An informational approach to the global optimization of expensive-to-evaluate functions

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each evaluation contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past evaluations, the uncertainty associated with the lack of information on the function can be expressed and used to compute a number of criteria accounting for the interest of an additional evaluation at any given point. This paper introduces minimizer entropy as a new Kriging-based criterion for the sequential choice of points at which the function should be evaluated. Based on \emph{stepwise uncertainty reduction}, it accounts for the informational gain on the minimizer expected from a new evaluation. The criterion is approximated using conditional simulations of the Gaussian process model behind Kriging, and then inserted into an algorithm similar in spirit to the \emph{Efficient Global Optimization} (EGO) algorithm. An empirical comparison is carried out between our criterion and \emph{expected improvement}, one of the reference criteria in the literature. Experimental results indicate major evaluation savings over EGO. Finally, the method, which we call IAGO (for Informational Approach to Global Optimization) is extended to robust optimization problems, where both the factors to be tuned and the function evaluations are corrupted by noise.Comment: Accepted for publication in the Journal of Global Optimization (This is the revised version, with additional details on computational problems, and some grammatical changes

An Upper Bound on the Average Size of Silhouettes

It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size $O(\sqrt{n})$ where the average is taken over all points of view and n is the complexity of the polyhedron

Triangulating the Real Projective Plane

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane

Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation

The accurate description of protein-protein interfaces remains a challenging task. Traditional criteria, based on atomic contacts or changes in solvent accessibility, tend to over or underpredict the interface itself and cannot discriminate active from less relevant parts. A recent simulation study by Mihalek and co-authors (2007, JMB 369, 584-95) concluded that active residues tend to be `dry', that is, insulated from water fluctuations. We show that patterns of `dry' residues can, to a large extent, be predicted by a fast, parameter-free and purely geometric analysis of protein interfaces. We introduce the shelling order of Voronoi facets as a straightforward quantitative measure of an atom's depth inside an interface. We analyze the correlation between Voronoi shelling order, dryness, and conservation on a set of 54 protein-protein complexes. Residues with high shelling order tend to be dry; evolutionary conservation also correlates with dryness and shelling order but, perhaps not surprisingly, is a much less accurate predictor of either property. Voronoi shelling order thus seems a meaningful and efficient descriptor of protein interfaces. Moreover, the strong correlation with dryness suggests that water dynamics within protein interfaces may, in first approximation, be described by simple diffusion models

Image based simulation of one-dimensional compression tests on carbonate sand

High factors of safety and conservative methods are commonly used on foundation design on shelly carbonate soils. A better understanding of the behavior of this material is, thus, critical for more sustainable approaches for the design of a number of offshore structures and submarine pipelines. In particular, understanding the physical phenomena taking place at the microscale has the potential to spur the development of robust computational methods. In this study, a one-dimensional compression test was performed inside an X-ray scanner to obtain 3D images of the evolving internal structure of a shelly carbonate sand. A preliminary inspection of the images through five loading increments has shown that the grains rearrange under loading and in some cases cracks develop at the contacts. In order to replicate of the experiments in the numerical domain, the 3D image of the soil prior to loading was imported into a micro Finite Element (µFE) framework. This image-based modelling tool enables measurements of the contact force and stress map inside the grains while making use of the real microstructure of the soil. The potential of the µFE model to contribute insights into yield initiation within the grain is demonstrated here. This is of particular interest to better understand the breakage of shelly grains underpinning their highly compressive behavior

Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$

Chaotic diffusion in the Solar System

A statistical analysis is performed over more than 1001 different integrations of the secular equations of the Solar system over 5 Gyr. With this secular system, the probability of the eccentricity of Mercury to reach 0.6 in 5 Gyr is about 1 to 2 %. In order to compare with (Ito and Tanikawa, 2002), we have performed the same analysis without general relativity, and obtained even more orbits of large eccentricity for Mercury. We have performed as well a direct integration of the planetary orbits, without averaging, for a dynamical model that do not include the Moon or general relativity with 10 very close initial conditions over 3 Gyr. The statistics obtained with this reduced set are comparable to the statistics of the secular equations, and in particular we obtain two trajectories for which the eccentricity of Mercury increases beyond 0.8 in less than 1.3 Gyr and 2.8 Gyr respectively. These strong instabilities in the orbital motion of Mecury results from secular resonance beween the perihelion of Jupiter and Mercury that are facilitated by the absence of general relativity. The statistical analysis of the 1001 orbits of the secular equations also provides probability density functions (PDF) for the eccentricity and inclination of the terrestrial planets.Comment: 17 pages, Accepted in Icaru

Socle interministériel des logiciels libres 2017

La modernisation des systèmes d\u27information de l\u27Etat passe notamment par le développement des usages et technologies innovantes et créatrices de valeur pour les utilisateurs, et par la maîtrise des coûts, ce qui implique en particulier de développer la réutilisation et la mutualisation, et d’ajuster au mieux les dépenses d’acquisition. L\u27approche de l\u27Etat privilégie l’efficacité globale, en dehors de tout dogmatisme, pour lui permettre de choisir entre les différentes solutions, libres, éditeurs ou mixtes. C’est l’objet de la circulaire du 19 septembre 2012, signée par le Premier ministre, qui recommande les voies du bon usage du logiciel libre dans l’Administration. L’ensemble des logiciels libres préconisés se présente sous la forme du socle interministériel de logiciels libres (SILL). Le périmètre du SILL n’inclut pas la totalité du SI de l’Etat. Dans sa version actuelle, il porte sur le poste de travail, la gestion de parc, l’exploitation de serveurs, les base de données et les environnements de développement. Le SILL se présente sous la forme d’un tableau par fonctionnalité ou cas d’usage. Pour chaque fonctionnalité, il présente le logiciel préconisé en précisant la version. Chaque logiciel du SILL est suivi par un ministère référent. Le SILL est géré par les correspondants ministériels, dans le cadre de l’instance de mutualisation sur les logiciels libres, sous le contrôle de la DINSIC. Il est mis à jour annuellement. Chaque version annuelle du SILL fait l’objet d’une validation