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DeepFlow: History Matching in the Space of Deep Generative ModelsMay 14 2019Jun 12 2019The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to ... More

Conditioning of three-dimensional generative adversarial networks for pore and reservoir-scale modelsFeb 15 2018Geostatistical modeling of petrophysical properties is a key step in modern integrated oil and gas reservoir studies. Recently, generative adversarial networks (GAN) have been shown to be a successful method for generating unconditional simulations of ... More

DeepFlow: History Matching in the Space of Deep Generative ModelsMay 14 2019The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to ... More

Reconstruction of three-dimensional porous media using generative adversarial neural networksApr 11 2017To evaluate the variability of multi-phase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract ... More

Stochastic seismic waveform inversion using generative adversarial networks as a geological priorJun 10 2018We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological ... More

Stochastic reconstruction of an oolitic limestone by generative adversarial networksDec 07 2017Stochastic image reconstruction is a key part of modern digital rock physics and materials analysis that aims to create numerous representative samples of material micro-structures for upscaling, numerical computation of effective properties and uncertainty ... More

The Clemens-Griffiths method over non-closed fieldsMar 19 2019We use the Clemens-Griffiths method to construct smooth projective threefolds, over any field $k$ admitting a separable quadratic extension, that are $k$-unirational and $\overline{k}$-rational but not $k$-rational. When $k=\mathbb{R}$, we can moreover ... More

On Packing Colorings of Distance GraphsNov 03 2010Feb 20 2014The {\em packing chromatic number} $\chi_{\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,\ldots ,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies ... More

Variants of a-T-menability for actions on non-commutative Lp spacesApr 20 2013We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on non-commutative Lp spaces. We introduce a variant (H_Lp) for orthogonal representations ... More

Property (T) with respect to non-commutative Lp-spacesJul 07 2011We show that a group with Kazhdan's property $(T)$ has property $(T_{B})$ for $B$ the Haagerup non-commutative $L_{p}(\mathcal{M})$-space associated with a von Neumann algebra $\mathcal{M}$, $1

Métriques hyperkählériennes pliéesMar 13 2015Oct 19 2015N. Hitchin recently introduced the notion of folded hyperK\"ahler metrics, in relation with SL(\infty,R) Higgs bundles. We provide a construction of such metrics, and prove the local existence of the Hitchin component for SL(\infty,R).

Optimal execution of ASR contracts with fixed notionalOct 06 2014May 04 2016Be it for taking advantage of stock undervaluation or in order to distribute part of their profits to shareholders, firms may buy back their own shares. One of the way they proceed is by including Accelerated Share Repurchases (ASR) as part of their repurchase ... More

Geometric Time and Causal Time in Relativistic Lagrangian MechanicsSep 06 2016In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from the past to the ... More

An Energy Preserving Monolithic Eulerian Fluid-Structure Numerical SchemeJul 27 2016The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for ... More

Verifiable Elections with Commitment Consistent Encryption -- A PrimerDec 23 2014This note provides an introduction to the PPATS Commitment Consistent Encryption (CCE) scheme proposed by Cuvelier, Pereira and Peters and its use in the design of end-to-end verifiable elections with a perfectly private audit trail. These elections can ... More

On the maximal use of Monte Carlo samples: re-weighting events at NLO accuracyJul 04 2016Accurate Monte Carlo simulations for high-energy events at CERN's Large Hadron Collider, are very expensive, both from the computing and storage points of view. We describe a method that allows to consistently re-use parton-level samples accurate up to ... More

Hierarchical Modeling of Multidimensional Data in Regularly Decomposed Spaces: Main PrinciplesMay 03 2016May 05 2016The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement and led by ADERSA, a French company of research under contract. The aim was to study the techniques of regular dividing of ... More

Deformations of the braid arrangement and TreesApr 22 2016We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical examples include the ... More

Dimensions of spaces of level one automorphic forms for split classical groups using the trace formulaJun 17 2014We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such that $\mathbf{G}(\R)$ has discrete series. Our main contribution is an algorithm ... More

Elements of proof for conjectures of Witte and Forrester about the combinatorial structure of Gaussian Beta EnsemblesMay 06 2014Aug 19 2014The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in "Moments of the Gaussian $\beta$ Ensembles and the large $N$ expansion of the densities" with the use of the topological recursion adapted for ... More

Asymptotic profiles for the third grade fluids equationsFeb 24 2014We study the long time behaviour of the solutions of the third grade fluids equations in dimension 2. Introducing scaled variables and performing several energy estimates in weighted Sobolev spaces, we describe the first order of an asymptotic expansion ... More

Sensitivity Analysis of Resonant CircuitsMay 30 2015We use first-order perturbation theory to provide a local linear relation between the circuit parameters and the poles of an RLC network. The sensitivity matrix, which defines this relationship, is obtained from the systems eigenvectors and the derivative ... More

Orthogonality and DimensionalitySep 18 2013Nov 06 2013In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal ... More

On the geometry and the deformation of shape represented by a piecewise continuous Bézier curve with application to shape optimizationFeb 18 2013In this work, we develop a framework based on piecewize B\'ezier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape optimization problem ... More

Epitaxial self-organization: from surfaces to magnetic materialsApr 18 2005Self-organization of magnetic materials is an emerging and active field. An overview of the use of self-organization for magnetic purposes is given, with a view to illustrate aspects that cannot be covered by lithography. A first set of issues concerns ... More

High Sensitivity Wavefront Sensing with a non-linear Curvature Wavefront SensorNov 06 2009A new wavefront sensing approach, derived from the successful curvature wavefront sensing concept but using a non-linear phase retrieval wavefront reconstruction scheme, is described. The non-linear curvature wavefront sensor (nlCWFS) approaches the theoretical ... More

On Albanese torsors and the elementary obstructionNov 09 2006Aug 16 2007We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are ... More

Bad groups in the sense of CherlinJul 11 2016There exists no bad group (in the sense of Gregory Cherlin), namely any simple group of Morley rank 3 is isomorphic to PSL2(K) for an algebraically closed field K.

On the number of points of the Lusztig nilpotent variety over a finite fieldDec 16 2012Dec 28 2012In this note we give a closed expression for the number of points over finite fields of the Lusztig nilpotent variety associated to any quiver without edge loops, in terms of Kac's A-polynomial. We conjecture a similar result for quivers in which edge ... More

Canonical bases of loop algebras via quot schemes IIAug 29 2004This paper is a sequel (and contains a better treatment) of math.QA/0404032; We construct some canonical bases for quantum toroidal algebras of types D_4, E_6, E_7, E_8 using perverse sheaves on quot schemes parametrizing equivariant coherent sheaves ... More

Canonical bases of loop algebras via Quot schemes, IApr 02 2004We propose a construction of some canonical bases for quantum loop algebras of Kac-Moody algebras. We consider a smooth projective curve X, a group of automorphism G of X such that X/G=P^1, and we consider some Quot schemes of G-equivariant coherent sheaves ... More

The Hall algebra of a cyclic quiver and canonical bases of the Fock spaceJun 11 1999Sep 08 1999We prove that the Hall algebra U^-_n of the cyclic quiver of type A^(1)_{n-1} decomposes as a direct product of the quantum negative nilpotent subalgebra U_q^-(\hat{sl}_{n)) and C[q,q^{-1},z_1,z_2...]. We use this to prove a conjecture of Varagnolo and ... More

High confidence estimates of the mean of heavy-tailed real random variablesSep 29 2009We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded variance or ... More

Dynamics and Hidden VariablesOct 16 2012We study the way the unitary evolution of spin 1/2 particules can be represented in a counterfactual definiteness setting. More precisely, by representing the state of such a particule by a triplet of values corresponding to the supposedly pre-existing ... More

An Intrisic Topology for Orthomodular LatticesFeb 03 2007We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of ... More

Representation Systems and Quantum StructuresMar 01 2006Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation systems, we ... More

Désingularisation de métriques d'Einstein. IMay 24 2011We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with boundary at infinity ... More

Undecidable Problems About Timed AutomataDec 09 2007We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS'2003, LNCS, Volume 2791, ... More

Ambiguity of ω-Languages of Turing MachinesSep 25 2012Aug 26 2014An {\omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {\omega}-languages, i.e. the class of {\omega}-languages accepted by Turing machines with a B\"uchi acceptance condition, which is also the class ... More

On Decidability Properties of One-Dimensional Cellular AutomataMar 26 2009Jun 01 2009In a recent paper Sutner proved that the first-order theory of the phase-space $\mathcal{S}_\mathcal{A}=(Q^\mathbb{Z}, \longrightarrow)$ of a one-dimensional cellular automaton $\mathcal{A}$ whose configurations are elements of $Q^\mathbb{Z}$, for a finite ... More

Wadge Degrees of Infinitary Rational RelationsApr 21 2008We show that, from the topological point of view, 2-tape B\"uchi automata have the same accepting power as Turing machines equipped with a B\"uchi acceptance condition. The Borel and the Wadge hierarchies of the class RAT_omega of infinitary rational ... More

On the expressive power of unit resolutionJun 17 2011This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we propose to ... More

A Simple Proof of the Entropy-Power Inequality via Properties of Mutual InformationJan 08 2007Apr 13 2007While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge ... More

Towards Conceptual Multidimensional Design in Decision Support SystemsMay 03 2010Multidimensional databases support efficiently on-line analytical processing (OLAP). In this paper, we depict a model dedicated to multidimensional databases. The approach we present designs decisional information through a constellation of facts and ... More

Online Expectation-MaximisationNov 08 2010Tutorial chapter on the Online EM algorithm to appear in the volume 'Mixtures' edited by Kerrie Mengersen, Mike Titterington and Christian P. Robert.

Absorbing boundary conditions for Einstein's field equationsAug 31 2007A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary conditions must ... More

Finite geometries and diffractive orbits in isospectral billiardsMar 31 2005Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the ... More

Diffractive orbits in isospectral billiardsDec 19 2003Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length ... More

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmasOct 26 2016In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, ... More

Complete families of smooth space curves and strong semistabilityNov 21 2013We study complete families of non-degenerate smooth space curves, that is proper subvarieties of the Hilbert scheme of non-degenerate smooth curves in P^3. On the one hand, we construct the first examples of such families. Our examples parametrize curves ... More

Large-Scale Distribution of Arrival Directions of Cosmic Rays Detected at the Pierre Auger Observatory Above $10~$PeVMar 25 2014Searches for large-scale anisotropies in the distribution of arrival directions of cosmic rays detected above $\simeq 10 $PeV at the Pierre Auger Observatory are presented. Although no significant deviation from isotropy is revealed at present, some of ... More

Convergence of quasi-Fuchsian groups using critical exponentFeb 01 2017We prove that a sequence of quasi-Fuchsian representations for which the critical exponent converges to the topological dimension of the boundary of the group (larger than 2), converges up to subsequence and conjugacy to a totally geodesic representation. ... More

Involutions and Chern numbers of varietiesMar 18 2019Consider an involution of a smooth projective variety over a field of characteristic not two. We look at the relations between the variety and the fixed locus of the involution from the point of view of cobordism. We show in particular that the fixed ... More

Limit theorems for the painting of graphs by clustersMar 05 2001We consider a generalization of the so-called divide and color model recently introduced by Haggstrom. We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit theorems are proved, ... More

Moduli spaces of orthogonal bundles over an algebraic curveSep 19 2006We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the invariants on the representation ... More

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxiesOct 19 2017Dec 14 2017We study the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carry out the analysis by developing a numerical resolution of the 2D2V Collisionless Boltzmann Equation (CBE) and ... More

Kac polynomials and Lie algebras associated to quivers and curvesFeb 27 2018A survey of the theory of Kac polynomials for quivers and for curves. In particular, we describe the representation-theoretic meaning of Kac polynomials in terms of Hall algebras, and the geometric meaning of Kac polynomials in relation to the geometry ... More

WKB solutions of difference equations and reconstruction by the topological recursionMar 17 2017Sep 29 2017The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a $\hbar$-difference equation: $\Psi(x+\hbar)=\left(e^{\hbar\frac{d}{dx}}\right) \Psi(x)=L(x;\hbar)\Psi(x)$ with $L(x;\hbar)\in ... More

Wadge Degrees of $ω$-Languages of Petri NetsDec 20 2017Mar 26 2018We prove that $\omega$-languages of (non-deterministic) Petri nets and $\omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) ... More

Refounding legitimacy towards AethogenesisNov 03 2017The fusion of humans and technology takes us into an unknown world described by some authors as populated by quasi living species that would relegate us - ordinary humans - to the rank of alienated agents emptied of our identity and consciousness. I argue ... More

Geometric Properties of Paths in Relativistic Lagrangian MechanicsJul 25 2017Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some properties ... More

On bi-unitary perfect polynomials over $F_2$Oct 23 2018We give all bi-unitary non splitting even perfect polynomials over the prime field of two elements, which are divisible by Mersenne irreducible polynomials raised to special exponents. We also identify all bi-unitary perfect polynomials over the same ... More

Pairs of Morse functionsMar 06 2017The goal of this paper is to classify pairs of Morse functions in general position modulo the action of different groups.In particular, we obtain the classification of generic pairs of Morse functions, with or without target diffeomorphisms, and that ... More

A Homological Approach to Belief Propagation and Bethe ApproximationsMar 14 2019We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a ... More

On the error term of a lattice counting problem, IIAug 24 2017Sep 25 2017Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of polynomials and ... More

PAC-Bayesian bounds for the Gram matrix and least squares regression with a random designMar 16 2016The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares regression with ... More

Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicleMar 10 2019In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set ... More

On Some Sets of Dictionaries Whose omega-Powers Have a Given ComplexityNov 17 2009A dictionary is a set of finite words over some finite alphabet X. The omega-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [Omega-powers and descriptive set theory, JSL 2005] ... More

Asymptotic convergence rates for coordinate descent in polyhedral setsSep 17 2015We consider a family of parallel methods for constrained optimization based on projected gradient descents along individual coordinate directions. In the case of polyhedral feasible sets, local convergence towards a regular solution occurs unconstrained ... More

Construction de courbes sur les surfaces K3 [d'après Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]Dec 22 2014Dec 23 2014We report on recent results concerning the construction of curves on K3 surfaces: the proof of the Tate conjecture for K3 surfaces in odd characteristic (after Maulik, Charles and Madapusi Pera), and the construction of infinitely many rational curves ... More

Detection by regular schemes in degree twoJul 22 2013Oct 08 2014Using Lipman's results on resolution of two-dimensional singularities, we provide a form of resolution of singularities in codimension two for reduced quasi-excellent schemes. We deduce that operations of degree less than two on algebraic cycles are characterised ... More

Integrality of the Chern character in small codimensionMar 21 2011Jan 17 2012We prove an integrality property of the Chern character with values in Chow groups. As a consequence we obtain, for a prime number p, a construction of the p-1 first homological Steenrod operations on Chow groups modulo p and p-primary torsion, over an ... More

Séparation et propriété de Deligne-Mumford des champs de modules d'intersections complètes lissesNov 07 2011Sep 10 2012We show that the moduli stacks of smooth complete intersections in P^N polarized by O(1) are separated (except for quadrics) and Deligne-Mumford (apart from a few exceptions). ----- On montre que les champs de modules d'intersections completes lisses ... More

Quelques espaces de modules d'intersections complètes lisses qui sont quasi-projectifsNov 07 2011Sep 10 2012For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in P^N is quasi-projective. ----- Pour certaines valeurs des degres des equations, on montre, a l'aide ... More

Determination du rang des tissus du plan et autres invariants geometriquesMay 26 2005Nous donnons un procede explicite de determination du rang d'un d-tissu non singulier du plan quelconque a l'aide de sa connexion associee. Une etude de quelques invariants du tissu est egalement proposee. We give an explicit process of determination ... More

The Algebra of Hurwitz Multizeta FunctionsApr 03 2014Multizeta values are real numbers which span a complicated algebra: there exist two different interacting products. A functional analog of these numbers is defined so as to obtain a better understanding of them, the Hurwitz multizeta functions, which ... More

Matrix models, Toeplitz determinants and recurrence times for powers of random unitary matricesDec 09 2014Jun 16 2015The purpose of this article is to study the eigenvalues $u_1^{\, t}=e^{it\theta_1},\dots,u_N^{\,t}=e^{it\theta_N}$ of $U^t$ where $U$ is a large $N\times N$ random unitary matrix and $t>0$. In particular we are interested in the typical times $t$ for ... More

On the birational geometry of the parameter space for codimension 2 complete intersectionsDec 19 2012Codimension 2 complete intersections in P^N have a natural parameter space \bar{H}: a projective bundle over a projective space given by the choice of the lower degree equation and of the higher degree equation up to a multiple of the first. Motivated ... More

On the integral Hodge conjecture for real varieties, IJan 03 2018May 11 2019We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. ... More

Conditional density estimation in a censored single-index regression modelJul 24 2008Mar 22 2009Under a single-index regression assumption, we introduce a new semiparametric procedure to estimate a conditional density of a censored response. The regression model can be seen as a generalization of Cox regression model and also as a profitable tool ... More

On the integral Hodge conjecture for real varieties, IIJan 03 2018May 11 2019We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations) and on conic bundles over higher-dimensional bases which themselves satisfy ... More

COP2: Continuously Observing Protocol PerformanceFeb 12 2019As enterprises move to a cloud-first approach, their network becomes crucial to their daily operations and has to be continuously monitored. Although passive monitoring can be convenient from a deployment viewpoint, inferring the state of each connection ... More

Three errors in the article: "The OPERA neutrino velocity result and the synchronisation of clocks"Oct 13 2011We found three mistakes in the article " The OPERA neutrino velocity result and the synchronisation of clocks" by Contaldi \cite{Contaldi}. First, the definition of the angle of the latitude in the geoid description leads to a prolate spheroid (rugby ... More

On Hilbert's 17th problem in low degreeFeb 23 2016Artin solved Hilbert's 17th problem, proving that a real polynomial in $n$ variables that is positive semidefinite is a sum of squares of rational functions, and Pfister showed that only $2^n$ squares are needed. In this paper, we investigate situations ... More

Indecomposable vector bundles and stable Higgs bundles over smooth projective curvesJun 15 2014Oct 04 2014We prove that the number of indecomposable vector bundles of fixed rank r and degree d over a smooth projective curve X defined over a finite field is given by a polynomial (depending only on the pair (r,d) and the genus g of X) in the Weil numbers of ... More

Infinite Games Specified by 2-Tape AutomataDec 13 2013We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal ... More

On the cosmic convergence mechanism of the massless dilatonDec 16 2013Jun 15 2014The converging mechanism discussed in [Damour & Nordtvedt, Physical Review Letters,70,15] for scalar-tensor theories has been applied to dilaton-like theories in several subsequent papers. In the present communication, we show that an unfortunate assumption ... More

Hierarchical Modeling of Multidimensional Data in Regularly Decomposed Spaces: Applications in Image AnalysisMay 04 2016This last document is showing the gradual introduction of hierarchical modeling techniques in image analysis. The first chapter is dealing with the first works carried out in the field of industrial applications of pattern recognition. The second chapter ... More

$p$-adic properties of motivic fundamental lines (Kato's conjecture is (probably) false for (not so) trivial reasons)Apr 21 2016We prove the conjectured compatibility of $p$-adic fundamental lines with specializations at motivic points for a wide class of $p$-adic families of $p$-adic Galois representations (for instance, the families which arise from $p$-adic families of automorphic ... More

Arbitrariness of peer review: A Bayesian analysis of the NIPS experimentJul 23 2015The principle of peer review is central to the evaluation of research, by ensuring that only high-quality items are funded or published. But peer review has also received criticism, as the selection of reviewers may introduce biases in the system. In ... More

Asymptotic expansions of some Toeplitz determinants via the topological recursionNov 17 2016In this article, we study the large $n$ asymptotic expansions of $n\times n$ Toeplitz determinants whose symbols are indicator functions of unions of arc-intervals of the unit circle. In particular, we use an Hermitian matrix model reformulation of the ... More

The critical Galton-Watson process vanishesOct 10 2016The Galton-Watson process belongs to standard teaching in probability. The basic theorem says that survival is only possible when the fecondity exceeds 1. The classical proof is essentially analytic, using generating functions and convexity arguments. ... More

Informations in models of evolutionary dynamicsApr 29 2015Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of evolutionary ... More

Yet Another Proof of the Entropy Power InequalityJun 20 2016Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or R\'enyi entropies. The proof is based on a simple change ... More

Full affine equivariance and weak natural transformations in numerical analysis - the case of B-SeriesMay 24 2016Many algorithms in numerical analysis are affine equivariant: they are immune to changes of affine coordinates. This is because those algorithms are defined using affine invariant constructions. There is, however, a crucial ingredient missing: most algorithms ... More

Wide field interferometric imaging with single-mode fibersApr 16 2002Classical single-mode fiber interferometers, using one fiber per aperture, have very limited imaging capabilities and small field of view. Observations of extended sources (resolved by one aperture) cannot be fully corrected for wavefront aberrations: ... More

Execution and block trade pricing with optimal constant rate of participationOct 29 2012Dec 03 2013When executing their orders, investors are proposed different strategies by brokers and investment banks. Most orders are executed using VWAP algorithms. Other basic execution strategies include POV (also called PVol) -- for percentage of volume --, IS ... More

Spherical Hall algebras of curves and Harder-Narasimhan stratasFeb 04 2010Let X be any smooth projective curve defined over a finite field. We show that the characteristic functions of any Harder-Narasimhan strata S_a of Bun_{GL_n}X belongs to the spherical Hall algebra H_X^{sph} of X. We give a geometric analog of the above ... More

On the Hall algebra of an elliptic curve, IIAug 28 2005Jul 28 2009This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to be a two-parameter deformation of the ring of diagonal ... More

Lectures on Hall algebrasNov 20 2006Oct 23 2009These are notes for a minicourse on Hall algebras given at the ICTP in Trieste in January 2006. After giving the definition and first properties of Hall algebras, we study in some details the classical Hall algebra, the Hall algebra of quivers, and the ... More