself but rather on a similarity measure between them, i.e., an inner product. © 2006 IEEE. Source

Panicaud B.,CNRS Risk Management Science and Technology
International Journal of Theoretical Physics

The multivectorial algebras present yet both an academic and a technological interest. Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish between polar and axial vectors and between scalars and pseudo scalars. Then a total of eight elements are often considered even if they are not given the correct name of multivectors. Eventually because of their simplicity, only the vectorial algebra or the quaternions algebra are explicitly used for physical applications. Nevertheless, it should be more convenient to use directly more complex algebras in order to have a wider range of application. The aim of this paper is to inquire into one particular Clifford algebra which could solve this problem. The present study is both didactic concerning its construction and pragmatic because of the introduced applications. The construction method is not an original one. But this latter allows to build up the associated real algebra as well as a peculiar formalism that enables a formal analogy with the classical vectorial algebra. Finally several fields of the theoretical physics will be described thanks to this algebra, as well as a more applied case in general relativity emphasizing simultaneously its relative validity in this particular domain and the easiness of modeling some physical problems. © 2011 Springer Science+Business Media, LLC. Source

Duhamel C.,CNRS Laboratory of Informatics, Modeling and Optimization of Systems | Lacomme P.,CNRS Laboratory of Informatics, Modeling and Optimization of Systems | Prodhon C.,CNRS Risk Management Science and Technology
Engineering Applications of Artificial Intelligence

Routing Problems have been deeply studied over the last decades. Split procedures have proved their efficiency for those problems, especially within global optimization frameworks. The purpose is to build a feasible routing solution by splitting a giant tour into trips. This is done by computing a shortest path on an auxiliary graph built from the giant tour. One of the latest advances consists in handling extra resource constraints through the generation of labels on the nodes of the auxiliary graph. Lately, the development of a new generic split family based on a Depth First Search (DFS) approach during label generation has highlighted the efficiency of this new method for the routing problems, through extensive numerical evaluations on the location-routing problem. In this paper, we present a hybrid Evolutionary Local Search (hybrid ELS) for non-homogeneous fleet Vehicle Routing Problems (VRP) based on the application of split strategies. Experiments show our method is able to handle all known benchmarks, from Vehicle Fleet Mix Problems to Heterogeneous Fleet VRP (HVRP). We also propose a set of new realistic HVRP instances from 50 to more than 250 nodes coming from French counties. It relies on real distances in kilometers between towns. Since many classical HVRP instance sets are solved to optimality, this new set of instances could allow a fair comparative study of methods. The DFS split strategy shows its efficiency and attests the fact that it can be a promising line of research for routing problems including numerous additional constraints. © 2011 Elsevier Ltd. All rights reserved. Source

Fillatre L.,CNRS Risk Management Science and Technology
IEEE Transactions on Signal Processing

This paper deals with the detection of hidden bits in the Least Significant Bit (LSB) plane of a natural image. The mean level and the covariance matrix of the image, considered as a quantized Gaussian random matrix, are unknown. An adaptive statistical test is designed such that its probability distribution is always independent of the unknown image parameters, while ensuring a high probability of hidden bits detection. This test is based on the likelihood ratio test except that the unknown parameters are replaced by estimates based on a local linear regression model. It is shown that this test maximizes the probability of detection as the image size becomes arbitrarily large and the quantization step vanishes. This provides an asymptotic upper-bound for the detection of hidden bits based on the LSB replacement mechanism. Numerical results on real natural images show the relevance of the method and the sharpness of the asymptotic expression for the probability of detection. © 2011 IEEE. Source

Barchiesi D.,CNRS Risk Management Science and Technology
Optics Communications

The surface plasmon resonance (SPR) is known since the late 1950s. Its understanding was popularized by analytical models, in simple cases such as metallic plane plates between two dielectric media. The optimization of such structure for SPR biosensor applications is traditionally based on the minimization of the reflectance. Nevertheless this approach suffers from instabilities that require the limitation of the domain of search. An alternative formulation using the scattering matrix is proposed to improve the efficiency of optimization of this setup. The proposed model is mathematically rigorous and is coherent with the description of resonances in other fields of physics. The results of optimization and sensitivity analysis are discussed. © 2012 Elsevier B.V. All rights reserved. Source

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