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Tighter bounds lead to improved classifiersJun 29 2016The standard approach to supervised classification involves the minimization of a log-loss as an upper bound to the classification error. While this is a tight bound early on in the optimization, it overemphasizes the influence of incorrectly classified ... More

Anytime Tail AveragingFeb 13 2019Feb 19 2019Tail averaging consists in averaging the last examples in a stream. Common techniques either have a memory requirement which grows with the number of samples to average, are not available at every timestep or do not accomodate growing windows. We propose ... More

Anytime Tail AveragingFeb 13 2019Tail averaging consists in averaging the last examples in a stream. Common techniques either have a memory requirement which grows with the number of samples to average, are not available at every timestep or do not accomodate growing windows. We propose ... More

Local Component AnalysisSep 01 2011Dec 10 2012Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier ... More

Fast Convergence of Stochastic Gradient Descent under a Strong Growth ConditionAug 29 2013We consider optimizing a function smooth convex function $f$ that is the average of a set of differentiable functions $f_i$, under the assumption considered by Solodov [1998] and Tseng [1998] that the norm of each gradient $f_i'$ is bounded by a linear ... More

Weakly Supervised Learning of Foreground-Background Segmentation using Masked RBMsJul 19 2011We propose an extension of the Restricted Boltzmann Machine (RBM) that allows the joint shape and appearance of foreground objects in cluttered images to be modeled independently of the background. We present a learning scheme that learns this representation ... More

A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training SetsFeb 28 2012Mar 11 2013We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates ... More

Convergence Rates of Inexact Proximal-Gradient Methods for Convex OptimizationSep 12 2011Dec 01 2011We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with ... More

Understanding the impact of entropy on policy optimizationNov 27 2018Feb 05 2019Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim using new visualizations ... More

Enhanced light emission from Carbon Nanotubes integrated in silicon micro-resonatorAug 05 2015Single-wall carbon nanotube are considered a fascinating nanomaterial for photonic applications and are especially promising for efficient light emitter in the telecommunication wavelength range. Furthermore, their hybrid integration with silicon photonic ... More

Understanding the impact of entropy on policy optimizationNov 27 2018Jun 07 2019Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim using new visualizations ... More

Controlling carbon nanotube photoluminescence using silicon microring resonatorsAug 05 2015We report on coupling between semiconducting single-wall carbon nanotubes (s-SWNT) photoluminescence and silicon microring resonators. Polyfluorene extracted s-SWNT deposited on such resonators exhibit sharp emission peaks, due to interaction with the ... More

Understanding the impact of entropy on policy optimizationNov 27 2018May 15 2019Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim using new visualizations ... More

Negative eigenvalues of the Hessian in deep neural networksFeb 06 2019The loss function of deep networks is known to be non-convex but the precise nature of this nonconvexity is still an active area of research. In this work, we study the loss landscape of deep networks through the eigendecompositions of their Hessian matrix. ... More

Tracking the gradients using the Hessian: A new look at variance reducing stochastic methodsOct 20 2017Mar 31 2018Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control ... More

Time-aware uniformization of winning strategiesJul 11 2019Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may help with actual ... More

Numerical Solution of a parabolic problem arising in financeMay 18 2009The optimal replication strategy for incomplete markets is obtained by solving a system of partial differential equations. In this paper, we study existence and uniqueness of the solution in suitable Sobolev spaces and propose a numerical method to compute ... More

There is no minimal action of Z^2 on the planeApr 29 2010Sep 10 2010In this paper it is proved that there is no minimal action (i.e. every orbit is dense) of Z^2 on the plane. The proof uses the non-existence of minimal homeomorphisms on the infinite annulus (Le Calvez-Yoccoz's theorem), and the theory of Brouwer homeomorphisms. ... More

Discrete Nondeterminism and Nash Equilibria for Strategy-Based GamesDec 10 2007Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium. Nash's approach ... More

Structure des homeomorphismes de BrouwerMar 24 2004Sep 27 2005For every Brouwer (ie planar, fixed point free, orientation preserving) homeomorphism h there exists a covering of the plane by translation domains, invariant simply-connected open subsets on which h is conjugate to an affine translation. We introduce ... More

Concurrent games and semi-random determinacyApr 29 2018Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of winning (finite-memory) ... More

Numerical Solution of a parabolic system with blowup of the solutionMay 18 2009In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution ... More

Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regimeMay 18 2009In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in two parts: ... More

Sound travellingwaves in wind instruments as solutions to non linear homogeneous gas dynamics equationsMay 19 2009The sound propagation is usually described by a linear homogeneous wave equation, though the air flow in a duct is described by the gas dynamics equations, using a variable cross section, which corresponds to a non linear non homogneous system. The aim ... More

An index for Brouwer homeomorphisms and homotopy Brouwer theoryJan 10 2014Sep 24 2015We use the homotopy Brouwer theory of Handel to define a Poincar{\'e} index between two orbits for an orientation preserving fixed point free homeomorphism of the plane. Furthermore, we prove that this index is almost additive.

An introduction to Handel's homotopy Brouwer theoryAug 05 2012Homotopy Brouwer theory is a tool to study the dynamics of surface homeomorphisms. We introduce and illustrate the main objects of homotopy Brouwer theory, and provide a proof of Handel's fixed point theorem. These are the notes of a mini-course held ... More

Acyclicity of Preferences, Nash Equilibria, and Subgame Perfect Equilibria: a Formal and Constructive EquivalenceMay 23 2007In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of Nash equilibria. ... More

From winning strategy to Nash equilibriumMar 08 2012May 08 2014Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the existence of a winning ... More

Distributional reinforcement learning with linear function approximationFeb 08 2019Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but ... More

On closed subgroups of the group of homeomorphisms of a manifoldJul 09 2012Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $\homeo_{0}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.

On terminating improvement in two-player gamesSep 23 2014Oct 16 2014A real-valued game has the finite improvement property (FIP), if starting from an arbitrary strategy profile and letting the players change strategies to increase their individual payoffs in a sequential but non-deterministic order always reaches a Nash ... More

Infinite subgame perfect equilibrium in the Hausdorff difference hierarchyMay 23 2015Sep 30 2015Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous real-valued payoffs, ... More

Un indice qui affine l'indice de Poincaré-Lefschetz pour les homéomorphismes de surfacesJun 02 2005We study the dynamics of surface homeomorphisms around isolated fixed points whose Poincar\'{e}-Lefschetz index is not equal to 1. We construct a new conjugacy invariant, which is a cyclic word on the alphabet $\{\ua, \ra, \da, \la\}$. This invariant ... More

Dynamics of surface homeomorphisms Topological versions of the Leau-Fatou flower theorem and the stable manifold theoremOct 22 2002The study of the dynamics of a surface homeomorphism in the neighbourhood of an isolated fixed point leads us to the following results. If the fixed point index is greater than 1, a family of attractive and repulsive petals is constructed, generalizing ... More

Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphismsJan 16 2009In 1980, Albert Fathi asked whether the group of area-preserving homeomorphisms of the 2-disc that are the identity near the boundary is a simple group. In this paper, we show that the simplicity of this group is equivalent to the following fragmentation ... More

Optical Gain in Carbon NanotubesNov 28 2010Semiconducting single-wall carbon nanotubes (s-SWNTs) have proved to be promising material for nanophotonics and optoelectronics. Due to the possibility of tuning their direct band gap and controlling excitonic recombinations in the near-infrared wavelength ... More

Reducing the variance in online optimization by transporting past gradientsJun 08 2019Jun 18 2019Most stochastic optimization methods use gradients once before discarding them. While variance reduction methods have shown that reusing past gradients can be beneficial when there is a finite number of datapoints, they do not easily extend to the online ... More

Information matrices and generalizationJun 18 2019This work revisits the use of information criteria to characterize the generalization of deep learning models. In particular, we empirically demonstrate the effectiveness of the Takeuchi information criterion (TIC), an extension of the Akaike information ... More

The Value Function Polytope in Reinforcement LearningJan 31 2019Feb 15 2019We establish geometric and topological properties of the space of value functions in finite state-action Markov decision processes. Our main contribution is the characterization of the nature of its shape: a general polytope (Aigner et al., 2010). To ... More

Optical microcavity with semiconducting single-wall carbon nanotubesOct 25 2010We report studies of optical Fabry-Perot microcavities based on semiconducting single-wall carbon nanotubes with a quality factor of 160. We experimentally demonstrate a huge photoluminescence signal enhancement by a factor of 30 in comparison with the ... More

Light Emission in Silicon from Carbon NanotubesAug 05 2015The use of optics in microelectronic circuits to overcome the limitation of metallic interconnects is more and more considered as a viable solution. Among future silicon compatible materials, carbon nanotubes are promising candidates thanks to their ability ... More

A semi-potential for finite and infinite sequential gamesSep 11 2013Aug 26 2016We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response ... More

Extending Finite Memory Determinacy to Multiplayer GamesJul 12 2016We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player ... More

Extending finite memory determinacy: General techniques and an application to energy parity gamesFeb 29 2016We provide several techniques to extend finite memory determinacy from some restricted class of games played on a finite graph to a larger class. As a particular example, we study energy parity games. First we show that under some general conditions the ... More

Computable Closed Euclidean Subsets with and without Computable PointsOct 13 2006Jun 22 2007The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are `large' in the ... More

Finite choice, convex choice and finding rootsFeb 02 2013Dec 01 2015We investigate choice principles in the Weihrauch lattice for finite sets on the one hand, and convex sets on the other hand. Increasing cardinality and increasing dimension both correspond to increasing Weihrauch degrees. Moreover, we demonstrate that ... More

Equilibria in multi-player multi-outcome infinite sequential gamesJan 14 2014Mar 16 2016We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental approaches: one requires ... More

Feature Unification in TAG Derivation TreesApr 29 2008The derivation trees of a tree adjoining grammar provide a first insight into the sentence semantics, and are thus prime targets for generation systems. We define a formalism, feature-based regular tree grammars, and a translation from feature based tree ... More

Polynomial entropy of Brouwer homeomorphismsDec 05 2017We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving homeomorphisms of ... More

A Semi-Potential for Finite and Infinite Sequential Games (Extended Abstract)Sep 14 2016We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response ... More

Stable states of perturbed Markov chainsAug 21 2015Feb 12 2016Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as the noise fades ... More

A mathematical model for rogue waves using Saint-Venant equations with frictionMay 19 2009We propose to construct a temporary wave on the surface of the ocean, as a particular solution of the Saint-Venant equations with a source term involving the friction, whose shape is expected to mimic a rogue wave.

Influence of the cooling-rate on the glass transition temperature and the structural properties of glassy GeS2: an ab initio molecular dynamics studyMar 15 2007Using density-functional molecular dynamics simulations we analyzed the cooling-rate effects on the physical properties of GeS$_2$ chalcogenide glasses. Liquid samples were cooled linearly in time according to $T(t) = T_0 - \gamma t$ where $\gamma$ is ... More

A semi-potential for finite and infinite sequential gamesSep 11 2013Apr 04 2017We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response ... More

Strong distortion in transformation groupsOct 21 2016Sep 28 2017We discuss boundedness and distortion in transformation groups. We show that the groups $\mathrm{Diff}^r_0(\mathbb{R}^n)$ and $\mathrm{Diff}^r(\mathbb{R}^n)$ have the strong distortion property, whenever $0 \leq r \leq \infty, r \neq n+1$. This implies ... More

Extending Finite Memory Determinacy to Multiplayer GamesFeb 29 2016Dec 31 2016We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player ... More

Weihrauch degrees of finding equilibria in sequential gamesJul 21 2014Jun 28 2015We consider the degrees of non-computability (Weihrauch degrees) of finding winning strategies (or more generally, Nash equilibria) in infinite sequential games with certain winning sets (or more generally, outcome sets). In particular, we show that as ... More

Conformational Control of Exciton-Polariton Physics in Metal - Poly(9,9-dioctylfluorene) - Metal CavitiesSep 05 2018Sep 07 2018Control is exerted over the exciton-polariton physics in metal - Poly(9,9-dioctyl fluorene) - metal microcavities via conformational changes to the polymer backbone. Using thin-film samples containing increasing fractions of $\beta$-phase chain segments, ... More

Connected Choice and the Brouwer Fixed Point TheoremJun 21 2012We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the ... More

Barcodes and area-preserving homeomorphismsOct 07 2018In this paper we use the theory of barcodes as a new tool for studying dynamics of area-preserving homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of a surface depends continuously on the diffeomorphism, and furthermore define ... More

The Complexity of Graph-Based Reductions for Reachability in Markov Decision ProcessesOct 22 2017Feb 24 2018We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most the same value ... More

Pseudo-rotations of the open annulusJun 02 2005In this paper, we study pseudo-rotations of the open annulus, \emph{i.e.} conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular that, for ... More

Fixed point sets of isotopies on surfacesOct 03 2016We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in mind, we prove ... More

Towards a dynamical interpretation of Hamiltonian spectral invariants on surfacesFeb 12 2015Inspired by Le Calvez' theory of transverse foliations for dynamical systems of surfaces, we introduce a dynamical invariant, denoted by N, for Hamiltonians of any surface other than the sphere. When the surface is the plane or is closed and aspherical, ... More

Transport of cosmic-ray protons in intermittent heliospheric turbulence: model and simulationsJan 04 2014The transport of charged energetic particles in the presence of strong intermittent heliospheric turbulence is computationally analyzed based on known properties of the interplanetary magnetic field and solar wind plasma at 1 Astronomical Unit (AU). The ... More

Analysis of Small-scale Magnetic Flux Ropes Covering the Whole Ulysses MissionMay 02 2019Small-scale magnetic flux ropes, in the solar wind, have been studied for decades via the approach of both simulation and observation. Statistical analysis utilizing various in-situ spacecraft measurements is the main observational approach. In this study, ... More

Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitionsJul 29 2016Aug 21 2016The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic ... More

Construction of curious minimal uniquely ergodic homeomorphisms on manifolds: the Denjoy-Rees techniqueMay 16 2006Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve Rees construction, allowing to start with any homeomorphism ... More

Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladderJul 27 2011Oct 10 2011The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and ... More

Magnetic responses of randomly depleted spin laddersJul 25 2013Sep 27 2013The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of ... More

A Geometric Perspective on Optimal Representations for Reinforcement LearningJan 31 2019This paper proposes a new approach to representation learning based on geometric properties of the space of value functions. We study a two-part approximation of the value function: a nonlinear map from states to vectors, or representation, followed by ... More

Solar energetic particle propagation in wave turbulence and the possibility of wave generationFeb 06 2019A complete theory for the complex interaction between solar energetic particles and the turbulent interplanetary magnetic field remains elusive. In this work we aim to contribute towards such a theory by modelling the propagation of solar energetic particle ... More

Extending finite-memory determinacy by Boolean combination of winning conditionsAug 17 2018Oct 04 2018We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM strategies suffice ... More

Projective transformations of rotation setsNov 10 2017We give a new proof and extend a result of J. Kwapisz: whenever a set C is realized as the rotation set of some torus homeomorphism, the image of C under certain projective transformations is also realized as a rotations set.

Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifoldsJul 21 2008We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational ... More

A Geometric Perspective on Optimal Representations for Reinforcement LearningJan 31 2019Jun 26 2019We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary ... More

Long time behavior in locally activated random walksNov 24 2016We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient: emergence of a non-Gaussian ... More

An Existence Theorem of Nash Equilibrium in Coq and IsabelleSep 07 2017Nash equilibrium (NE) is a central concept in game theory. Here we prove formally a published theorem on existence of an NE in two proof assistants, Coq and Isabelle: starting from a game with finitely many outcomes, one may derive a game by rewriting ... More

Class-conditional embeddings for music source separationNov 07 2018Isolating individual instruments in a musical mixture has a myriad of potential applications, and seems imminently achievable given the levels of performance reached by recent deep learning methods. While most musical source separation techniques learn ... More

Pseudo-rotations of the closed annulus : variation on a theorem of J. KwapiszSep 30 2003Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove ... More

Minkowski gamesSep 22 2016We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded, and the ... More

Minkowski gamesSep 22 2016Nov 25 2016We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded, and the ... More

Denjoy constructions for fibred homeomorphisms of the torusJul 30 2007We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincar\'e-like classification for this class of maps of Jaeger-Stark, we demonstrate that transitive but non-minimal ... More

SDR - half-baked or well done?Nov 06 2018In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS_eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their ... More

On the existence of weak subgame perfect equilibriaDec 05 2016Oct 05 2017We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We focus on the ... More

Deep clustering: Discriminative embeddings for segmentation and separationAug 18 2015We address the problem of acoustic source separation in a deep learning framework we call "deep clustering." Rather than directly estimating signals or masking functions, we train a deep network to produce spectrogram embeddings that are discriminative ... More

Scaling of Information in TurbulenceJul 19 2016Sep 29 2016We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to describe the distribution ... More

The geometry of proper quaternion random variablesMay 15 2015Nov 23 2016Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing ... More

On the existence of weak subgame perfect equilibriaDec 05 2016We study multi-player turn-based games played on a directed graph, where the number of players and vertices can be infinite. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him ... More

Acceleration of solar wind particles by traveling interplanetary shocksMay 21 2019The acceleration of thermal solar wind protons at spherical interplanetary shocks driven by coronal mass ejections is investigated. The solar wind velocity distribution is represented using $\kappa$-functions, which are transformed in response to simulated ... More

The geometry of proper quaternion random variablesMay 15 2015Properness of a quaternion random variable is related to the symmetries of its probability density function in $4D$ space. Thus, properness should be defined with respect to the most general isometries in $4D$, i.e. rotations from $SO(4)$. Based on this, ... More

Information Theory to probe Intrapartum Fetal Heart Rate DynamicsNov 29 2017Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of Intrapartum ... More

Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scatteringMar 26 2009In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering ... More

Connected greedy colouring in claw-free graphsMay 04 2018An ordering of the vertices of a graph is \emph{connected} if every vertex (but the first) has a neighbor among its predecessors. The greedy colouring algorithm of a graph with a connected order consists in taking the vertices in order, and assigning ... More

Higher Order Statistsics of Stokes Parameters in a Random Birefringent MediumMay 14 2007Jun 18 2007We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation ... More

Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditionsDec 15 2010We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the ... More

CROSS-MBCR: Exact Minimum Bandwith Coordinated Regenerating CodesJul 03 2012We study the exact and optimal repair of multiple failures in codes for distributed storage. More particularly, we provide an explicit construction of exact minimum bandwidth coordinated regenerating codes (MBCR) for n=d+t,k,d >= k,t >= 1. Our construction ... More

Phasebook and Friends: Leveraging Discrete Representations for Source SeparationOct 02 2018Mar 07 2019Deep learning based speech enhancement and source separation systems have recently reached unprecedented levels of quality, to the point that performance is reaching a new ceiling. Most systems rely on estimating the magnitude of a target source by estimating ... More

A Purely End-to-end System for Multi-speaker Speech RecognitionMay 15 2018Recently, there has been growing interest in multi-speaker speech recognition, where the utterances of multiple speakers are recognized from their mixture. Promising techniques have been proposed for this task, but earlier works have required additional ... More

Universal Sound SeparationMay 08 2019Aug 02 2019Recent deep learning approaches have achieved impressive performance on speech enhancement and separation tasks. However, these approaches have not been investigated for separating mixtures of arbitrary sounds of different types, a task we refer to as ... More