Generic design of Chinese remaindering schemes

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a radix ladder, for the intermediate storage and computations. Our design is structured into three main modules: a black box residue computation in charge of computing each residue; a Chinese remaindering controller in charge of launching the computation and of the termination decision; an integer builder in charge of the reconstruction computation. We then show that this design enables many different forms of Chinese remaindering (e.g. deterministic, early terminated, distributed, etc.), easy comparisons between these forms and e.g. user-transparent parallelism at different parallel grains

3D printing of gas jet nozzles for laser-plasma accelerators

Recent results on laser wakefield acceleration in tailored plasma channels have underlined the importance of controlling the density profile of the gas target. In particular it was reported that appropriate density tailoring can result in improved injection, acceleration and collimation of laser-accelerated electron beams. To achieve such profiles innovative target designs are required. For this purpose we have reviewed the usage of additive layer manufacturing, commonly known as 3D printing, in order to produce gas jet nozzles. Notably we have compared the performance of two industry standard techniques, namely selective laser sintering (SLS) and stereolithography (SLA). Furthermore we have used the common fused deposition modeling (FDM) to reproduce basic gas jet designs and used SLA and SLS for more sophisticated nozzle designs. The nozzles are characterized interferometrically and used for electron acceleration experiments with the Salle Jaune terawatt laser at Laboratoire d'Optique Appliqu\'ee

On two ways to use determinantal point processes for Monte Carlo integration -- Long version

International audienceWhen approximating an integral by a weighted sum of function evaluations, determinantal point processes (DPPs) provide a way to enforce repulsion between the evaluation points. This negative dependence is encoded by a kernel. Fifteen years before the discovery of DPPs, Ermakov & Zolotukhin (EZ, 1960) had the intuition of sampling a DPP and solving a linear system to compute an unbiased Monte Carlo estimator of the integral. In the absence of DPP machinery to derive an efficient sampler and analyze their estimator, the idea of Monte Carlo integration with DPPs was stored in the cellar of numerical integration. Recently, Bardenet & Hardy (BH, 2019) came up with a more natural estimator with a fast central limit theorem (CLT). In this paper, we first take the EZ estimator out of the cellar, and an- alyze it using modern arguments. Second, we provide an efficient implementation1 to sample exactly a particular multidimensional DPP called multivariate Jacobi ensemble. The latter satisfies the assumptions of the aforementioned CLT. Third, our new implementation lets us investigate the behavior of the two unbiased Monte Carlo estimators in yet unexplored regimes. We demonstrate experimentally good properties when the kernel is adapted to basis of functions in which the integrand is sparse or has fast-decaying coefficients. If such a basis and the level of sparsity are known (e.g., we integrate a linear combination of kernel eigenfunctions), the EZ estimator can be the right choice, but otherwise it can display an erratic behavior

On two ways to use determinantal point processes for Monte Carlo integration

International audienceThis paper focuses on Monte Carlo integration with determinantal point processes (DPPs) which enforce negative dependence between quadrature nodes. We survey the properties of two unbiased Monte Carlo estimators of the integral of interest: a direct one proposed by Bardenet & Hardy (2016) and a less obvious 60-year-old estimator by Ermakov & Zolotukhin (1960) that actually also relies on DPPs. We provide an efficient implementation to sample exactly a particular multidimen-sional DPP called multivariate Jacobi ensemble. This let us investigate the behavior of both estima-tors on toy problems in yet unexplored regimes

Goal-oriented adaptive sampling under random field modelling of response probability distributions

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation

Fast sampling from β\beta-ensembles

We study sampling algorithms for $\beta$-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of $\beta$-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size $N$ mixes in $\mathcal{O}(\log(N))$.Comment: 37 pages, 8 figures, code at https://github.com/guilgautier/DPP

A subspace fitting method based on finite elements for fast identification of damages in vibrating mechanical systems

International audienceIn this paper, a method based on subspace fitting is proposed for identification of faults in mechanical systems. The method uses the modal information from an observability matrix, provided by a stochastic subspace identification. It is used for updating a Finite Element Model through the Variable Projection algorithm. Experimental example aims to demonstrate the ability and the efficiency of the method for diagnosis of structural faults in a mechanical system

A Subspace Fitting Method based on Finite Elements for Identification and Localization of Damage in Mechanical Systems

International audienceIn this work, a subspace fitting method based on finite elements for identification of modal parameters of a mechanical system is proposed. The technique uses prior knowledge resulting from a coarse finite element model (FEM) of the structure. The proposed technique is applied to identify the parameters of several mechanical systems under deterministic and stochastic excitations. Numerical experiments highlight the relevance of the technique compared to the conventional identification techniques. Identification, localization and estimation of severity of damages are carried out