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Computational Complexity versus Statistical Performance on Sparse Recovery ProblemsJun 10 2015Nov 02 2018We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity. We first describe linearly convergent restart schemes on first-order methods solving a broad range ... More

Iterative Linearized Control: Stable Algorithms and Complexity GuaranteesAug 20 2019We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational ... More

Sharpness, Restart and AccelerationFeb 13 2017The {\L}ojasievicz inequality shows that sharpness bounds on the minimum of convex optimization problems hold almost generically. Here, we show that sharpness directly controls the performance of restart schemes. The constants quantifying sharpness are ... More

Electron neutrino opacity in magnetised mediaNov 03 1997We study the effects of strong magnetic fields ($B> 10^{13}$~G) in the cross section for $\nu_e n\to p e$ scattering in the presence of a degenerate electron background. This can be relevant for the $\nu_e$ propagation in the proto-neutron star stage ... More

Renegar's Condition Number and Compressed Sensing PerformanceJun 10 2015Renegar's condition number is a data-driven computational complexity measure for convex programs, generalizing classical condition numbers in linear systems. We provide evidence that for a broad class of compressed sensing problems, the worst case value ... More

Kernel-based Translations of Convolutional NetworksMar 19 2019Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, ... More

Leptogenesis, Z' bosons, and the reheating temperature of the UniverseDec 22 2008Jan 16 2009We study the impact for leptogenesis of new U(1) gauge bosons coupled to the heavy Majorana neutrinos. They can significantly enhance the efficiency of thermal scenarios in the weak washout regime as long as the Z' masses are not much larger than the ... More

Learning with Clustering StructureJun 16 2015Sep 19 2016We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text classification for instance, ... More

On the capture rates of big bang neutrinos by nuclei within the Dirac and Majorana hypothesesOct 01 2018The capture rates of non-relativistic neutrinos on beta decaying nuclei depends on whether their mass is Dirac or Majorana. It is known that for relic neutrinos from the big-bang, and within minimal assumptions, the rate is a factor two larger in the ... More

Kicked neutron stars and microlensingSep 02 1996Due to the large kick velocities with which neutron stars are born in supernovae explosions, their spatial distribution is more extended than that of their progenitor stars. The large scale height of the neutron stars above the disk plane makes them potential ... More

Integration Methods and Accelerated Optimization AlgorithmsFeb 22 2017We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the differential equation ... More

A Smoother Way to Train Structured Prediction ModelsFeb 08 2019We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for ... More

Limits on Neutrino Mixing with new Heavy ParticlesFeb 03 1994Mar 04 1994We study the effects induced by new neutral fermions below their mass threshold, due to their possible mixing with the standard neutrinos. We use as experimental constraints the recent results on lepton universality, together with the measurement of the ... More

The most energetic particles in the universeJan 31 2000Several issues related to the lensing of ultra-high energy cosmic rays by the Galactic magnetic field are discussed.

Recent results from the Pierre Auger ObservatorySep 12 2008The main results from the Auger Observatory are described. A steepening of the spectrum is observed at the highest energies, supporting the expectation that above $4\times 10^{19}$ eV the cosmic ray energies are significantly degraded by interactions ... More

Astrophysical magnetic field reconstruction and spectroscopy with ultra high energy cosmic raysMay 28 2002The next generation of ultra high energy cosmic ray experiments will probably detect several dozens of events clustered around the direction towards each of the most powerful extragalactic sources. We develop a method which could make possible to reconstruct, ... More

Cosmic ray photodisintegration and the knee of the spectrumNov 01 2000Jun 26 2001We explore in some detail the scenario proposed to explain the observed knee of the cosmic ray (CR) spectrum as due to the effects of photodisintegration of the CR nuclei by interactions with optical and soft UV photons in the source region. We show that ... More

Signatures of galactic magnetic lensing upon ultra high energy cosmic raysJan 06 2000We analyse several implications of lensing by the regular component of the galactic magnetic field upon the observed properties of ultra high energy cosmic rays. Magnetic fields deflect cosmic ray trajectories, causing flux (de)magnification, formation ... More

Spin glasses : experimental signatures and salient outcomesSep 29 2017Apr 01 2019Within the wide class of disordered materials, spin glasses occupy a special place because of their conceptually simple definition of randomly interacting spins. Their modelling has triggered spectacular developments of out-of-equilibrium statistical ... More

Neutrinos in physics and astrophysicsOct 18 1999An elementary general overview of the neutrino physics and astrophysics is given. We start by a historical account of the development of our understanding of neutrinos and how they helped to unravel the structure of the Standard Model. We discuss why ... More

Revealing the work cost of generalized thermal bathsSep 14 2018We derive the work cost of using generalized thermal baths from the physical equivalence of quantum mechanics under unitary transformations. We demonstrate our method by considering a qubit extracting work from a single bath to amplify a cavity field. ... More

Neutrino PhenomenologyDec 27 2004A general overview of neutrino physics is given, starting with a historical account of the development of our understanding of neutrinos and how they helped to unravel the structure of the Standard Model. We discuss why it is so important to establish ... More

Microlensing searches of dark matterApr 25 2000The evolution of the observational results of microlensing towards the LMC and some of the suggested interpretations to account for them are discussed. It is emphasized that the results at present are indicative of a lensing population of white dwarfs, ... More

Beyond the Standard ModelDec 28 2001May 07 2007The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological implications for ... More

Reconstructing compositionsOct 16 2006We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutations). We show that every composition w of n\ge 3k+1 can be reconstructed ... More

Simple physics of the partly pinned fluid systemsMay 12 2014Sep 08 2014In this paper, we consider some aspects of the physics of the partly pinned (PP) systems obtained by freezing in place particles in equilibrium bulk fluid configurations in the normal (nonglassy) state. We first discuss the configurational overlap and ... More

Statistical mechanics of homogeneous partly pinned fluid systemsJun 24 2010Dec 05 2010The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, ... More

Semantic Vector MachinesMay 14 2011We first present our work in machine translation, during which we used aligned sentences to train a neural network to embed n-grams of different languages into an $d$-dimensional space, such that n-grams that are the translation of each other are close ... More

Gluon Mass, Glueballs and Gluonic MesonsFeb 18 2011We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar ... More

Philosophy in the Face of Artificial IntelligenceMay 19 2016In this article, I discuss how the AI community views concerns about the emergence of superintelligent AI and related philosophical issues.

Cosmic anisotropies from quasars: from polarization to structural-axis alignmentsApr 18 2016The comparison of the orientations of the optical-polarization vectors of quasars that are separated by billions of light-years has led to the discovery that they are aligned instead of pointing in random directions as expected. This discovery has been ... More

Approximation of stochastic processes by non-expansive flows and coming down from infinityNov 23 2015May 25 2016We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property of the flow, ... More

Growth rates of permutation classes: from countable to uncountableMay 13 2016Sep 05 2016We establish that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi$, there are only countably many less than $\xi$. Central to the proof are various ... More

Mean-field microrheology of a very soft colloidal suspension: inertia induces shear-thickeningMar 03 2015Apr 27 2015Colloidal suspensions have a rich rheology and can exhibit shear-thinning as well as shear-thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions ... More

A new test of uniformity for object orientations in astronomyJul 20 2015We briefly present a new coordinate-invariant statistical test dedicated to the study of the orientations of transverse quantities of non-uniformly distributed sources on the celestial sphere. These quantities can be projected spin-axes or polarization ... More

Why are tensor field theories asymptotically free?Jul 15 2015In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate ... More

A Contribution to the Theory Behind the M0 Capture-Recapture Model: An Improved EstimatorDec 10 2012Nov 28 2018We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator ... More

Recent Advances on Estimating Population Size with Link-Tracing SamplingSep 22 2017A new approach to estimate population size based on a stratified link-tracing sampling design is presented. The method extends on the Frank and Snijders (1994) approach by allowing for heterogeneity in the initial sample selection procedure. Rao-Blackwell ... More

Rao-Blackwellization to give Improved Estimates in Multi-List StudiesSep 26 2017Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented. As Rao-Blackwellization ... More

Definability of types over finite partial order indiscerniblesAug 11 2011In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by giving a decomposition ... More

Gradient trajectories for plane singular metrics I: oscillating trajectoriesMay 30 2012We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries ... More

The Relaxation Normal Form of Braids is RegularJul 12 2015Oct 12 2017Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations ... More

Theia: A multi-purpose water-based liquid scintillator detectorSep 17 2018Recent developments in the field of liquid scintillator chemistry and fast-timing photosensors paved the way for a new generation of large-scale detectors capable of tackling a broad range of physics issues. Water-based Liquid Scintillator is a novel ... More

Inexact cuts in Stochastic Dual Dynamic ProgrammingSep 04 2018Jul 07 2019We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of ... More

The one-dimensional asymmetric persistent random walkDec 18 2017Feb 12 2018Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric ... More

Multistage stochastic programs with a random number of stages: dynamic programming equations, solution methods, and application to portfolio selectionMar 15 2018Jul 17 2019We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to solve these equations. ... More

A Puzzle about Further FactsFeb 04 2018In metaphysics, there are a number of distinct but related questions about the existence of "further facts" -- facts that are contingent relative to the physical structure of the universe. These include further facts about qualia, personal identity, and ... More

The Joint Physics Analysis Center WebsiteJan 08 2016The Joint Physics Analysis Center is a collaboration between theorists and experimentalists working in hadronic physics. In order to facilitate the exchange of information between the different actors in hadron spectroscopy, we created an interactive ... More

Dessins d'enfants for analystsApr 01 2015We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus 0 or 1, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with subsequent lattice ... More

VisJSClassificator -- Manual Visual Collaborative Classification Graph-based ToolAug 08 2019Analysts need to classify, search and correlate numerous images. Automatic classification tools improve the efficiency of such tasks. However, classified data is a prerequisite to develop these tools. Labelling tools are of great use in case of already ... More

Numerical Simulations of the Ising Model on the Union Jack LatticeJan 26 2011The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by Lars Onsager ... More

Estimates for Weierstrass division in ultradifferentiable classesNov 26 2015Mar 23 2016We study the Weierstrass division theorem for function germs in strongly non-quasianalytic Denjoy-Carleman classes $\mathcal{C}_M$. For suitable divisors $P(x,t)=x^d+a_1(t)x^{d-1}+\cdots+a_d(t)$ with real-analytic coefficients $a_j$, we show that the ... More

Fonctorial Construction of Frobenius CategoriesMar 16 2009Let $\Ascr,\Bscr$ be exact categories with $\Ascr$ karoubian and $M$ be an exact functor. Under suitable adjonction hypotheses for $M$, we are able to show that the direct factors of the objects of $\Ascr$ of the form $MY$ with $Y \in \Bscr$ make up a ... More

Lecture notes on Liouville theory and the DOZZ formulaDec 03 2017The purpose of these notes, based on a series of 4 lectures given by the author at IHES, is to explain the recent proof of the DOZZ formula for the three point correlation functions of Liouville conformal field theory (LCFT). We first review the probabilistic ... More

Conic intersections, Maximal Cohen-Macaulay modules and the Four Subspace problemFeb 21 2017Mar 10 2017Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by reducing the classification to the Four Subspace problem solved by Nazarova and Gel$'$fand-Ponomarev, ... More

Abelianization of Subgroups of Reflection Group and their Braid Group; an Application to CohomologyMar 03 2010Aug 31 2010The final result of this article gives the order of the extension $$\xymatrix{1\ar[r] & P/[P,P] \ar^{j}[r] & B/[P,P] \ar^-{p}[r] & W \ar[r] & 1}$$ as an element of the cohomology group $H^2(W,P/[P,P])$ (where $B$ and $P$ stands for the braid group and ... More

Brick polytopes, lattice quotients, and Hopf algebrasMay 28 2015Nov 30 2017This paper is motivated by the interplay between the Tamari lattice, J.-L. Loday's realization of the associahedron, and J.-L. Loday and M. Ronco's Hopf algebra on binary trees. We show that these constructions extend in the world of acyclic $k$-triangulations, ... More

A very short proof of Forester's rigidity resultJan 24 2003May 22 2003The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester ... More

Cardinality of Rauzy classesJun 04 2011Rauzy classes define a partition of the set of irreducible (or indecomposable) permutations. They were defined by G. Rauzy as part of an induction algorithm for interval exchange transformations. In this article we prove an explicit formula for the cardinality ... More

On the non-extendability of quasianalytic germsJun 21 2010Sep 07 2010Let $\mathcal{E}_1(M)^+$ be the local ring of germs at 0 of functions belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0 in $[0,+\infty[$. We show that the ring $\mathcal{E}_1(M)^+$ contains elements that cannot be extended ... More

The metric completion of the Riemannian space of Kähler metricsJan 30 2014Apr 09 2014Let $X$ be a compact K\"ahler manifold and $\a \in H^{1,1}(X,\R)$ a K\"ahler class. We study the metric completion of the space $\HH_\a$ of K\"ahler metrics in $\a$, when endowed with the Mabuchi $L^2$-metric $d$. Using recent ideas of Darvas, we show ... More

Latest results from the Pierre Auger ObservatoryJan 10 2011Recent results obtained with the Pierre Auger Observatory are described. These include measurements of the spectrum, anisotropies and composition of ultra-high energy cosmic rays. The ankle of the spectrum is measured at $4\times 10^{18}$~eV and a suppression ... More

Neutrino AstrophysicsNov 30 2000Dec 04 2000A general overview of neutrino physics and astrophysics is given, starting with a historical account of the development of our understanding of neutrinos and how they helped to unravel the structure of the Standard Model. We discuss why it is so important ... More

Astroparticle Theory: Some New Insights into High Energy Cosmic RaysOct 14 2003Some new developments obtained in the last few years concerning the propagation of high energy cosmic rays are discussed. In particular, it is shown how the inclusion of drift effects in the transport diffusion equations leads naturally to an explanation ... More

Results from the Pierre Auger ObservatoryNov 20 2018I describe some of the results on ultrahigh-energy cosmic rays that have been obtained with the Pierre Auger Observatory. These include measurements of the spectrum, composition and anisotropies. Possible astrophysical scenarios that account for these ... More

Rabi oscillation in a quantum cavity: Markovian and non-Markovian dynamicsMay 29 2015Feb 05 2016We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the ... More

Supersymmetric radiative corrections to neutrino indices of refractionJun 02 1995We compute the one-loop effects on the neutrino propagation through matter induced by virtual supersymmetric particles. We show that, in the minimal version of the supersymmetric standard model, a non-degeneracy between sleptons of the second and third ... More

Lensing of ultra-high energy cosmic rays in turbulent magnetic fieldsFeb 20 2002Mar 26 2002We consider the propagation of ultra high energy cosmic rays through turbulent magnetic fields and study the transition between the regimes of single and multiple images of point-like sources. The transition occurs at energies around $E_c\simeq Z~41 {\rm ... More

Flatness, accessibility and metric spacesMar 09 2004This paper studies a notion of parameterized flatness in the enriched context: p-flatness where the parameter p stands for a class of presheaves. One obtains a completion of a category A by considering the category F_p(A) of p-flat presheaves over A. ... More

Chtoucas pour les groupes réductifs et paramétrisation de Langlands globaleSep 24 2012Sep 28 2016For any reductive group G over a global function field, we use the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the direction "from automorphic to Galois". ... More

Radio emission and nonlinear diffusive shock acceleration of cosmic rays in the supernova SN 1993JMar 17 2009The extensive observations of the supernova SN 1993J at radio wavelengths make this object a unique target for the study of particle acceleration in a supernova shock. To describe the radio synchrotron emission we use a model that couples a semianalytic ... More

On the shoulders of students? The contribution of PhD students to the advancement of knowledgeAug 29 2011Using the participation in peer reviewed publications of all doctoral students in Quebec over the 2000-2007 period this paper provides the first large scale analysis of their research effort. It shows that PhD students contribute to about a third of the ... More

Modelling Chaotic DataJul 31 2011This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common methods, including ... More

Limit groups and groups acting freely on $\bbR^n$-treesJul 21 2003We give a simple proof of the finite presentation of Sela's limit groups by using free actions on $\bbR^n$-trees. We first prove that Sela's limit groups do have a free action on an $\bbR^n$-tree. We then prove that a finitely generated group having a ... More

Lehmer code transforms and Mahonian statistics on permutationsMar 18 2012In 2000 Babson and Steingr{\'\i}msson introduced the notion of vincular patterns in permutations. They shown that essentially all well-known Mahonian permutation statistics can be written as combinations of such patterns. Also, they proved and conjectured ... More

On the Inverse Scattering Method for Integrable PDEs on a Star GraphSep 18 2014May 31 2015We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend ... More

Permutation classesSep 17 2014Jan 04 2015This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.

Comment on: "Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry" [J. Chem. Phys. 138, 12A509 (2013)]Nov 11 2015Jun 15 2016In this Comment, we argue that the behavior of the overlap functions reported in the commented paper can be fully understood in terms of the physics of simple liquids in contact with disordered substrates, without appealing to any particular glassy phenomenology. ... More

The Tensor Track, IVApr 26 2016This note is a sequel to the previous series "Tensor Track I-III". Assuming some familiarity with the tensor track approach to quantum gravity, we provide a brief introduction to the developments of the last two years and to their corresponding bibliography. ... More

Chemotactic waves of bacteria at the mesoscaleJul 01 2016The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two reaction-diffusion equations ... More

A Local limit theorem for directed polymers in random media: the continuous and the discrete caseMar 25 2005In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function is bounded in ... More

On Time-frequency Scattering and Computer MusicOct 10 2018Jan 22 2019Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of sounds, it ... More

A library to compute the density of the distance between a point and a random variable uniformly distributed in some setsJun 03 2019In [3], algorithms to compute the density of the distance to a random variable uniformly distributed in (a) a ball, (b) a disk, (c) a line segment, or (d) a polygone were introduced. For case (d), the algorithm, based on Green's theorem, has complexity ... More

Re-parameterizing and reducing families of normal operatorsOct 08 2017We present a new proof of results of Kurdyka & Paunescu, and of Rainer, about real-analytic multi-parameters generalizations of classical results by Rellich and Kato about the reduction in families of univariate deformations of normal operators over real ... More

Une ou deux composantes ? La réponse de la diffusion en ondelettesMay 21 2019With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order ... More

Infinite determinacy on a closed set for smooth germs with non-isolated singularitiesJun 13 2004Oct 18 2004We give necessary and sufficient conditions of infinite determinacy for smooth function germs whose critical locus contains a given set. This set is assumed to be the zero variety X of some analytic map germ having maximal rank on a dense subset of X. ... More

On VC-density in VC-minimal theoriesSep 29 2014We show that any formula with two free variables in a VC-minimal theory has VC-codensity at most two. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acl = dcl, the VC-codensity of a formula is at most ... More

Dependence and Isolated ExtensionsNov 06 2009In this paper, we show that \phi is a dependent formula if and only if all \phi-types have an extension to a \phi-isolated \phi-type that is an "elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain of this extension ... More

Une ou deux composantes ? La réponse de la diffusion en ondelettesMay 21 2019Jun 21 2019With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order ... More

Inexact Stochastic Mirror Descent for two-stage nonlinear stochastic programsMay 29 2018Jul 08 2019We introduce an inexact variant of Stochastic Mirror Descent (SMD), called Inexact Stochastic Mirror Descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling constraints and a nonlinear ... More

Category-valued traces for bimodule categories: a representation-theoretic realizationFeb 27 2018The category-valued trace assigns to a bimodule category over a linear monoidal category a linear category. It generalizes Drinfeld centers of monoidal categories and the relative Deligne product of bimodule categories. In this article, we study bimodule ... More

Search for neutrinoless double-beta decay with SNO+Sep 17 2018The SNO+ experiment, located in SNOLAB, 2 kilometers underground in the Creighton mine, near Sudbury, Canada, is a large scale neutrino detector whose main purpose is to search for neutrinoless double-beta decay and thus probe the Majorana nature of the ... More

Asymptotics of lieanders with fixed composition sizesDec 10 2018Lieanders are special cases of meanders and first appeared in connection with Lie algebras. Using the results from the author with E. Goujard, P. Zograf and A. Zorich, we prove a polynomial asymptotics for the number of lieanders with fixed composition ... More

Eigentriads and Eigenprogressions on the TonnetzOct 01 2018We introduce a new multidimensional representation, named eigenprogression transform, that characterizes some essential patterns of Western tonal harmony while being equivariant to time shifts and pitch transpositions. This representation is deep, multiscale, ... More

Asymptotic stabilization of stationnary shock waves using a boundary feedback lawJan 19 2018In this paper we consider scalar conservation laws with a convex flux. Given a stationnary shock, we provide a feedback law acting at one boundary point such that this solution is now asymptotically stable in L 1-norm in the class of entropy solution. ... More

Affine pavings for affine Springer fibers for split elements in PGL(3)Sep 07 2003This paper constructs pavings by affine spaces for the affine Springer fibers for PGL(3) obtained from regular compact elements in a split maximal torus. These pavings are constructed by intersecting the affine Springer fiber with a non-standard paving ... More

A characterization of the U(Omega,m) sets of a hyperelliptic curve as Omega and m varyMar 20 2019In this article we consider a certain distinguished set $U(\Omega,m) \subseteq \{1,2,\ldots,2g+1,\infty\}$ that can be attached to a marked hyperelliptic curve of genus $g$ equipped with a small period matrix $\Omega$ for its polarized Jacobian. We show ... More

On the Stability of Analytic Germs under Ultradifferentiable PerturbationsJan 05 2006Let $ f$ be a real-analytic function germ whose critical locus contains a given real-analytic set $ X $, and let $ Y $ be a germ of closed subset of $ \mathbb{R}^n $ at the origin. We study the stability of $ f $ under perturbations $ u $ that are flat ... More

Łojasiewicz ideals in Denjoy-Carleman classesOct 23 2012Jul 22 2013The classical notion of {\L}ojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of {\L}ojasiewicz ideals in terms of properties of ... More

Une infinite de structures de contact tendues sur les varietes toroidalesDec 12 2000We show that every closed toroidal irreducible orientable 3-manifold carries infinitely many universally tight contact structures.