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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

Conformalized Quantile RegressionMay 08 2019Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because ... More

The Likelihood Ratio Test in High-Dimensional Logistic Regression Is Asymptotically a Rescaled Chi-SquareJun 05 2017Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression ... More

Gene Hunting with Knockoffs for Hidden Markov ModelsJun 14 2017Modern scientific studies often require the identification of a subset of relevant explanatory variables, in the attempt to understand an interesting phenomenon. Several statistical methods have been developed to automate this task, but only recently ... More

Robust inference with knockoffsJan 11 2018Feb 11 2019We 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

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

Holographic Phase Retrieval and Reference DesignJan 19 2019Apr 22 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

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

Deep KnockoffsNov 16 2018This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring ... 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

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 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

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

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]

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

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

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

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

A modern maximum-likelihood theory for high-dimensional logistic regressionMar 19 2018Jun 16 2018Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there are formulas ... 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

Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear SystemsMay 19 2015Mar 22 2016We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We propose a novel ... 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

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

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

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

Super-Resolution of Positive Sources: the Discrete SetupApr 03 2015In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper rigorously establishes ... 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

A Radio Spectral Line Study of the 2-Jy IRAS-NVSS Sample: Part IMar 22 2010Apr 06 2010We present results from an on-going survey for the HI 21 cm line and the OH 18 cm lines in IR galaxies with the Arecibo 305 m Radio Telescope. The observations of 85 galaxies extracted from the 2 Jy IRAS-NVSS sample in the R.A. (B1950) range 20 h-00 h ... 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

Computer Assisted Proofs of Contracting Invariant Tori for ODEsMay 20 2019This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which applies to explicit ... More

Cognitive Science in the era of Artificial Intelligence: A roadmap for reverse-engineering the infant language-learnerJul 29 2016Aug 31 2016During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still escapes current ... More

Positivite et discretion des points algebriques des courbesJun 27 1996We prove the discreteness of algebraic points (with respect to the Neron-Tate height) on a curve of genus greater than one embedded in his jacobian. This result was conjectured by Bogomolov. We also prove the positivity of the self intersection of the ... More

Models for cohesive sediments describing the evolution of the characteristics of particlesMar 03 2009The goal of this paper is to set up a framework designed to take into account the characteristics of sediment particles when transported by water. Our protocol consists in describing the characteristics of sediment particles via an additional variable, ... More

Regulation of Heart Beats by the Autonomous Nervous System in Health and Disease: Point-Process-Theory based Models and Simulation [V-I]Apr 17 2019We have advanced a point-process based framework for the regulation of heart beats by the autonomous nervous system and analyzed the model with and without feedback. The model without feedback was found amenable to several analytical results that help ... 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

Predictive inference with the jackknife+May 08 2019This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by ... More

KPConv: Flexible and Deformable Convolution for Point CloudsApr 18 2019We present Kernel Point Convolution (KPConv), a new design of point convolution, i.e. that operates on point clouds without any intermediate representation. The convolution weights of KPConv are located in Euclidean space by kernel points, and applied ... More

Large Scale Structure in CHILESApr 23 2019We demonstrate that the Discrete Persistent Source Extractor (DisPerSE) can be used with spectroscopic redshifts to define the cosmic web and its distance to galaxies in small area deepfields. Here we analyze the use of DisPerSE to identify structure ... 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

Critical Elliptic Systems in Potential FormJul 18 2005Jul 18 2005We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

Sharp Sobolev Inequalities for Vector Valued MapsJul 18 2005We discuss sharp Sobolev inequalities for vector valued maps.

On the group of rational spectral units with finite orderJul 05 2009The problem of phase retrieval is a difficult one which remains far from solved. Two homometric sets are always connected by way of a convolution product by some spectral unit, though not necessarily in a unique way. Here we elucidate one small aspect, ... More

Thermal rectification in quantum graded mass systemsMar 01 2010We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in ... More

Sufficient conditions for thermal rectification in graded materialsJan 24 2011We address a fundamental problem for the advance of phononics: the search of a feasible thermal diode. We establish sufficient conditions for the existence of thermal rectification in general graded materials. By starting from simple assumptions satisfied ... 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

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

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

Equations, inequations and inequalities characterizing the configurations of two real projective conicsMay 29 2005Feb 13 2006Couples of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The ... 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 variant of Ostrowski numerationApr 03 2019In this article, we propose a variant of the usual Ostrowski $\alpha$-numeration (where $\alpha$ is a real in [0, 1[) that codes integers (positive as well as negative) and reals of [0, 1[ (instead of [--$\alpha$, 1--$\alpha$[), so that for every integer ... More

Cognitive Science in the era of Artificial Intelligence: A roadmap for reverse-engineering the infant language-learnerJul 29 2016Feb 14 2018During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still escapes current ... More

Ab Initio Models of DislocationsJan 07 2019This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where the crystal ... More

Renewal Structure of the Brownian Taut StringSep 24 2015In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large ... More

Beyond heights: slopes and distribution of rational pointsJun 29 2018Jul 30 2018The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise the points ... 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

Unifying type systems for mobile processesMay 28 2015We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to previously known ... More

Enumeration Reducibility in Closure Spaces with Applications to Logic and AlgebraMay 28 2015Aug 07 2017In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of theorems in many ... More

Dimension of gram spectrahedra of univariate polynomialsApr 16 2015The Gram Spectrahedron of a polynomial parametrizes its sums-of-squares representations. In this note, we determine the dimension of Gram Spectrahedra of univariate polynomials.

Toward predictive machine learning for active visionOct 28 2017Jan 08 2018We develop a comprehensive description of the active inference framework, as proposed by Friston (2010), under a machine-learning compliant perspective. Stemming from a biological inspiration and the auto-encoding principles, the sketch of a cognitive ... More

Rectification and One-Way Street for the Energy Current in Boundary-Driven Asymmetric Quantum Spin ChainsMar 16 2017Motivated by the demand of efficient quantum devices to engineer the energy transport, we analyze some inhomogeneous quantum spin systems, including the XXZ chains, with magnetization baths at the ends. Aimed at finding general properties, we study the ... More

The distance-dependent two-point function of triangulations: a new derivation from old resultsNov 05 2015We present a new derivation of the distance-dependent two-point function of random planar triangulations. As it is well-known, this function is intimately related to the generating functions of so-called slices, which are pieces of triangulation having ... More

Aperiodic Subshifts on Polycyclic GroupsOct 08 2015Aug 19 2016We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].

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

Non-genericity of variations of Hodge structure for hypersurfaces of high degreeMar 17 2005In this paper we are interested in proving that the infinitesimal variations of Hodge structure of hypersurfaces of high enough degree lie in a proper subvariety of the variety of all infinitesimal variations. This is proved using a space of symmetrizers ... More

Quotients of numerical semigroups generated by two numbersApr 17 2019In this article, we study the quotients of numerical semigroups, generated by two coprime positive numbers, denoted <a,b> d. We give formulae for the usual invariants of these semigroups, expressed in terms of continued fraction expansions and Ostrowski-like ... 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

Ergodic properties of Poissonian ID processesJul 25 2007We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its L\'{e}vy ... 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

Conformal Prediction Under Covariate ShiftApr 12 2019Apr 25 2019We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the test and training ... 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

A Strong Tits AlternativeApr 09 2008We show that for every integer $d$, there is a constant $N(d)$ such that if $K$ is any field and $F$ is a finite subset of $GL_d(K)$, which generates a non amenable subgroup, then $F^{N(d)}$ contains two elements, which freely generate a non abelian free ... More

On Legendrian knots and polynomial invariantsFeb 29 2000Jul 21 2000It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the lower degree in the framing variable ... More

Sieve in expansionDec 13 2010This is a survey report for the Bourbaki Seminar (Exp. no. 1028, November 2010) concerning sieve and expanders, in particular the recent works of Bourgain, Gamburd and Sarnak introducing "sieve in orbits", and the related developments concerning expansion ... More

Efficient prediction in $L^2$-differentiable families of distributionsDec 12 2013Apr 11 2014A proof of the Cram\'er-Rao inequality for prediction is presented under conditions of $L^2$-differentiability of the family of distributions of the model. The assumptions and the proof differ from those of Miyata (2001) who also proved this inequality ... More

Relative Yamabe invariant and c-concordant metricsAug 06 2008Feb 02 2009We show a surgery formula for the relative Yamabe invariant and give applications to the study of concordance classes of metrics.

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

Growth, Industrial Externality, Prospect Dynamics and Well-being on MarketsNov 10 2018Mar 22 2019Functions or 'functionings' enable to give a structure to any economic activity whether they are used to describe a good or a service that is exchanged on a market or they constitute the capability of an agent to provide the labor market with specific ... More

A modified block Lanczos algorithm with fewer vectorsApr 08 2016The block Lanczos algorithm proposed by Peter Montgomery is an efficient means to tackle the sparse linear algebra problem which arises in the context of the number field sieve factoring algorithm and its predecessors. We present here a modified version ... More

Heat, Work and Energy Currents in the Boundary-Driven XXZ Spin ChainNov 09 2018We address the detailed study of the energy current and its components, heat and work, in the boundary-driven 1D XXZ quantum model. We carry out the investigation by considering two different approaches present in the literature. First, we take the repeated ... More

The rational fragment of the ZX-calculusOct 12 2018We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but relies instead ... More

Translation-like Actions and Aperiodic Subshifts on GroupsAug 26 2015It is well known that if $G$ admits a f.g. subgroup $H$ with a weaklyaperiodic SFT (resp. an undecidable domino problem), then $G$itself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can replace the property "$H$ is ... More

Exponential gaps in the length spectrumJun 18 2018We present a separation property for the gaps in the length spectrum of a compact Riemannian manifold with negative curvature. In arbitrary small neighborhoods of the metric for some suitable topology, we show that there are negatively curved metrics ... More

Motivic Integration and Logarithmic GeometryMay 21 2015In this thesis, we use logarithmic methods to study motivic objects. Let R be a complete discrete valuation ring with perfect residue field k, and denote by K its fraction field. We give in chapter 2 a new construction of the motivic Serre invariant of ... More

Optimization of Non Binary Parity Check CoefficientsAug 05 2017Jun 07 2018This paper generalizes the method proposed by Poulliat et al. for the determination of the optimal Galois Field coefficients of a Non-Binary LDPC parity check constraint based on the binary image of the code. Optimal, or almost-optimal, parity check coefficients ... More

On a conjecture by Chapuy about Voronoi cells in large mapsMar 08 2017In a recent paper, Chapuy conjectured that, for any positive integer k, the law for the fractions of total area covered by the k Voronoi cells defined by k points picked uniformly at random in the Brownian map of any fixed genus is the same law as that ... More

Higgs bundles and indecomposable parabolic bundles over the projective lineSep 15 2016In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretation ... More

Some results on the statistics of hull perimeters in large planar triangulations and quadrangulationsFeb 24 2016The hull perimeter at distance d in a planar map with two marked vertices at distance k from each other is the length of the closed curve separating these two vertices and lying at distance d from the first one (d<k). We study the statistics of hull perimeters ... More

Lectures on approximate groups and Hilbert's 5th problemDec 04 2015This paper gathers four lectures, based on a mini-course at IMA in 2014, whose aim was to discuss the structure of approximate subgroups of an arbitrary group, following the works of Hrushovski and of Green, Tao and the author. Along the way we discuss ... More

A Wong-Rosay type theorem for proper holomorphic self-mapsSep 19 2008We show that the only proper-holomorphic self-maps of bounded domains in C^k whose dynamics escape to a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type result for a sequence of maps whose ... More

Sur le spectre des longueurs des groupes de trianglesJan 29 2009Feb 25 2009We describe in this report the beginning of the length spectra of fuchsian triangular groups

Théorie ergodique et géométrie arithmétiqueApr 16 2003We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.

On the rank of quadratic twists of elliptic curvers over function fieldsMar 31 2005We prove quantitative upper bounds for the number of quadratic twists of a given elliptic curve $E/\Fp_q(C)$ over a function field over a finite field that have rank $\geq 2$, and for their average rank. The main tools are constructions and results of ... More