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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

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

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

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

Products of Ordinary Differential Operators by Evaluation and InterpolationApr 14 2008It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than the previously-known ... More

Minimizing Finite Sums with the Stochastic Average GradientSep 10 2013May 11 2016We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, ... 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 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

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

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

Graphs and Path EquilibriaDec 10 2007The quest for optimal/stable paths in graphs has gained attention in a few practical or theoretical areas. To take part in this quest this chapter adopts an equilibrium-oriented approach that is abstract and general: it works with (quasi-arbitrary) arc-labelled ... 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.

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

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

Infinite sequential Nash equilibriumFeb 16 2013May 21 2013In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn. Two ... More

A mathematical model for Tsunami generation using a conservative velocity-pressure hyperbolic systemMay 19 2009By using the Hugoniot curve in detonics as a Riemann invariant of a velocity-pressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant (= 8.678 instead of ... 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

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

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

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

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

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

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

The Value Function Polytope in Reinforcement LearningJan 31 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

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

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

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

Strong distortion in transformation groupsOct 21 2016We 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

Multi-scale metastable dynamics and the asymptotic stationary distribution of perturbed Markov chainsDec 22 2014We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$. We further ... 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

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

Electroabsorption study of index-defined semiconducting carbon nanotubesAug 05 2015Electroabsorption spectroscopy of well-identified index-defined semiconducting carbon nanotubes is reported. The measurement of high definition electroabsorption spectra allows direct indexation with unique nanotube chirality. Results show that at least ... More

Matching Edges in Images ; Application to Face RecognitionMar 22 2006This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in this computation ... More

Conversion/Preference GamesNov 03 2008We introduce the concept of Conversion/Preference Games, or CP games for short. CP games generalize the standard notion of strategic games. First we exemplify the use of CP games. Second we formally introduce and define the CP-games formalism. Then we ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Deep Unfolding: Model-Based Inspiration of Novel Deep ArchitecturesSep 09 2014Nov 20 2014Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of difficulties ... More

Bootstrapping single-channel source separation via unsupervised spatial clustering on stereo mixturesNov 06 2018Separating an audio scene into isolated sources is a fundamental problem in computer audition, analogous to image segmentation in visual scene analysis. Source separation systems based on deep learning are currently the most successful approaches for ... More

Flowability of plane homeomorphismsDec 10 2009Apr 04 2011We describe necessary and sufficient conditions for an orientation preserving fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.

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

Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator - Luttinger liquid - Bose glassMar 30 2011One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart ... 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

Full-Capacity Unitary Recurrent Neural NetworksOct 31 2016Recurrent neural networks are powerful models for processing sequential data, but they are generally plagued by vanishing and exploding gradient problems. Unitary recurrent neural networks (uRNNs), which use unitary recurrence matrices, have recently ... 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

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

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

Cycle-consistency training for end-to-end speech recognitionNov 02 2018This paper presents a method to train end-to-end automatic speech recognition (ASR) models using unpaired data. Although the end-to-end approach can eliminate the need for expert knowledge such as pronunciation dictionaries to build ASR systems, it still ... 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

The $B \to πK$ Puzzle RevisitedSep 21 2017Jan 15 2018For a number of years, there has been a certain inconsistency among the measurements of the branching ratios and CP asymmetries of the four $B \to \pi K$ decays ($B^+ \to \pi^+ K^0$, $B^+ \to \pi^0 K^+$, $B^0 \to \pi^- K^+$, $B^0 \to \pi^0 K^0$). In this ... More

Adaptive band selection snapshot multispectral imaging in the VIS/NIR domainSep 29 2010Hyperspectral imaging has proven its efficiency for target detection applications but the acquisition mode and the data rate are major issues when dealing with real-time detection applications. It can be useful to use snapshot spectral imagers able to ... More

Single-Channel Multi-Speaker Separation using Deep ClusteringJul 07 2016Deep clustering is a recently introduced deep learning architecture that uses discriminatively trained embeddings as the basis for clustering. It was recently applied to spectrogram segmentation, resulting in impressive results on speaker-independent ... More

End-to-End Speech Separation with Unfolded Iterative Phase ReconstructionApr 26 2018This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. ... More

Deep Clustering and Conventional Networks for Music Separation: Stronger TogetherNov 18 2016Jun 15 2017Deep clustering is the first method to handle general audio separation scenarios with multiple sources of the same type and an arbitrary number of sources, performing impressively in speaker-independent speech separation tasks. However, little is known ... More

The effects of a kappa-distribution in the heliosheath on the global heliosphere and ENA flux at 1 AUMar 17 2008We investigate heliosheath energetic neutral atom (ENA) fluxes at keV energies, by assuming that the heliosheath proton distribution can be approximated by a kappa-distribution. The choice of the kappa parameter derives from observational data of the ... More

The Wide-field High-resolution Infrared TElescope (WHITE)Feb 05 2008The Wide-field High-resolution Infrared TElescope (WHITE) will be dedicated in the first years of its life to carrying out a few (well focused in terms of science objectives and time) legacy surveys. WHITE would have an angular resolution of ~0.3'' homogeneous ... More

Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with LightMay 01 2015Jan 15 2016We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving ... More

Phasebook and Friends: Leveraging Discrete Representations for Source SeparationOct 02 2018Deep 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

The Brownian planeApr 26 2012We introduce and study the random non-compact metric space called the Brownian plane, which is obtained as the scaling limit of the uniform infinite planar quadrangulation. Alternatively, the Brownian plane is identified as the Gromov-Hausdorff tangent ... More

The harmonic measure of balls in random treesApr 26 2013Mar 31 2014We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius n centered at the root, we prove that, although the size of the boundary is of order n, most of the harmonic measure is supported on a boundary ... More

First-passage percolation and local modifications of distances in random triangulationsNov 13 2015We study local modifications of the graph distance in large random triangulations. Our main results show that, in large scales, the modified distance behaves like a deterministic constant $\mathbf{c}~\in~(0,\infty)$ times the usual graph distance. This ... More

On the MIT bag model: self-adjointness and non-relativistic limitJul 09 2016This paper is devoted to the mathematical investigation of the MIT bag model, that is the Dirac operator on a smooth and bounded domain with certain boundary conditions. We prove that the operator is self-adjoint and, when the mass goes to infinity, we ... More

How Useful is Region-based Classification of Remote Sensing Images in a Deep Learning Framework?Sep 22 2016In this paper, we investigate the impact of segmentation algorithms as a preprocessing step for classification of remote sensing images in a deep learning framework. Especially, we address the issue of segmenting the image into regions to be classified ... More

Generative Adversarial Networks for Realistic Synthesis of Hyperspectral SamplesJun 07 2018This work addresses the scarcity of annotated hyperspectral data required to train deep neural networks. Especially, we investigate generative adversarial networks and their application to the synthesis of consistent labeled spectra. By training such ... More

Stochastic description of geometric phase for polarized waves in random mediaJul 11 2012We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an ... More

The hyperanalytic signalJun 24 2010The concept of the analytic signal is extended from the case of a real signal with a complex analytic signal to a complex signal with a hypercomplex analytic signal (which we call a hyperanalytic signal) The hyperanalytic signal may be interpreted as ... More

Time-frequency analysis of bivariate signalsSep 08 2016Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate quantities, ... More

Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson formFeb 06 2008Feb 22 2008We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two complex numbers ... More

Semantic Segmentation of Earth Observation Data Using Multimodal and Multi-scale Deep NetworksSep 22 2016This work investigates the use of deep fully convolutional neural networks (DFCNN) for pixel-wise scene labeling of Earth Observation images. Especially, we train a variant of the SegNet architecture on remote sensing data over an urban area and study ... More

The hull process of the Brownian planeSep 14 2014We study the random metric space called the Brownian plane, which is closely related to the Brownian map and is conjectured to be the universal scaling limit of many discrete random lattices such as the uniform infinite planar triangulation. We obtain ... More

Eigenfunctions and Random Waves in the Benjamini-Schramm limitOct 12 2018We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we present a mathematically ... More

Scaling limits for the peeling process on random mapsDec 17 2014Jul 19 2015We study the scaling limit of the volume and perimeter of the discovered regions in the Markovian explorations known as peeling processes for infinite random planar maps such as the uniform infinite planar triangulation (UIPT) or quadrangulation (UIPQ). ... More

Random recursive triangulations of the disk via fragmentation theoryJun 04 2010Jan 18 2012We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those chords that do ... More

On the usability of deep networks for object-based image analysisSep 22 2016As computer vision before, remote sensing has been radically changed by the introduction of Convolution Neural Networks. Land cover use, object detection and scene understanding in aerial images rely more and more on deep learning to achieve new state-of-the-art ... More

SALZA: Soft algorithmic complexity estimates for clustering and causality inferenceJul 18 2016A complete set of practical estimators for the conditional, simple and joint algorihmic complexities is presented, from which a semi-metric is derived. Also, new directed information estimators are proposed that are applied to causality inference on Directed ... More

Cache policies for cloud-based systems: To keep or not to keepDec 02 2013Apr 24 2014In this paper, we study cache policies for cloud-based caching. Cloud-based caching uses cloud storage services such as Amazon S3 as a cache for data items that would have been recomputed otherwise. Cloud-based caching departs from classical caching: ... More

Identification of Invariant Sensorimotor Structures as a Prerequisite for the Discovery of ObjectsOct 11 2018Perceiving the surrounding environment in terms of objects is useful for any general purpose intelligent agent. In this paper, we investigate a fundamental mechanism making object perception possible, namely the identification of spatio-temporally invariant ... More

A complete framework for linear filtering of bivariate signalsFeb 07 2018A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties ... More

A Cyber Infrastructure for the SKA Telescope ManagerJul 08 2016The Square Kilometre Array Telescope Manager (SKA TM) will be responsible for assisting the SKA Operations and Observation Management, carrying out System diagnosis and collecting Monitoring & Control data from the SKA sub-systems and components. To provide ... More