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Iterated Gilbert Mosaics and Poisson Tropical Plane CurvesOct 26 2016We propose an iterated version of the Gilbert model, which results in a sequence of random mosaics of the plane. We prove that under appropriate scaling, this sequence of mosaics converges to that obtained by a classical Poisson line process with explicit ... More

On Association Cells in Random Heterogeneous NetworksOct 04 2013Characterizing user to access point (AP) association strategies in heterogeneous cellular networks (HetNets) is critical for their performance analysis, as it directly influences the load across the network. In this letter, we introduce and analyze a ... More

Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive DisplacementsDec 22 2010This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in $\R^n$ give rise to one daughter point, the location of which is obtained by adding a random vector ... More

Poisson Hail on a Hot GroundMay 10 2011We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACS) of the Euclidean space. These RACS arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling ... More

The radial spanning tree of a Poisson point processMar 01 2007We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments to analyze ... More

Spatial Birth-Death Wireless NetworksApr 26 2016Dec 12 2016We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an interacting particle ... More

Stationary flows and uniqueness of invariant measuresFeb 13 2007In this short paper, we consider a quadruple $(\Omega, \AA, \theta, \mu)$,where $\AA$ is a $\sigma$-algebra of subsets of $\Omega$, and $\theta$ is a measurable bijection from $\Omega$ into itself that preserves the measure $\mu$. For each $B \in \AA$, ... More

Spatial Birth-Death Wireless NetworksApr 26 2016May 02 2016We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an interacting particle ... More

A Stochastic Geometry Framework for Analyzing Pairwise-Cooperative Cellular NetworksMay 27 2013Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance, especially for cell-edge users. In this work, we use stochastic geometry to analyze cooperation models where the positions of Base Stations ... More

Coverage by Pairwise Base Station Cooperation under Adaptive Geometric PoliciesNov 21 2013We study a cooperation model where the positions of base stations follow a Poisson point process distribution and where Voronoi cells define the planar areas associated with them. For the service of each user, either one or two base stations are involved. ... More

On the Effect of Shadowing Correlation on Wireless Network PerformanceDec 04 2017We propose and analyze a new shadowing field model meant to capture spatial correlations. The interference field associated with this new model is compared to that of the widely used independent shadowing model. Independent shadowing over links is adopted ... More

Moments and tails in monotone-separable stochastic networksMay 14 2004A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was first introduced to derive the stability region for stochastic networks with ... More

Gibbsian Method for the Self-Optimization of Cellular NetworksJul 16 2012Aug 08 2012In this work, we propose and analyze a class of distributed algorithms performing the joint optimization of radio resources in heterogeneous cellular networks made of a juxtaposition of macro and small cells. Within this context, it is essential to use ... More

Generating Functionals of Random Packing Point Processes: From Hard-Core to Carrier SensingFeb 01 2012Apr 22 2012In this paper we study the generating functionals of several random packing processes: the classical Mat\'ern hard-core model; its extensions, the $k$-Mat\'ern models and the $\infty$-Mat\'ern model, which is an example of random sequential packing process. ... More

Zeros of random tropical polynomials, random polytopes and stick-breakingMar 30 2014For $i = 0, 1, \ldots, n$, let $C_i$ be independent and identically distributed random variables with distribution $F$ with support $(0,\infty)$. The number of zeros of the random tropical polynomials $\mathcal{T}f_n(x) = \min_{i=1,\ldots,n}(C_i + ix)$ ... More

Stochastic Geometry based Medium Access Games in Mobile Ad hoc NetworksDec 16 2011Jan 04 2012This paper studies the performance of Mobile Ad hoc Networks (MANETs) when the nodes, that form a Poisson point process, selfishly choose their Medium Access Probability (MAP). We consider goodput and delay as the performance metric that each node is ... More

Interference Networks with Point-to-Point CodesFeb 14 2011The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable rate regions ... More

Delay Comparison of Delivery and Coding Policies in Data ClustersJun 07 2017Jun 09 2017A key function of cloud infrastructure is to store and deliver diverse files, e.g., scientific datasets, social network information, videos, etc. In such systems, for the purpose of fast and reliable delivery, files are divided into chunks, replicated ... More

Scaling Laws for Ergodic Spectral Efficiency in MIMO Poisson NetworksAug 22 2016In this paper, we examine the benefits of multiple antenna communication in random wireless networks, the topology of which is modeled by stochastic geometry. The setting is that of the Poisson bipolar model introduced in [1], which is a natural model ... More

Stability and Metastability of Traffic Dynamics in Uplink Random Access NetworksJun 11 2019We characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson point process ... More

Community Detection on Euclidean Random GraphsJun 29 2017Apr 11 2018We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point process of ... More

On Spatial Point Processes with Uniform Births and Deaths by Random ConnectionAug 29 2014This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration ... More

A 3-D Spatial Model for In-building Wireless Networks with Correlated ShadowingMar 23 2016Consider orthogonal planes in the 3-D space representing floors and walls in a large building. These planes divide the space into rooms where a wireless infrastructure is deployed. This paper is focused on the analysis of the correlated shadowing field ... More

A Unified Asymptotic Analysis of Area Spectral Efficiency in Ultradense Cellular NetworksDec 20 2017Apr 11 2018This paper studies the asymptotic properties of average area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: (1) interference ... More

Performance-Oriented Association in Large Cellular Networks with Technology DiversityMar 22 2016The development of mobile virtual network operators, where multiple wireless technologies (e.g. 3G and 4G) or operators with non-overlapping bandwidths are pooled and shared is expected to provide enhanced service with broader coverage, without incurring ... More

Renewal Population Dynamics and their Eternal Family TreesMar 21 2018Based on a simple object, an i.i.d. sequence of positive integer-valued random variables, $\{a_n\}_{n\in \mathbb{Z}}$, we introduce and study two random structures and their connections. First, a population dynamics, in which each individual is born at ... More

Adaptive Spatial Aloha, Fairness and Stochastic GeometryMar 06 2013This work aims at combining adaptive protocol design, utility maximization and stochastic geometry. We focus on a spatial adaptation of Aloha within the framework of ad hoc networks. We consider quasi-static networks in which mobiles learn the local topology ... More

A Tractable Approach to Coverage and Rate in Cellular NetworksSep 02 2010Feb 21 2011Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, ... More

Series Expansion for Interference in Wireless NetworksJan 20 2011The spatial correlations in transmitter node locations introduced by common multiple access protocols makes the analysis of interference, outage, and other related metrics in a wireless network extremely difficult. Most works therefore assume that nodes ... More

Spectral Efficiency Scaling Laws in Dense Random Wireless Networks with Multiple Receive AntennasOct 28 2014This paper considers large random wireless networks where transmit-and-receive node pairs communicate within a certain range while sharing a common spectrum. By modeling the spatial locations of nodes based on stochastic geometry, analytical expressions ... More

Optimal Paths on the Space-Time SINR Random GraphNov 19 2009We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast to previous studies on the SINR graphs, we consider both a space and a ... More

Analysis of Data Harvesting by Unmanned Aerial VehiclesFeb 17 2019This paper explores an emerging wireless architecture based on Unmanned Aerial Vehicles (UAVs), i.e., drones. We consider a network where UAVs at fixed altitude harvest data from Internet-of-Things (IoT) devices on the ground. In such a system, the UAVs' ... More

Directional Cell Search Delay Analysis for Cellular Networks with Static UsersSep 04 2017Cell search is the process for a user to detect its neighboring base stations (BSs) and make a cell selection decision. Due to the importance of beamforming gain in millimeter wave (mmWave) and massive MIMO cellular networks, the directional cell search ... More

End-to-End Optimization of High Throughput DNA SequencingAug 04 2015At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The statistical properties ... More

Modeling and Analyzing the Coexistence of Wi-Fi and LTE in Unlicensed SpectrumOct 05 2015Feb 19 2016We leverage stochastic geometry to characterize key performance metrics for neighboring Wi-Fi and LTE networks in unlicensed spectrum. Our analysis focuses on a single unlicensed frequency band, where the locations for the Wi-Fi access points (APs) and ... More

Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular NetworksMar 11 2011Dec 23 2012Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well ... More

Design and Analysis of Initial Access in Millimeter Wave Cellular NetworksSep 19 2016Initial access is the process which allows a mobile user to first connect to a cellular network. It consists of two main steps: cell search (CS) on the downlink and random access (RA) on the uplink. Millimeter wave (mmWave) cellular systems typically ... More

Design and Analysis of Initial Access in Millimeter Wave Cellular NetworksSep 19 2016Mar 24 2017Initial access is the process which allows a mobile user to first connect to a cellular network. It consists of two main steps: cell search (CS) on the downlink and random access (RA) on the uplink. Millimeter wave (mmWave) cellular systems typically ... More

Lightweight and Optimized Sound Source Localization and Tracking Methods for Open and Closed Microphone Array ConfigurationsDec 01 2018Human-robot interaction in natural settings requires filtering out the different sources of sounds from the environment. Such ability usually involves the use of microphone arrays to localize, track and separate sound sources online. Multi-microphone ... More

Decomposition of the Diagonal Action of S_n on the Coinvariant Space of S_n x S_nJun 27 2004The purpose of this paper is to give an explicit description of the irreducible decomposition of the multigraded S_n-module of coinvariants of S_n x S_n. Many of the results presented can be extended to analogous questions for other finite reflection ... More

Globular Cluster Formation in MergersJun 01 2006Mergers of gas-rich galaxies lead to gravitationally driven increases in gas pressure that can trigger intense bursts of star and cluster formation. Although star formation itself is clustered, most newborn stellar aggregates are unbound associations ... More

Young Globular ClustersJun 29 1999Star formation in starbursts appears to be biased toward compact clusters, with up to 20% of all stars formed in them. Observations with HST show that many of these clusters have luminosities (-9 > Mv > -16), UBVI colors, and half-light radii (R_eff = ... More

Analyticity of the entropy for some random walksSep 27 2010Dec 13 2010We consider non-degenerate, finitely supported random walks on a free group. We show that the entropy and the linear drift vary analytically with th eprobability of constant support.

The reach of a future Linear Collider after the g-2 resultApr 11 2001Combining the cosmological requirement on dark matter with the recent BNL g-2 measurement it is argued that, within the mSUGRA framework, the preferred region for SUSY mass parameters falls well inside the area covered by the future linear colliders under ... More

Scenarios for ILC in 2010Jul 25 2007Assuming that first significant results from LHC become available, this presentation assumes 4 different scenarios and discuss the implications for ILC

A Riemann-Roch Theorem for dg AlgebrasApr 02 2010Nov 19 2012Given a smooth proper dg-algebra $A$, a perfect dg $A$-module $M$, and an endomorphism $f$ of $M$, we define the Hochschild class of the pair $(M,f)$ with values in the Hochschild homology of $A$. Our main result is a Riemann-Roch type formula involving ... More

Constraints on quark energy loss from Drell-Yan dataJan 09 2002Feb 20 2002A leading-order analysis of E866/NuSea and NA3 Drell-Yan data in nuclei is carried out. At Fermilab energy, the large uncertainties in the amount of sea quark shadowing prohibit clarifying the origin of the nuclear dependence observed experimentally. ... More

QCD calculations of thermal photon and dilepton productionSep 06 2002In this talk, I review new developments of QCD calculations of photon and dilepton production rates in a Quark-Gluon plasma. All the rates are now known up to $O(\alpha_s)$ both for photons and dileptons, thanks to the resummation of multiple scatterings. ... More

A new approach for the vertical part of the contour in thermal field theoriesJan 11 1999A lot of work has been devoted in the past to understand the role of vertical branch of the time path in thermal field theories, and in particular to see how to deal with it in the real-time formalism. Unlike what is commonly believed, I emphasize on ... More

Photons, dileptons and hard thermal loopsMay 20 1997The production rate of soft real photons or soft lepton pairs by a hot QCD plasma is dominated by strong collinear divergences. As a consequence, it appears that the effective theory based on the resummation of hard thermal loops fails to handle properly ... More

Crosstalk between nanotube devices: contact and channel effectsJan 31 2006At reduced dimensionality, Coulomb interactions play a crucial role in determining device properties. While such interactions within the same carbon nanotube have been shown to have unexpected properties, device integration and multi-nanotube devices ... More

Multi-spectral piston sensor for co-phasing giant segmented mirrors and multi-aperture interferometric arraysAug 27 2009This paper presents the optical design of a multi-spectral piston sensor suitable to co-phasing giant segmented mirrors equipping the Future Extremely Large Telescopes (ELTs). The general theory of the sensor is described in detail and numerical simulations ... More

Computing extinction maps of star nulling interferometersFeb 14 2008Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase ... More

Fully achromatic nulling interferometer (FANI) for high SNR exoplanet characterizationAug 29 2015Space-borne nulling interferometers have long been considered as the best option for searching and characterizing extra-solar planets located in the habitable zone of their parent stars. Solutions for achieving deep starlight extinction are now numerous ... More

Can violations of Bell's inequalities be considere as the final proof of quantum physics ?Oct 09 2013Nowadays, it is commonly admitted that the experimental violation of Bell's inequalities that was successfully demonstrated in the last decades by many experimenters, are indeed the ultimate proof of quantum physics and of its ability to describe the ... More

Simple Fourier optics formalism for high angular resolution systems and nulling interferometryApr 24 2009Aug 27 2009In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging ... More

Signal-to-noise ratio of phase sensing telescope interferometersFeb 14 2008This paper is the third part of a trilogy dealing with the principles, performance and limitations of what I named "Telescope-Interferometers" (TIs). The basic idea consists in transforming one telescope into a Wavefront Error (WFE) sensing device. This ... More

Supersymetrie et mathematiquesMay 16 1994May 17 1994Nous presentons une introduction aux concepts de la supersymetrie par l'intermediaire de trois exemples: (i) Mecanique quantique supersymetrique, (ii) Superalgebres de Lie, (iii) Superconnexions de Quillen. Les points communs a toutes ces notions sont ... More

Indecomposable injective modules of finite Malcev rank over local commutative ringsAug 29 2011Feb 06 2014It is proven that each indecomposable injective module over a valuation domain $R$ is polyserial if and only if each maximal immediate extension $\widehat{R}$ of $R$ is of finite rank over the completion $\widetilde{R}$ of $R$ in the $R$-topology. In ... More

Local rings of bounded module type are almost maximal valuation ringsSep 28 2004Oct 04 2005It is shown that every commutative local ring of bounded module type is an almost maximal valuation ring.

(Generalized) Post Correspondence Problem and semi-Thue systemsFeb 06 2008Nov 12 2008Let PCP(k) denote the Post Correspondence Problem for k input pairs of strings. Let ACCESSIBILITY(k) denote the the word problem for k-rule semi-Thue systems. In 1980, Claus showed that if ACCESSIBILITY(k) is undecidable then PCP(k + 4) is also undecidable. ... More

A generating algorithm for ribbon tableaux and spin polynomialsNov 27 2006We describe a general algorithm for generating various families of ribbon tableaux and computing their spin polynomials. This algorithm is derived from a new matricial coding. An advantage of this new notation lies in the fact that it permits one to generate ... More

Commutative rings whose finitely generated ideals are quasi-flatNov 03 2016A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutative rings for which each ideal is quasi-flat (resp. quasi-projective) is ... More

Weak dimension of FP-injective modules over chain ringsJan 06 2016It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2.

Gaussian trivial ring extensions and fqp-ringsJul 08 2015Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be B{\'e}zout is also studied, but a response ... More

Commutative rings whose cotorsion modules are pure-injectiveJun 09 2015Mar 24 2016Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1 R (G, M) = 0 for any flat R-module G. It is well known that each pure-injective left R-module is cotorsion, but the converse does not hold: for instance, if ... More

A Morse complex on manifolds with boundaryMar 26 2010May 31 2010Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or relative to the boundary) ... More

Parabolic groups acting on one-dimensional compact spacesJan 07 2004May 29 2007Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite ... More

Tempered subanalytic topology on algebraic varietiesMar 02 2017On a smooth algebraic variety over $\mathbb{C}$, we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at infinity over these sites and study their relations with the sheaf of ... More

New Formulas and Conjectures for the Nabla OperatorMay 29 2011The operator nabla, introduced by Garsia and the author, plays a crucial role in many aspect of the study of diagonal harmonics. Besides giving several new formulas involving this operator, we show how one is lead to representation theoretic explanations ... More

Multivariate Diagonal Coinvariant Spaces for Complex Reflection GroupsMay 22 2011Nov 02 2011For finite complex reflexion groups, we consider the graded $W$-modules of diagonally harmonic polynomials in $r$ sets of variables, and show that associated Hilbert series may be described in a global manner, independent of the value of $r$.

Eternal Family Trees and Dynamics on Unimodular Random GraphsAug 21 2016Jun 22 2017This paper is centered on covariant dynamics on unimodular random graphs and random networks, namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as vertex-shifts here. The ... More

Merger-Induced StarburstsFeb 04 2005Extragalactic starbursts induced by gravitational interactions can now be studied from z = ~0 to ~2. The evidence that mergers of gas-rich galaxies tend to trigger galaxy-wide starbursts is strong, both statistically and in individual cases of major disk-disk ... More

Evolution of Globular Clusters Formed in MergersJun 20 2001Globular clusters formed in galactic mergers (e.g., The Antennae) can now be studied at different stages of their evolution. In young merger remnants (e.g., NGC 7252) these "second-generation" globulars appear by the hundreds as young halo clusters of ... More

Formation of Globular Clusters in Merging GalaxiesDec 10 2002Collisions and mergers of gas-rich galaxies trigger bursts of star and cluster formation. Of the thousands of clusters typically formed during a major merger, only the most massive and compact survive for Gigayears as globular clusters (GCs). In <~1 Gyr ... More

Present and future constraints on top EW couplingsMar 12 2014Various BSM models predict large deviations of the top electroweak couplings. Many examples will be given emphasizing the need for precise and model independent measurements of these couplings. Here I address the question of compatibility between theoretical ... More

Quenching of photon and pion spectra at intermediate RHIC energyJun 13 2007Single prompt photon and pion spectra in p-p and Au-Au collisions at intermediate RHIC energy, s^1/2 = 62.4 GeV, are computed at large transverse momentum in perturbative QCD. Next-to-leading order calculations in p-p scattering are first presented. The ... More

Tomography of nuclear matter: Comparing Drell-Yan with deep inelastic scattering dataOct 07 2002We set tight constraints on the energy loss of hard quarks in nuclear matter from NA3 Drell-Yan measurements. Our estimate then allows for the description of HERMES preliminary deep inelastic scattering data on hadron production.

Quenching of hadron and photon spectra in heavy-ion collisions from RHIC to LHCSep 14 2011The generic features of parton energy loss effects on the quenching of single hadron spectra in heavy-ion collisions are discussed, paying attention to the expected differences from RHIC to LHC. The need for precise baseline measurements in p-Pb collisions ... More

Hard pion and prompt photon at RHIC, from single to double inclusive productionJan 10 2006Single pion and prompt photon large transverse momentum spectra in p-p and Au-Au collisions are computed in perturbative QCD at RHIC energy, s^1/2 = 200 GeV. Next-to-leading order calculations are discussed and compared with p-p scattering data. Subsequently, ... More

Phase-shifting technique for improving the imaging capacity of sparse-aperture optical interferometersMay 12 2011Jun 24 2011In this paper, we describe the principle of a multi-aperture interferometer that uses a phase-shifting technique and is suitable for quick, snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A few advantages ... More

An analysis of stellar interferometers as wavefront sensorsOct 25 2005This paper presents the basic principle and theoretical relationships of an original method allowing to retrieve the Wavefront Errors (WFE) of a ground or space-borne telescope when combining its main pupil with a second, decentered reference optical ... More

Kinetic theory of a longitudinally expanding systemFeb 01 2016We use kinetic theory in order to study the role of quantum fluctuations in the isotropization of the pressure tensor in a system subject to fast longitudinal expansion, such as the matter produced in the early stages of a heavy ion collision.

About Symmetries in PhysicsDec 16 1997The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of a lecture presented ... More

On the holomorphic factorization for superconformal fieldsSep 22 1992For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as functionals ... More

Luminosity Profiles of Resolved Young Massive ClustersApr 20 2004Young massive clusters (YMCs) differ markedly from old globular clusters in featuring extended, rather than tidally truncated, envelopes. Their projected- luminosity profiles are well fit by Elson-Fall-Freeman (EFF) models with core radii of 0.3 pc < ... More

Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unityJan 08 2007Apr 17 2007Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling's bijection between ribbon tableaux and ribbon rigged ... More

Duality of subanalytic setsJun 10 1997Jun 11 1997We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise to a kind of ... More

Dynamo theoriesMar 15 2019Aug 29 2019These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids ... More

Anisotropy, inhomogeneity and inertial range scalings in turbulent convectionJan 25 2006This paper provides a detailed study of scale-by-scale budgets in turbulent Rayleigh-B\'enard convection and aims at testing the applicability of Kolmogorov (1941) and Bolgiano (1959) theories for this flow. Particular emphasis is laid on anisotropic ... More

Dynamo theoriesMar 15 2019These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids ... More

Localized Quantum StatesOct 29 2013Apr 11 2014Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large ... More

Value at 2 of the L-function of an elliptic curveFeb 09 2006We study the special value at 2 of L-functions of modular forms of weight 2 on congruence subgroups of the modular group. We prove an explicit version of Beilinson's theorem for the modular curve X_1(N). When N is prime, we deduce that the target space ... More

A Note on the Chas-Sullivan productMar 16 2009Feb 11 2010We give a finite dimensional approach to the Chas-Sullivan product on the free loop space of a manifold, orientable or not.

On the Wiener-Khinchin transform of functions that behave as approximate power-laws. Applications to fluid turbulenceSep 13 2019As we all know, the Fourier transform is continuous in the weak sense of tempered distribution; this ensures the weak stability of Fourier pairs. This article investigates a stronger form of stability of the pair of homogeneous profiles $(|x|^{-\alpha}, ... More

Rang maximal pour $T_P^n$Jun 12 1995Jun 20 1995In this paper, I compute the last non-trivial term of the minimal free resolution of the homogeneous ideal of $s$ points of $P^n$ in sufficiently general position, for any $s$, showing that this term is the one conjectured by the Minimal Resolution Conjecture ... More

Interlacing Property of Zeros of Eigenvectors of Schrödinger Operators on TreesApr 08 2009May 16 2014We prove an analogue for trees of Courant's theorem on the interlacing property of zeros of eigenfunctions of a Schr\"{o}dinger operator. Let $\Gamma$ be a finite tree, and $\mathcal A$ a Schr\"{o}dinger operator on $\Gamma$. If the eigenvectors of $\mathcal ... More

On open normal subgroups of parahoricsFeb 24 2005Feb 25 2005Let $F$ be a local complete field with discrete valuation, and let $G$ be a quasi-split group over $F$ which splits over some unramified extension of $F$. Let $P$ be a parahoric subgroup of the group $G(F)$ of $F$-points of $G$; t he open normal pro-nilpotent ... More

Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structuresMay 16 2005Feb 19 2008This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic ... More

Localization of injective modules over arithmetical ringsJan 12 2009It is proved that localizations of injective $R$-modules of finite Goldie dimension are injective if $R$ is an arithmetical ring satisfying the following condition: for every maximal ideal $P$, $R_P$ is either coherent or not semicoherent. If, in addition, ... More