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On conjugate times of LQ optimal control problems
No full textInternational audienceMotivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field . We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of
A semi-Lagrangian scheme for Lp-penalized minimum time problems
No full textInternational audienceIn this paper we consider a semi-Lagrangian scheme for minimum time problems with Lp-penalization. The minimum time function of the penalized control problem can be characterized as the solution of a Hamilton-Jacobi Bellman (HJB) equation. Furthermore, the minimum time converges with respect to the penalization parameter to the minimum time of the non-penalized problem. To solve the control problem we formulate the discrete dynamic programming principle and set up a semi-Lagrangian scheme. Various numerical examples are presented studying the effects of different choices of the penalization parameters
Euclidean Distance Geometry and Applications
No full textInternational audienceEuclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics
Automatically Deriving Schematic Theorems for Dynamic Contexts
No full textInternational audienceHypothetical judgments go hand-in-hand with higher-order abstract syntax for meta-theoretic reasoning. Such judgments have two kinds of assumptions: those that are statically known from the specification, and the dynamic assumptions that result from building derivations out of the specification clauses. These dynamic assumptions often have a simple regular structure of repetitions of blocks of related assumptions, with each block generally involving one or several variables and their properties, that are added to the context in a single backchaining step. Reflecting on this regular structure can let us derive a number of structural properties about the elements of the context. We present an extension of the Abella theorem prover, which is based on a simply typed intuitionistic reasoning logic supporting (co-)inductive definitions and generic quantification. Dynamic contexts are repre-sented in Abella using lists of formulas for the assumptions and quantifier nesting for the variables, together with an inductively defined context relation that specifies their structure. We add a new mechanism for defining particular kinds of regular context relations, called schemas, and tacticals to derive theorems from these schemas as needed. Importantly, our extension leaves the trusted kernel of Abella unchanged. We show that these tacticals can eliminate many commonly encountered kinds of administrative lemmas that would otherwise have to be proven manually, which is a common source of complaints from Abella users
ConQuR-Bio: Consensus Ranking with Query Reformulation for Biological Data
No full textInternational audienceThis paper introduces ConQuR-Bio which aims at assisting scientists when they query public biological databases. Various reformu-lations of the user query are generated using medical terminologies. Such alternative reformulations are then used to rank the query results using a new consensus ranking strategy. The originality of our approach thus lies in using consensus ranking techniques within the context of query reformulation. The ConQuR-Bio system is able to query the Entrez-Gene NCBI database. Our experiments demonstrate the benefit of using ConQuR-Bio compared to what is currently provided to users. ConQuR-Bio is available to the bioinformatics community at http://conqur-bio.lri.fr
New insights on P-related paramagnetic point defects in irradiated phosphate glasses: Impact of glass network type and irradiation dose
No full textInternational audienceP-related paramagnetic point defects were studied in irradiated Yb-doped phosphate glasses by electron paramagnetic resonance spectroscopy (X and Q-bands). A strong impact of the glass network type on the defect nature is shown. In all glasses, r-POHC defects formation is in strong correlation with Q(2) tetrahedra amount supporting the structure of r-POHC. Ultra-phosphate glasses contain the larger defect type: Peroxy radicals, P-1, P-2, and P-4 defects whose formation is linked to Q(3) tetrahedra presence. In meta-phosphate and poly-phosphate glasses, peroxy radicals appear with r-POHC thermal recovery. In meta-phosphate glasses, a combination of P-1 and P-3 defects was evidenced for the first time, whereas in poly-phosphate glasses, only P-3 defects were identified. Dose effect as well as defect recovery were analyzed. (C) 2014 AIP Publishing LLC
Mars surface thermal inertia and heterogeneities from OMEGA/MEX
No full textInternational audienceThe thermophysical structure of the martian surface is the result of various processes that have shaped the martian surface through time. Previous dedicated heliosynchronous measurements of the thermal infrared (IR) flux of the martian surface have revealed the diversity of martian surface thermal properties, as well as its complexity linked to the heterogeneous nature of terrains. We present the first retrieval of thermophysical properties of the martian surface using near-infrared (NIR) Observatoire pour la Minéralogie, l'Eau, les Glaces et l'Activité (OMEGA) onboard Mars Express (MEX) thermal measurements from 5 to 5.1. µm. MEX orbit around Mars is elliptical and therefore OMEGA has performed surface temperature measurements at various local times and seasons over more than 4 full martian years. We have developed a method to exploit these unprecedented measurements using a one-dimensional energy balance code derived from a Global Climate Model that allows retrieval of the thermal properties of the martian surface using OMEGA data. Regional maps of the thermal inertia at a resolution up to 32 pixels per degree and a global map at 4 pixels per degree are presented. OMEGA-derived thermal inertia values agree with previous mappings by the Thermal Emission Spectrometer (TES) onboard Mars Global Surveyor (MGS) and Thermal Emission Imaging Spectrometer (THEMIS) onboard Mars Odyssey and highlight the key role of dust for the thermal behavior of the martian surface. OMEGA directly reveals for the first time some diurnal variations of apparent TI attributable to surface heterogeneities at macroscopic scale and enables to quantify these heterogeneities. In Nili Patera and Tharsis, local surface heterogeneities are modeled with layering and horizontal admixture of divergent slopes respectively. © 2014 Elsevier Inc
Ranking-Based Black-Box Complexity
No full textInternational audienceRandomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a growing field. While several strong runtime analysis results have appeared in the last 20 years, a powerful complexity theory for such algorithms is yet to be developed. We enrich the existing notions of black-box complexity by the additional restriction that not the actual objective values, but only the relative quality of the previously evaluated solutions may be taken into account by the black-box algorithm. Many randomized search heuristics belong to this class of algorithms.We show that the new ranking-based model can give more realistic complexity estimates. The class of all binary-value functions has a black-box complexity of O(logn) in the previous black-box models, but has a ranking-based complexity of Θ(n).On the other hand, for the class of all OneMax functions, we present a ranking-based black-box algorithm that has a runtime of Θ(n/logn), which shows that the OneMax problem does not become harder with the additional ranking-basedness restriction
The unbiased black-box complexity of partition is polynomial
No full textInternational audienceUnbiased black-box complexity was introduced as a refined complexity model for randomized search heuristics (Lehre and Witt (2012) [24]). For several problems, this notion avoids the unrealistically low complexity results given by the classical model of Droste et al. (2006) [10]. We show that for some problems the unbiased black-box complexity remains artificially small. More precisely, for two different formulations of an NP-hard subclass of the well-known Partition problem, we give mutation-only unbiased black-box algorithms having complexity O(nlogn). This indicates that also the unary unbiased black-box complexity does not give a complete picture of the true difficulty of this problem for randomized search heuristics
Énumération et analyse de modèles de cartes planaires par la méthode bijective
No full textBijective combinatorics is a field which consists in studying the enumerative properties of some families of mathematical objects, by exhibiting bijections (ideally explicit) which preserve these properties between such families and already known objects. One can then apply any tool of analytic combinatorics to these new objets, in order to get explicit enumeration, asymptotics properties, or to perform random sampling.In this thesis, we will be interested in planar maps – graphs drawn on the plane with no crossing edges. First, we will recover a simple formula –obtained by Eynard – for the generating series of bipartite maps and quasi-bipartite maps with boundaries of prescribed lengths, and we will give anatural generalization to p-constellations and quasi-p-constellations. In the second part of this thesis, we will present an original bijection for outertriangular simple maps – with no loops nor multiple edges – and eulerian triangulations. We then use this bijection to design random samplers for rooted simple maps according to the number of vertices and edges. We will also study the metric properties of simple maps by proving the convergence of the rescaled distance-profile towards an explicit random measure related to the Brownian snake.La combinatoire bijective est un domaine qui consiste à étudier les propriétés énumératives de familles d’objets mathématiques en exhibant des bijections (idéalement explicites) qui préservent ces propriétés entre de telles familles et des objets déjà connus. Cela permet alors d’appliquer tous les outils de la combinatoire analytique à ces nouveaux objets, afin d’en obtenir une énumération explicite, des propriétés asymptotiques, ou encore d’en faire la génération aléatoire.Dans cette thèse, nous nous intéresserons aux cartes planaires qui sont des graphes dessinés dans le plan sans croisement d’arêtes. Dans un premier temps, nous retrouverons une formule simple – établie par Eynard – pour la série génératrice des cartes biparties et cartes quasi-biparties avec des bords de longueurs définies, et nous en donnerons la généralisation naturelle aux p-constellations et quasi-p-constellations. Dans la seconde partie de cette thèse, nous présenterons une bijection originale pour les cartes simples – sans boucles, ni arêtes multiples – à face externe triangulaire et les triangulations eulériennes, nous permettant notamment de faire la génération aléatoire des cartes simples enracinées en contrôlant le nombre de sommets et d’arêtes. Grâce à cette bijection, nous étudierons également les propriétés métriques des cartes simples en démontrant la convergence du profil normalisé des distances vers une mesure aléatoire explicite liée au serpent brownien