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Near-ideal model selection by $\ell_1$ minimizationJan 02 2008Aug 21 2009We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called "$p>n$" setup. ... More

Controlling the false discovery rate via knockoffsApr 22 2014Oct 14 2015In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know ... More

Rejoinder: "Gene Hunting with Hidden Markov Model Knockoffs"Mar 13 2019In this paper we deepen and enlarge the reflection on the possible advantages of a knockoff approach to genome wide association studies (Sesia et al., 2018), starting from the discussions in Bottolo & Richardson (2019); Jewell & Witten (2019); Rosenblatt ... More

Searching for a trail of evidence in a mazeJan 24 2007Aug 07 2008Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing ... More

Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticismJul 08 2010Feb 23 2012Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption ... More

Templates for Convex Cone Problems with Applications to Sparse Signal RecoverySep 10 2010Dec 19 2011This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the ... More

Dual-Reference Design for Holographic Coherent Diffraction ImagingFeb 07 2019A new reference design is introduced for Holographic Coherent Diffraction Imaging. This consists of two reference portions - being "block" and "pinhole" shaped regions - adjacent to the imaging specimen. Expected error analysis on data following a Poisson ... More

The limits of distribution-free conditional predictive inferenceMar 12 2019We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, ... More

How well can we estimate a sparse vector?Apr 27 2011Mar 01 2013The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix ... More

Robust subspace clusteringJan 11 2013May 23 2014Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference ... More

Robust inference with knockoffsJan 11 2018Jan 23 2018We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_1, \ldots, X_p$. We wish to do so while offering finite-sample guarantees about the fraction of false ... More

Rejoinder: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$Mar 21 2008Rejoinder to ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]

Detection of an anomalous cluster in a networkJan 19 2010Mar 09 2011We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization ... More

Gravitational wave detection using multiscale chirpletsJun 27 2008Jul 01 2008A generic `chirp' of the form h(t) = A(t) cos(phi(t)) can be closely approximated by a connected set of multiscale chirplets with quadratically-evolving phase. The problem of finding the best approximation to a given signal using chirplets can be reduced ... More

The Power of Convex Relaxation: Near-Optimal Matrix CompletionMar 09 2009This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other ... More

A probabilistic and RIPless theory of compressed sensingNov 16 2010Nov 19 2010This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g. Gaussian, frequency ... More

Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurementsJan 02 2010This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm minimization stably ... More

Accurate low-rank matrix recovery from a small number of linear measurementsOct 02 2009We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the entries, and ... More

The Curvelet Representation of Wave Propagators is Optimally SparseJul 13 2004This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly anisotropic at ... More

SLOPE - Adaptive variable selection via convex optimizationJul 14 2014Nov 04 2015We introduce a new estimator for the vector of coefficients $\beta$ in the linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to \[\min_{b\in\mathbb{R}^p}\frac{1}{2}\Vert ... More

Highly robust error correction by convex programmingDec 22 2006This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x in R^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction ... More

EigenPrism: Inference for High-Dimensional Signal-to-Noise RatiosMay 08 2015Jun 28 2016Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional ($p>n$) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ... More

On Fourier coefficients of modular forms of half integral weight at squarefree integersFeb 29 2016Apr 20 2016We show that the Dirichlet series associated to the Fourier coefficients of a half-integral weight Hecke eigenform at squarefree integers extends analytically to a holomorphic function in the half-plane $\re s\textgreater{}\tfrac{1}{2}$. This exhibits ... More

Enhancing Sparsity by Reweighted L1 MinimizationNov 10 2007It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we study a novel ... More

Metropolized Knockoff SamplingMar 01 2019Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge ... More

Compressed Sensing with Coherent and Redundant DictionariesMay 14 2010Dec 04 2010This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus ... More

Robust Principal Component Analysis?Dec 18 2009This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible ... More

Detecting Highly Oscillatory Signals by Chirplet Path PursuitApr 05 2006This paper considers the problem of detecting nonstationary phenomena, and chirps in particular, from very noisy data. Chirps are waveforms of the very general form A(t) exp(i\lambda \phi(t)), where \lambda is a (large) base frequency, the phase \phi(t) ... More

Inverse Participation Ratios in the XX spin chainNov 06 2016We continue the study of the Inverse Participation Ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Misguich, Pasquier and Luck (2016) by focusing on the case of the XX Heisenberg Spin Chain. For the ground state, Misguich et al. note that ... More

Evaluating convolutions of divisor sums with quasimodular formsOct 20 2005Apr 11 2006We provide a systematic method to compute arithmetic sums including some previously computed by Alaca, Alaca, Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi, Ou, Ramanujan, Spearman and Williams. Our method is based on quasimodular forms. This extension ... More

A Height Gap Theorem For Finite Subsets Of GL_d(\bar{Q}) and Non Amenable SubgroupsApr 09 2008Nov 04 2011We show a global adelic analog of the classical Margulis Lemma from hyperbolic geometry. We introduce a conjugation invariant normalized height $\hat{h}(F)$ of a finite set of matrices $F$ in $GL_{n}(\bar{\Bbb{Q}})$ which is the adelic analog of the minimal ... More

Extension of the first mixed volume to nonconvex setsJul 26 2016We study the first mixed volume for nonconvex sets and apply the results to limits of discrete isoperimetric problems. Let $ M,N \subset \mathbb{R}^d$. Define $D_N (M)=\lim_{\epsilon \downarrow 0} \frac{|M+\epsilon N|-|M|}{\epsilon}$ whenever the limit ... More

The Dirichlet problem for some nonlocal diffusion equationsFeb 21 2007May 30 2007We study the Dirichlet problem for the non-local diffusion equation $u_t=\int\{u(x+z,t)-u(x,t)\}\dmu(z)$, where $\mu$ is a $L^1$ function and $``u=\phi$ on $\partial\Omega\times(0,\infty)$'' has to be understood in a non-classical sense. We prove existence ... More

Coverings in p-adic analytic geometry and log coverings I: Cospecialization of the (p')-tempered fundamental group for a family of curvesSep 15 2009Sep 22 2011The tempered fundamental group of a p-adic analytic space classifies coverings that are dominated by a topological covering (for the Berkovich topology) of a finite etale covering of the space. Here we construct cospecialization homomorphisms between ... More

Structures de contact sur les varietes fibrees en cercles au-dessus d'une surfaceNov 29 1999In this paper, we study the global behaviour of contact structures on oriented manifolds V which are circle bundles over a closed orientable surface S of genus g>0. We establish in particular contact analogs of a number of classical results about foliations ... More

Computation of the cover of Shimura curves $X_0(2) \to X(1)$ for the cyclic cubic field of discriminant 13^2Jul 11 2007We compute the canonical model of the cover of Shimura curves $X_0(2) \to X(1)$ for the cubic field of discriminant 13^2 described at the end of Elkies' paper "Shimura curves for level 3 subgroups of the (2,3,7) triangle group". Last, we list the coordinates ... More

Multilingual Sentence Categorization according to LanguageFeb 28 1995Mar 10 1995In this paper, we describe an approach to sentence categorization which has the originality to be based on natural properties of languages with no training set dependency. The implementation is fast, small, robust and textual errors tolerant. Tested for ... More

Gauge theories in noncommutative geometry and generalization of the Born-Infeld modelDec 30 2005Endomorphisms algebras can replace the concept of principal fiber bundle. Gauge theories are reformulated within this algebraic framework and further generalized to unify ordinary connections and Higgs fields. A 'noncommutative Maxwell' model is built ... More

Randomness and dependencies extraction via polarization, with applications to Slepian-Wolf coding and secrecyFeb 07 2011Nov 12 2014The polarization phenomenon for a single source is extended to a framework with multiple correlated sources. It is shown in addition to extracting the randomness of the source, the polar transforms takes the original arbitrary dependencies to extremal ... More

Global behaviour of radially symmetric solutions stable at infinity for gradient systemsMar 06 2017This paper is concerned with radially symmetric solutions of systems of the form \[ u_t = -\nabla V(u) + \Delta_x u \] where space variable $x$ and and state-parameter $u$ are multidimensional, and the potential $V$ is coercive at infinity. For such systems, ... More

Global behaviour of bistable solutions for gradient systems in one unbounded spatial dimensionApr 07 2016Mar 08 2017This paper is concerned with spatially extended gradient systems of the form \[ u_t=-\nabla V (u) + u_{xx}\,, \] where spatial domain is the whole real line, state-parameter $u$ is multidimensional, and the potential $V$ is coercive at infinity. For such ... More

Global relaxation of bistable solutions for gradient systems in one unbounded spatial dimensionApr 04 2016Mar 13 2017This paper is concerned with spatially extended gradient systems of the form \[ u_t=-\nabla V (u) + \mathcal{D} u_{xx}\,, \] where spatial domain is the whole real line, state-parameter $u$ is multidimensional, $\mathcal{D}$ denotes a fixed diffusion ... More

Holographic Phase Retrieval and Optimal Reference DesignJan 19 2019A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered via phase ... More

Maharam extension and stationary stable processesJan 05 2010May 28 2012We give a second look at stationary stable processes by interpreting the self-similar property at the level of the L\'evy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.

Selective advantage for sexual reproduction with random haploid fusionSep 08 2007This paper develops a simplified set of models describing asexual and sexual replication in unicel- lular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be functional if it ... More

Excursions of the integral of the Brownian motionJan 22 2009Jun 18 2009The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a ... More

Existence result for a model of Proteus mirabilis swarmFeb 26 2007In this paper we present a modification of the usual Proteus mirabilis swarm model. For the obtained model (which is a two phase model with a non-linear diffusion term containing memory) we set up a collection of a priori estimates. Those estimates allow ... More

Weyl laws for partially open quantum mapsNov 19 2008Apr 03 2009We study a toy model for "partially open" wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping ... More

Competition between stable equilibria in reaction-diffusion systems: the influence of mobility on dominanceMar 07 2017This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front when the symmetry ... More

Astrocladistics: a phylogenetic analysis of galaxy evolution II. Formation and diversification of galaxiesFeb 27 2006This series of papers is intended to evaluate astrocladistics in reconstructing phylogenies of galaxies. The objective of this second paper is to formalize the concept of galaxy formation and to identify the processes of diversification. We show that ... More

Astrocladistics: a phylogenetic analysis of galaxy evolution I. Character evolutions and galaxy historiesFeb 27 2006This series of papers is intended to present astrocladistics in some detail and evaluate this methodology in reconstructing phylogenies of galaxies. Being based on the evolution of all the characters describing galaxies, it is an objective way of understanding ... More

On vertical variations of gas flow in protoplanetary disks and their impact on the transport of solidsJan 24 2013A major uncertainty in accretion disk theory is the nature and properties of gas turbulence, which drives transport in protoplanetary disks. The commonly used viscous prescription for the Maxwell-Reynolds stress tensor gives rise to a meridional circulation ... More

Asymptotically efficient prediction for LAN familiesDec 11 2013In a previous paper (Bosq & Onzon (2012)) we did a first generalization of the concept of asymptotic efficiency for statistical prediction, i.e. for the problems where the unknown quantity to infer is not deterministic but random. However, in some instances, ... More

Maximal Symplectic packings of $¶^2$Oct 23 2006In this paper we describe the intersection between the balls of maximal symplectic packings of $\P^2$. This analysis shows the existence of singular points for maximal packings of $\P^2$ by more than three equal balls. It also yields a construction of ... More

Equidistribution of Dense Subgroups on Nilpotent Lie GroupsOct 24 2007Let $\Gamma$ be a dense subgroup of a simply connected nilpotent Lie group $G$ generated by a finite symmetric set $S$. We consider the $n$-ball $S_n$ for the word metric induced by $S$ on $\Gamma$. We show that $S_n$ (with uniform measure) becomes equidistributed ... More

Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectiviteJan 19 2005This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in $\C^2$. We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the weakly pseudoconvex ... More

The large sieve, monodromy and zeta functions of algebraic curves, II: independence of the zerosJul 14 2008Using the sieve for Frobenius, we show that, in a certain sense, the roots of the L-functions of "most" algebraic curves over finite fields do not satisfy any non-trivial (linear or multiplicative) rational dependency relations. This can be seen as an ... More

Weil numbers generated by other Weil numbers and torsion fields of abelian varietiesApr 03 2005Using properties of the Frobenius eigenvalues, we show that, in a precise sense, ``most'' isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized up to isogeny by the sequence of their division fields, ... More

The large sieve, monodromy and zeta functions of curvesMar 30 2005We prove a large sieve statement for the average distribution of Frobenius conjugacy classes in arithmetic monodromy groups over finite fields. As a first application we prove a stronger version of a result of Chavdarov on the ``generic'' irreducibility ... More

A useful underestimate for the convergence of integral functionalsJun 19 2015This article deals with the lower compactness property of a sequence of integrands and the use of this key notion in various domains: convergence theory, optimal control, non-smooth analysis. First about the interchange of the weak epi-limit and the symbol ... More

Maximizing the Power of Principal Components Analysis of Correlated Phenotypes in Genome-wide Association StudiesSep 11 2013Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs) explaining most of ... More

Unramified cohomology of degree 3 and Noether's problemDec 03 2002Let $G$ be a finite group and $W$ be a faithful representation of $G$ over {\bf C}. The group $G$ acts on the field of rational functions $\mathbf C(W)$. The aim of this paper is to give a description of the unramified cohomology group of degree 3 of ... More

About the number of generators of a musical scaleAug 31 2009Several musical scales, like the major scale, can be described as finite arithmetic sequences modulo octave, i.e. chunks of an arithmetic sequence in a cyclic group. Hence the question of how many different arithmetic sequences in a cyclic group will ... More

Geometry of Locally Compact Groups of Polynomial Growth and Shape of Large BallsApr 01 2007Apr 10 2012We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study of the geometry of G and a generalization of P. Pansu's thesis. In particular, we show that any such G is weakly ... More

Langevin process reflected on a partially elastic boundary IIMar 15 2011A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the critical value ... More

Relativité générale (d'après M.Vaugon) et quelques problèmes mathématiques qui en sont issusApr 13 2010Jun 12 2013This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.

On a nonlinear compactness lemma in L^p(0,T;B)Jul 04 2001Feb 06 2002We consider a nonlinear counterpart of a compactness lemma of J. Simon, which arises naturally in the study of doubly nonlinear equations of elliptic-parabolic type. Our work was motivated by previous results J. Simon, recently sharpened by H. Amann, ... More

The Perpendicular Bisector Construction in $n$-dimensional Euclidean and Non-euclidean GeometriesMar 29 2012The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this iterative construction to a construction on polytopes with $n$ vertices ... More

Coverings in p-adic analytic geometry and log coverings II: Cospecialization of the p'-tempered fundamental group in higher dimensionsMar 13 2009Sep 15 2009This paper constructs cospecialization homomorphisms between the (p') versions of the tempered fundamental group of the fibers of a smooth morphism with polystable reduction (the tempered fundamental group is a sort of analog of the topological fundamental ... More

Perfect Thermal Rectification in a Many-Body Quantum Ising ModelFeb 28 2019We address a keystone problem for the progress of phononics: the proposal of efficient thermal diodes. Aiming the disclosure of an easy itinerary for the building of a heat rectifier, we investigate unsophisticated systems linked to simple thermal baths, ... More

Approximate subgroups and super-strong approximationJul 11 2014Jul 18 2014Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification of approximate ... More

The principle of the large sieveSep 30 2006Oct 29 2006We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function fields. The ... More

Averages of Euler products, distribution of singular series and the ubiquity of Poisson distributionMay 30 2008May 27 2010We discuss in some detail the general problem of computing averages of convergent Euler products, and apply this to examples arising from singular series for the $k$-tuple conjecture and more general problems of polynomial representation of primes. We ... More

Exponential sums over definable subsets of finite fieldsApr 15 2005Jun 04 2005We prove some general estimates for exponential sums over subsets of finite fields which are definable in the language of rings. This generalizes both the classical exponential sum estimates over varieties over finite fields due to Weil, Deligne and others, ... More

Global behaviour of bistable solutions for hyperbolic gradient systems in one unbounded spatial dimensionMar 03 2017This paper is concerned with damped hyperbolic gradient systems of the form \[ \alpha u_{tt} + u_t = -\nabla V(u) + u_{xx}\,, \] where spatial domain is the whole real line, state-parameter $u$ is multidimensional, $\alpha$ is a positive quantity, and ... More

Resonances near the real axis for manifolds with hyperbolic trapped setsJun 18 2018For manifolds Euclidian at infinity and compact perturbations of the Laplacian, we show that under assumptions involving hyperbolicity of the classical flow on the trapped set and its period spectrum, there are strips below the real axis where the resonance ... More

On beryllium-10 production in gaseous protoplanetary disks and implications on the astrophysical setting of refractory inclusionsMar 07 2019Calcium-Aluminum-rich Inclusions (CAIs), the oldest known solids of the solar system, show evidence for the past presence of short-lived radionuclide beryllium-10, which was likely produced by spallation during protosolar flares. While such $^{10}$Be ... More

Computation of some Moduli Spaces of covers and explicit S_n and A_n regular Q(T)-extensions with totally real fibersFeb 13 2002We study and compute an infinite family of Hurwitz spaces parameterizing covers of P_C branched at four points and deduce explicit regular S_n and A_n-extensions over Q(T) with totally real fibers.

Gas, Dust, and Young Stars in the Outer Disk of M 31Feb 21 2001Using the Canada-France-Hawaii Telescope we have obtained deep high-resolution CCD images in V and I of a 28'x28' field in the outer disk of M 31 at ~ 116' from the center along the major axis to the south-west, and covering a range of projected galactocentric ... More

Dynamic Predictions with Time-Dependent Covariates in Survival Analysis using Joint Modeling and LandmarkingJun 27 2013A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often performed on a regular ... More

Searching For Rapid Orbital Decay of WASP-18bFeb 03 2017The WASP-18 system, with its massive and extremely close-in planet, WASP-18b (M$_{p}$ = 10.3M$_{J}$, a = 0.02 AU, P = 22.6 hours), is one of the best known exoplanet laboratories to directly measure Q', the modified tidal quality factor and proxy for ... More

Galaxy Pairs in the Sloan Digital Sky Survey - X: Does gas content alter star formation rate enhancement in galaxy interactions?Mar 17 2015New spectral line observations, obtained with the Jansky Very Large Array (VLA), of a sample of 34 galaxies in 17 close pairs are presented in this paper. The sample of galaxy pairs is selected to contain galaxies in close, major interactions (i.e., projected ... More

Weakly Supervised Multi-Embeddings Learning of Acoustic ModelsDec 20 2014Apr 20 2015We trained a Siamese network with multi-task same/different information on a speech dataset, and found that it was possible to share a network for both tasks without a loss in performance. The first task was to discriminate between two same or different ... More

Screening like-charges in one-dimensional Coulomb systems: Exact resultsJul 22 2015The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted to some limiting ... More

On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equationsOct 12 2015We give a simplified proof of regularizing effects for first-order Hamilton-Jacobi Equations of the form $u\_t+H(x,t,Du)=0$ in $\R^N\times(0,+\infty)$ in the case where the idea is to first estimate $u\_t$. As a consequence, we have a Lipschitz regularity ... More

A program logic for higher-order procedural variables and non-local jumpsDec 07 2011Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this programming language. ... More

The second Yamabe invariantFeb 04 2005Mar 15 2005Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it is attained. ... More

Groups of smooth diffeomorphisms of Cantor sets embedded in a lineFeb 27 2019Let K be a Cantor set embedded in the real line R. Following Funar and Neretin, we define the diffeomorphism group of K as the group of homeomorphisms of K which locally look like a diffeomorphism between two intervals of R. Higman-Thompson's groups Vn ... More

Asymptotic distribution of least square estimators for linear models with dependent errors : regular designsOct 16 2017Jan 08 2019In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least square estimator under general conditions ... More

Linear Universal Decoding for Compound Channels: a Local to Global Geometric ApproachSep 30 2008Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithm with manageable complexities is permitted. Maximum likelihood ... More

The Perpendicular Bisectors Construction, the Isoptic Point and the Simson Line of a QuadrilateralDec 24 2011Given a noncyclic quadrilateral, we consider an iterative procedure producing a new quadrilateral at each step. At each iteration, the vertices of the new quadrilateral are the circumcenters of the triad circles of the previous generation quadrilateral. ... More

Conjugacy of 2-spherical subgroups of Coxeter groups and parallel wallsAug 02 2005Jun 29 2009Let (W,S) be a Coxeter system of finite rank (ie |S| is finite) and let A be the associated Coxeter (or Davis) complex. We study chains of pairwise parallel walls in A using Tits' bilinear form associated to the standard root system of (W,S). As an application, ... More

Applications of singular connections in symplectic and almost complex geometryDec 05 2016In this paper, we give two direct applications of the theory of singular connections developped by Harvey-Lawson [10]. The first one is a version of Lelong-Poincar\'e formula for vector bundle over an almost complex manifold. The second is a convergence ... More

On the contact mapping class group of Legendrian circle bundlesJun 03 2015In this paper, we determine the group of contact transformations modulo contact isotopies for Legendrian circle bundles over closed surfaces of nonpositive Euler characteristic. These results extend and correct those presented by the first author in a ... More

Complex variables for fractional-order systemsNov 05 2018This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this document will serve ... More

Mass functions of a compact manifoldJun 20 2018Let $M$ be a compact manifold of dimension $n$. In this paper, we introduce the {\em Mass Function} $a \geq 0 \mapsto \xp{M}{a}$ (resp. $a \geq 0 \mapsto \xm{M}{a}$) which is defined as the supremum (resp. infimum) of the masses of all metrics on $M$ ... More

Counting points of homogeneous varieties over finite fieldsMar 23 2008Apr 17 2009Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer coefficients. Moreover, ... More

Structuring multi-dimensional subshiftsSep 24 2013We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural properties of two-dimensional subshifts: We characterize the simplest aperiodic ... More

On the kernel of the norm in some unramified number fields extensionsJun 04 2007We determine the -1 Tate cohomology group of the units for principal abelian extensions of type (p^a, p^b) of a number field.

Finite and infinite quotients of discrete and indiscrete groupsSep 18 2017May 31 2018These notes are devoted to lattices in products of trees and related topics. They provide an introduction to the construction, by M. Burger and S. Mozes, of examples of such lattices that are simple as abstract groups. Two features of that construction ... More