Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.Comment: 21 pages, 6 figure

Maximin design on non hypercube domain and kernel interpolation

In the paradigm of computer experiments, the choice of an experimental design is an important issue. When no information is available about the black-box function to be approximated, an exploratory design have to be used. In this context, two dispersion criteria are usually considered: the minimax and the maximin ones. In the case of a hypercube domain, a standard strategy consists of taking the maximin design within the class of Latin hypercube designs. However, in a non hypercube context, it does not make sense to use the Latin hypercube strategy. Moreover, whatever the design is, the black-box function is typically approximated thanks to kernel interpolation. Here, we first provide a theoretical justification to the maximin criterion with respect to kernel interpolations. Then, we propose simulated annealing algorithms to determine maximin designs in any bounded connected domain. We prove the convergence of the different schemes.Comment: 3 figure

A variational interpretation of classification EM

EM and CEM algorithms which respectively implement mixture approach and classification approach of clustering problem are shown to be instances of the same varia-tional scheme

Performance of MMSE STBC MC-CDMA over Rayleigh and MIMO METRA channels

International audienceThe performance of MMSE Single-user Detection (SD) and Multi-user Detection (MD) STBC MC-CDMA systems are analysed and compared in the case of two transmit antennas and one or two receive antennas over Rayleigh fading channels and then over the stochastic MIMO METRA channel model. With two transmit and one receive antennas, MD achieves a gain of roughly 1 dB for non-full load systems while the same performance are obtained with MD and SD for full load systems. Besides, with two receive antennas, we present a sub-optimal and an optimal MMSE SD MIMO MC-CDMA schemes, this last one offering a very good performance/complexity trade-off. Finally, the very good behaviour of MMSE STBC MC-CDMA systems is confirmed over the realistic METRA MIMO channel

STBC MC-CDMA systems: Comparison of MMSE single user and multiple user detection schemes over Rayleigh and MIMO METRA channels

International audienceThe performance of MMSE single-user detection (SD) and multi-user detection (MD) STBC multi-carrier code division multiple access (MC-CDMA) systems are analysed and compared in the case of two transmit antennas and one or two receive antennas over Rayleigh fading channels and then over the stochastic multiple input multiple output (MIMO) METRA channel model. With two transmit and one receive antennas, MD achieves a gain of roughly 1 dB for non-full load systems while the same performance is obtained with MD and SD for full load systems. Besides, with two receive antennas, we present a sub-optimal and an optimal MMSE SD MIMO MC-CDMA schemes, this last one offering a very good performance. Finally, the very good behaviour of MMSE space-time block coding (STBC) MC-CDMA systems is confirmed over the realistic multi element transmit receive antennas (METRA) MIMO channel

Multicarrier CDMA: A very promissing multiple access scheme for future wideband wireless networks

International audienceIn this paper, multicarrier techniques are studied in the context of the future wideband wireless networks. After a brief presentation of the third generation mobile networks, MC-CDMA systems are considered for the downlink of the future high rate cellular networks. The performance of different mono-user and multi-user detection techniques are compared with the help of Monte Carlo simulations over a frequency selective Rayleigh channel. Thus, the efficiency of MC-CDMA as a very promising multiple access and robust modulation scheme is successfully demonstrated for the downlink of the future wideband mobile networks. Finally, the first results concerning the performance of Multicarrier CDMA technique combined with space-time block coding in order to build a Multiple Input Multiple Output/MC-CDMA system are presented over a Rayleigh channel

Conditionally positive definite kernels: theoretical contribution, application to interpolation and approximation

Since Aronszajn (1950), it is well known that a functional Hilbert space, called Reproducing Kernel Hilbert Space (RKHS), can be associated to any positive definite kernel K. This correspondence is the basis of many useful algorithms. In the more general context of conditionally positive definite kernels the native spaces are the usual theoretical framework. However, the definition of conditionally positive definite used in that framework is not adapted to extend the results of the positive definite case. We propose a more natural and general definition from which we state a full generalization of Aronszajn's theorem. It states that for every couple (K,P) such that P is a finite-dimensional vector space of functions and K is a P-conditionally definite positive kernel, there is a unique functional semi-Hilbert space satisfying a generalized reproducing property. Eventually, we verify that this tool, as native spaces, leads to the same interpolation operator than the one provided by the Kriging method and that, using representer theorem, we can identify the solution of a regularized regression problem in the space associated to the conditionally positive definite kernel

STBC MC-CDMA systems for indoor and outdoor scenarios

We compare the performance of Alamouti's space-time block coded MC-CDMA systems for indoor and outdoor realistic scenarios with zero forcing or minimum mean square error detection schemes. Two different configurations of the system are considered for the two scenarios. The different results obtained as well for indoor as for outdoor scenarios demonstrate that spatial diversity improves significantly the performance of MC-CDMA systems. Then, Alamouti's STBC MC-CDMA schemes derive full benefit from the frequency and spatial diversities and can be considered as a very realistic and promising candidate for the air interface downlink of the 4th generation mobile radio systems

Modèles d'acoustique phénoménologiques - Application à la conception de matériaux sur mesure

Les modèles d'acoustique phénoménologique permettent, à partir de la description géométrique d'un matériau poreux, d'obtenir sa courbe d'absorption en fonction de la fréquence d'une onde le traversant. Faciles à programmer et à calculer, ces modèles permettent lors de la phase de conception d'une architecture poreuse d'accorder la structure aux exigences d'un cahier des charges. Nous présenterons une utilisation de ces modèles dans le cadre d'une approche Material-by-design

Representation graphique des coefficients d'anisotropies des milieux élastiques généralisés

On s'intéressera à des modèles d’élasticité généralisé : modèles se caractérisant par la prise en compte de longueurs internes. Nous introduirons une méthode graphique permettant de savoir, a priori, pour un modèle généralisé quelconque et pour un groupe de symétrie quelconque, le nombre de coefficients définissant l'opérateur de comportement associé. Cette approche permet d’obtenir les informations nécessaires pour dériver l’expression analytique de l’opérateur concerné