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Stability of stationary solutions for nonintegrable peakon equationsJun 08 2013The Camassa-Holm equation with linear dispersion was originally derived as an asymptotic equation in shallow water wave theory. Among its many interesting mathematical properties, which include complete integrability, perhaps the most striking is the ... More

Spectral stability of periodic NLS and CGL solutionsMay 08 2007We consider periodic traveling wave solutions to the focusing nonlinear Schrodinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg-Landau equation (CGL). In particular, we show that these periodic traveling ... More

When is negativity not a problem for the ultra-discrete limit?Sep 13 2006The `ultra-discrete limit' has provided a link between integrable difference equations and cellular automata displaying soliton like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic difference equations ... More

Transforming opacity verification to nonblocking verification in modular systemsApr 12 2019We consider the verification of current-state and K-step opacity for systems modeled as interacting non-deterministic finite-state automata. We describe a new methodology for compositional opacity verification that employs abstraction, in the form of ... More

Stability of closed solutions to the VFE hierarchy with application to the Hirota equationJun 28 2016The Vortex Filament Equation (VFE) is part of an integrable hierarchy of filament equations. Several equations part of this hierarchy have been derived to describe vortex filaments in various situations. Inspired by these results, we develop a general ... More

Constructing Integrable Third Order Systems:The Gambier ApproachMay 12 1997We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. ... More

Stability analysis for combustion fronts traveling in hydraulically resistant porous mediaNov 11 2014We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our results suggest ... More

Automated Synthesis of Secure Platform MappingsMay 10 2017Nov 23 2018System development often involves decisions about how a high-level design is to be implemented using primitives from a low-level platform. Certain decisions, however, may introduce undesirable behavior into the resulting implementation, possibly leading ... More

Combustion waves in hydraulically resistant porous media in a special parameter regimeOct 15 2015May 11 2016In this paper we study the stability of fronts in a reduction of a well-known PDE system that is used to model the combustion in hydraulically resistant porous media. More precisely, we consider the original PDE system under the assumption that one of ... More

Matrix integral solutions to the discrete KP hierarchy and its Pfaffianized versionJan 20 2016Matrix integrals used in random matrix theory for the study of eigenvalues of Hermitian ensembles have been shown to provide $\tau$-functions for several hierarchies of integrable equations. In this article, we extend this relation by showing that such ... More

Point Symmetries of Generalized Toda Field TheoriesApr 12 2000A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point symmetries ... More

Linearisable Mappings and the Low-Growth CriterionApr 06 2001We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion ... More

Symmetries of Discrete Dynamical Systems Involving Two SpeciesDec 16 1998The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The equations can ... More

Dilogarithme Quantique et 6j-Symboles CycliquesFeb 26 2002Let $\mathcal{W}_N$ be a quantized Borel subalgebra of $U_q(sl(2,\mc))$, specialized at a primitive root of unity $\omega = \exp(2i\pi/N)$ of odd order $N >1$. One shows that the $6j$-symbols of cyclic representations of $\mathcal{W}_N$ are representations ... More

On prediction with the LASSO when the design is not incoherentMar 23 2012Jun 23 2014The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence index, the LASSO ... More

Ten scenarios from early radiation to late time acceleration with a minimally coupled dark energyJan 28 2015We consider General Relativity with matter, radiation and a minimally coupled dark energy defined by an equation of state w. Using dynamical system method, we find the equilibrium points of such a theory assuming an expanding Universe and a positive dark ... More

N=2 supersymmetric pseudodifferential symbols and super W-algebrasDec 17 1998We study the superconformally covariant pseudodifferential symbols defined on N=2 super Riemann surfaces. This allows us to construct a primary basis for N=2 super W_KP^(n)-algebras and, by reduction, for N=2 super W_n-algebras.

Lecture notes on "Quantum chromodynamics and statistical physics"Oct 23 2014The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant ... More

Towards an explicit expression of the Seiberg-Witten map at all ordersDec 04 2001Sep 26 2002The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative parameter theta ... More

Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theoryNov 15 2014We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic ... More

Abel transformation and algebraic differential formsOct 02 2010We prove in this article that given a linearly concave domain $D$ in the projective space $\Bbb{CP}^{n}$, a 1-dimensional comlex analytic set $V$ in $D$, and a meromorphic 1-form $\phi$ on $V$, $V$ is a subset of an algebraic variety of $\Bbb{CP}^{n}$ ... More

Growth of quotients of groups acting by isometries on Gromov hyperbolic spacesDec 29 2012We show that every non-elementary group $G$ acting properly and cocompactly by isometries on a proper geodesic Gromov hyperbolic space $X$ is growth tight. In other words, the exponential growth rate of $G$ for the geometric (pseudo)-distance induced ... More

Detection and Mitigation of Classes of Attacks in Supervisory Control SystemsJul 13 2018The deployment of control systems with network-connected components has made feedback control systems vulnerable to attacks over the network. This paper considers the problem of intrusion detection and mitigation in supervisory control systems, where ... More

Statistical Curse of the Second Half Rank, Eulerian numbers and Stirling numbersOct 14 2013I describe the occurence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the Statistical Curse of the Second Half Rank problem.

The ECLAIRs telescope onboard the SVOM mission for gamma-ray burst studiesJul 04 2008The X- and gamma-ray telescope ECLAIRs onboard the future mission for gamma-ray burst studies SVOM (Space-based multi-band astronomical Variable Objects Monitor) is foreseen to operate in orbit from 2013 on. ECLAIRs will provide fast and accurate GRB ... More

An Alternating l1 approach to the compressed sensing problemSep 03 2008Sep 23 2009Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined ... More

Relativistic Jets in the RXTE EraSep 07 2004Since the launch of the Rossi X-ray Timing Explorer in 1995 our understanding of jetted outflows has significantly improved. Indeed, relativistic jets are now believed to be a fairly ubiquitous property of accreting compact objects, that are intimately ... More

Minimal vertex covers of random treesNov 15 2004We study minimal vertex covers of trees. Contrarily to the number $N_{vc}(A)$ of minimal vertex covers of the tree $A$, $\log N_{vc}(A)$ is a self-averaging quantity. We show that, for large sizes $n$, $\lim_{n\to +\infty} <\log N_{vc}(A)>_n/n= 0.1033252\pm ... More

Beyond the Standard Model Searches at the LHCJan 04 2007This report presents recent results from studies of Beyond the Standard Model physics at the LHC. A focus is placed on heavy gauge bosons, electroweak symmetry breaking and left-right symmetry.

DG-methods for microlocalizationNov 25 2008For a complex manifold $X$ the ring of microdifferential operators $\E_X$ acts on the microlocalization $\mu hom(F,\O_X)$, for $F$ in the derived category of sheaves on $X$. Kashiwara, Schapira, Ivorra, Waschkies proved, as a byproduct of their new microlocalization ... More

Fonctions critiques et équations aux dérivées partielles sur les variétés Riemanniennes compactesOct 01 2010We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u = f.u^{\frac{n+2}{n-2}}$ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this ... More

Descente de torseurs, gerbes et points rationnels - Descent of torsors, gerbes and rational pointsJan 14 2004Jan 16 2004Let $k$ be a field of characteristic 0 and $G$ a linear algebraic $k$-group. When $G$ is abelian, it is well known that torsors under $G_{X}$ over a $k$-scheme $\pi:X\to \textup{Spec} k$ provide an obstruction to the existence of $k$-rational points on ... More

Estimation of Gaussian mixtures in small sample studies using $l_1$ penalizationJan 29 2009Oct 08 2014Many experiments in medicine and ecology can be conveniently modeled by finite Gaussian mixtures but face the problem of dealing with small data sets. We propose a robust version of the estimator based on self-regression and sparsity promoting penalization ... More

Singularites symplectiquesNov 05 2001Sep 17 2002Soit (V,o) une singularit\'e symplectique isol\'ee de dimension au moins 6 et soit p : $X\longrightarrow V$ l'\'eclatement normalis\'e de o dans V. On suppose que le diviseur $p^{-1}(o)$ est r\'eduit, globalement \`a croisements normaux et qu'il a au ... More

Parametrix techniques and martingale problem for some degenerate Kolmogorov's equationsNov 08 2010We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins (From Probability to Geometry, vol. in honor of J.M Bismut ... More

On a relation between production processes and total cross sectionsJul 11 2013Perturbative QCD is the appropriate tool to describe many important properties of the inclusive observables measured at electron-proton (or ion) colliders, such as the energy dependence of the total cross sections in well-chosen kinematical regions. This ... More

Anyons and lowest Landau level AnyonsDec 13 2007A review on the Anyon model and the lowest Landau level Anyon model is presented.

Weakly convex closed subsets of spaces with bounded nonpositive curvatureJul 08 2005On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.

Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesicJul 13 2009Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical singularities ... More

Systolic volume and minimal entropy of aspherical manifoldsMar 30 2006We establish isosystolic inequalities for a class of manifolds which includes the aspherical manifolds. In particular, we relate the systolic volume of aspherical manifolds first to their minimal entropy, then to the algebraic entropy of their fundamental ... More

Marked length spectrum of magnetized surfacesFeb 20 2005The main result presented here is that the flow associated with a riemannian metric and a non zero magnetic field on a compact oriented surface without boundary, under assumptions of hyperbolic type, cannot have the same length spectrum of topologically ... More

Constraints from growth-rate data on some coupled dark energy models mimicking a $ΛCDM$ expansionMay 05 2016The $\Lambda CDM$ expansion could be mimicked by a dark energy coupled to matter. Then, the equation of state $\bar w$ and coupling $\bar Q$ of this coupled dark energy could not be constrained by observations of the Hubble function alone. Also, in this ... More

On the restricted invertibility problem with an additional orthogonality constraint for random matricesNov 17 2015Dec 04 2015The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address this problem ... More

The analytical solution of the Laplace equation with the Robin boundary conditions on a sphere: Applications to some inverse problemsMar 18 2015Oct 22 2015This paper studies the third boundary problem of the Laplace equation with azimuthal symmetry.Many solutions of the boundary value problems in spherical coordinates are available in the form of infinite series of Legendre polynomials but the evaluation ... More

Multi-epoch study of the gamma-ray emission within the M87 magnetosphere modelNov 07 2014May 28 2015M87 is a nearby radio galaxy that has been detected at energies ranging from radio to very high energy (VHE) gamma-rays. Its proximity and its jet, misaligned from the line of sight allow detailed morphological studies. The imaging atmospheric Cherenkov ... More

Fractional Superspace Formulation of Generalized MechanicsMay 25 1993Jul 23 1993Supersymmetric (pseudo-classical) mechanics has recently been generalized to {\it fractional}\/ supersymmetric mechanics. In such a construction, the action is invariant under fractional supersymmetry transformations, which are the $F^{\,\rm th}$ roots ... More

Fractional Superspace Formulation of Generalized Super-Virasoro AlgebrasMay 26 1992Jun 26 1992We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms ... More

Extended Fractional Supersymmetric Quantum MechanicsMay 25 1993May 25 1993Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,...\,.$ This construction, called fractional supersymmetric quantum mechanics, was realized in ... More

Confined free-electrons in an applied electric field: Discontinuous electron densityDec 22 2004We consider free electrons in rectangular quantum dots, with either hard wall boundary conditions or anharmonic confinement. In both cases, due to finite size effects, a homogeneous electric field applied along one of the rectangular axis is shown to ... More

Deep Neural Networks for Survival Analysis Based on a Multi-Task FrameworkJan 17 2018Survival analysis/time-to-event models are extremely useful as they can help companies predict when a customer will buy a product, churn or default on a loan, and therefore help them improve their ROI. In this paper, we introduce a new method to calculate ... More

L'indice de Maslov dans les $JB^*$-triplesApr 18 2007Jun 16 2009We construct a homotopy invariant index for pathes in the set of invertible tripotents in a JB*-triple that satisfy a Fredholm type condition with respect to a fixed invertible tripotent. That index generalizes the Maslov index in the Fredholm-Lagrangian ... More

Critical functions and elliptic PDE on compact riemannian manifoldsOct 02 2010We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u=f .u^{\frac{n+2}{n-2}} $ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this ... More

On the modified Basis Pursuit reconstruction for Compressed Sensing with partially known supportJun 02 2009Sep 04 2015The goal of this short note is to present a refined analysis of the modified Basis Pursuit ($\ell_1$-minimization) approach to signal recovery in Compressed Sensing with partially known support, as introduced by Vaswani and Lu. The problem is to recover ... More

An easy journey from Galilean to General RelativityNov 23 2015We explain in a very concise way the basic principles that lead from Galilean to General Relativity to make them understandable to students or general audience, even with little knowledge in physics and mathematics.

Martingale problems for some degenerate Kolmogorov equationsApr 02 2014Sep 17 2015We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore uniqueness ... More

Spectral properties of noisy classical and quantum propagatorsJan 15 2003Jun 06 2003We study classical and quantum maps on the torus phase space, in the presence of noise. We focus on the spectral properties of the noisy evolution operator, and prove that for any amount of noise, the quantum spectrum converges to the classical one in ... More

On parton number fluctuationsOct 21 2014Parton evolution with the rapidity essentially is a branching diffusion process. We describe the fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at moderately high energies. We arrive at different functional ... More

Probing short-lived fluctuations in hadrons and nucleiNov 12 2014We develop a picture of dipole-nucleus (namely dilute-dense) and dipole-dipole (dilute-dilute) scattering in the high-energy regime based on the analysis of the fluctuations in the quantum evolution. We emphasize the difference in the nature of the fluctuations ... More

Random Aharonov-Bohm vortices and some exact families of integrals: Part IIIJan 30 2014As a sequel to [1] and [2], I present some recent progress on Bessel integrals $\int_0^{\infty}{\rmd u}\; uK_0(u)^{n}$, $\int_0^{\infty}{\rmd u}\; u^{3}K_0(u)^{n}$, ... where the power of the integration variable is odd and where $n$, the Bessel weight, ... More

Random Aharonov-Bohm vortices and some funny families of integralsFeb 15 2005A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. ... More

C_l interpolation for cosmological parameter estimationOct 27 2003I will briefly present my work on cosmological parameters estimation. Classical methods for parameters estimation involve the exploration of the parameter space on a precalculated grid of cosmological models. Here we try to estimate the cosmological parameters ... More

Fractional Supersymmetry and Quantum MechanicsMay 25 1993Jul 23 1993We present a set of quantum-mechanical Hamiltonians which can be written as the $F^{\,\rm th}$ power of a conserved charge: $H=Q^F$ with $[H,Q]=0$ and $F=2,3,...\, .$ This new construction, which we call {\it fractional}\/ supersymmetric quantum mechanics, ... More

SPECTRA OF YOUNG GALAXIESJan 24 1995Invited review, Ringberg conference on "Galaxies in the Young Universe" (Sept94)

On multifractality and time subordination for continuous functionsApr 11 2008We show that if $Z$ is "homogeneously multifractal" (in a sense we precisely define), then $Z$ is the composition of a monofractal function $g$ with a time subordinator $f$ (i.e. $f$ is the integral of a positive Borel measure supported by $\zu$). When ... More

Baryon-Strangeness Correlations from Hadron/String- and Quark-DynamicsNov 01 2006Baryon-strangeness correlations ($C_{BS}$) are studied with a hadron/string transport approach (UrQMD) and a dynamical quark recombination model (quark molecular dynamics, qMD) for various energies from $E_{lab}=4A$ GeV to $\sqrt{s_{NN}}=200$ GeV. As ... More

Far Field measurement in the focal plane of a lens : a cautionary noteJul 18 2013We study theoretically the accuracy of the method based on the Fourier property of lenses that is commonly used for the far field measurement. We consider a simple optical setup in which the far-field intensity pattern of a light beam passing through ... More

Off equilibrium dynamics in the 3d-XY systemMay 26 2004Jun 03 2004We investigate through Monte Carlo simulations the non-equilibrium behaviour of the three-dimensional XY-model quenched from a high temperature state to its ferromagnetic and critical phases. The two-times autocorrelation and response functions are determined ... More

Psi' to J/Psi Ratio in Diffractive PhotoproductionSep 27 1999We evaluate the Psi' to J/Psi ratio in diffractive photoproduction in a light-cone framework, using charmonium wave functions extracted from non-relativistic potential models. Contrary to current belief, we find that the best estimate for the ratio is ... More

Rescattering Effects in Quarkonium ProductionJun 24 1997Nov 17 1997We study eta_c and J/psi hadroproduction induced by multiple scattering off fixed centres in the target. We determine the minimum number of hard scatterings required and show that additional soft scatterings may be factorized, at the level of the production ... More

Large scale numerical simulations of "ultrametric" long-range depinningJan 26 2004The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for a drastic reduction ... More

B Physics at the Z0 ResonanceDec 19 2000B physics results from e+ e- annihilation at the Z0 resonance are reviewed. A vast program is summarised, including the study of B+, B0d, B0s and b baryon lifetimes, the time dependence of B0d and B0s oscillations, the width difference in the B0s system, ... More

A conjecture concerning optimality of the Karhunen-Loeve basis in nonlinear reconstructionSep 02 2011Sep 16 2011We present a conjecture regarding the expectation of the maxima of $L^2$ norms of sub-vectors of a Gaussian vector; this has application to nonlinear reconstruction.

Poisson (co)homology of truncated polynomial algebras in two variablesMay 30 2008We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such ... More

Bessel Integrals, Periods and Zeta NumbersSep 05 2012Jan 30 2014We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.

Projection on higher Landau levels and non-commutative geometryDec 19 2001Oct 21 2002The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.

White Dwarfs in GALEX SurveyFeb 15 2007We have cross-correlated the 2dF QSO Redshift Survey (2QZ) white dwarf catalog with the GALEX 2nd Data Release and the Sloan Digital Sky Survey (SDSS) data release 5 to obtain ultraviolet photometry (FUV, NUV) for approximately 700 objects and optical ... More

A Diophantine duality applied to the KAM and Nekhoroshev theoremsApr 07 2012Jun 20 2012In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms. As a consequence, we develop a new approach to the perturbation theory for quasi-periodic ... More

Groupes $p$-divisibles avec condition de Pappas-Rapoport et invariants de HasseNov 30 2016We study $p$-divisible groups $G$ endowed with an action of the ring of integers of a finite (possibly ramified) extension of $\mathbb{Q}_p$ over a scheme of characteristic $p$. We suppose moreover that the $p$-divisible group $G$ satisfies the Pappas-Rapoport ... More

Coherence properties of Kerr frequency combsOct 21 2013Nov 29 2013We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of ... More

An elementary approach to the problem of column selection in a rectangular matrixSep 02 2015The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see \cite{BourgainTzafriri:IJM87,Tropp:StudiaMath08,Vershynin:IJM01} for methods ... More

Perturbation bounds on the extremal singular values of a matrix after appending a columnJun 20 2014Dec 16 2014In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal processing, control ... More

From n+1-level atom chains to n-dimensional noisesFeb 04 2004In quantum physics, the state space of a countable chain of (n+1)-level atoms becomes, in the continuous field limit, a Fock space with multiplicity n. In a more functional analytic language, the continuous tensor product space over R of copies of the ... More

The complexity of linear-time temporal logic over the class of ordinalsSep 27 2010Dec 21 2010We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem over the class ... More

Decay of correlations for normally hyperbolic trappingFeb 18 2013Sep 14 2014We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic in directions ... More

Weighted simplicial complex reconstruction from mobile laser scanning using sensor topologyApr 10 2018Jun 11 2018We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our method uses the inherent topology of the MLS sensor to define a spatial adjacency ... More

Sensor-topology based simplicial complex reconstructionFeb 21 2018Apr 09 2018We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our main goal is to produce a reconstruction of a scene that is adapted to the local ... More

On Thouless bandwidth formula in the Hofstadter modelMar 28 2017We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.

The Perron-Frobenius Theorem for Homogeneous, Monotone FunctionsMay 11 2001Aug 18 2003If A is a nonnegative matrix whose associated directed graph is strongly connected, the Perron-Frobenius theorem asserts that A has an eigenvector in the positive cone, (R^+)^n. We associate a directed graph to any homogeneous, monotone function, f: (R^+)^n ... More

An elementary approach to the problem of column selection in a rectangular matrixSep 02 2015Dec 06 2016The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see \cite{BourgainTzafriri:IJM87,Tropp:StudiaMath08,Vershynin:IJM01} for methods ... More

The K-band luminosity function at z=1: a powerful constraint on galaxy formation theoryFeb 18 1998There are two major approaches to modelling galaxy evolution. The traditional view is that the most massive galaxies were assembled early and have evolved with steeply declining star formation rates since a redshift of 2 or higher. According to hierarchical ... 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

Heterogeneous ubiquitous systems in $\mathbb{R}^{d}$ and Hausdorff dimensionMar 21 2005Let $\{x\_n\}\_{n\geq 0}$ be a sequence of $[0,1]^d$, $\{\lambda\_n\} \_{n\geq 0}$ a sequence of positive real numbers converging to 0, and $\delta>1$. Let $\mu$ be a positive Borel measure on $[0,1]^d$, $\rho\in (0,1]$ and $\alpha>0$. Consider the limsup-set ... More

Renewal of singularity sets of statistically self-similar measuresMar 21 2005This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We ... More

A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matricesMay 08 2018We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of an entropy ... More

The orbit method for Poisson ordersNov 15 2017Dec 19 2017A version of Kirillov's orbit method states that the primitive spectrum of a generic quantisation $A$ of a Poisson algebra $Z$ should correspond bijectively to the symplectic leaves of Spec$(Z)$. In this article we consider a Poisson order $A$ over a ... More

A localized Jarnik-Besicovitch TheoremMar 12 2009Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form $\{x\in \mathbb{R}: \delta_x = \delta\}$, where $\delta \geq 1$ and $\delta_x$ is the Diophantine approximation rate of an irrational number ... More

The Minkowski Theorem for Max-plus Convex SetsMay 02 2006We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of $(R\cup\{-\infty\})^n$ can be written as the max-plus convex combination of at most $n+1$ of the extreme points of this subset. We establish ... More

Optimization problem and mean variance hedging on defaultable claimsSep 26 2012We study the pricing and the hedging of claim {\psi} which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade defaultable bond of the ... More

The higher-dimensional Ablowitz-Ladik model: from (non-)integrability and solitary waves to surprising collapse properties and more exotic solutionsJul 08 2009We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schrodinger (NLS) model. We use singularity confinement techniques to suggest that the relevant discretization should not be ... More

Numerical studies of planar closed random walksApr 07 2008Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account ... More