Results for "Guillaume Valette"

total 2449took 0.13s
Efroymson's approximation theorem for globally subanalytic functionsMay 14 2019Efroymson's approximation theorem asserts that if $f$ is a $\mathcal{C}^0$ semialgebraic mapping on a $\mathcal{C}^\infty$ semialgebraic submanifold $M$ of $\mathbb{R}^n$ and if $\varepsilon:M\to \mathbb{R}$ is a positive continuous semialgebraic function ... More
A generalized Sard theorem on real closed fieldsMar 14 2015We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
$L^1$ cohomology of bounded subanalytic manifoldsNov 09 2010We prove some de Rham theorems on bounded subanalytic submanifolds of $\R^n$ (not necessarily compact). We show that the $L^1$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where the closure of the underlying manifold ... More
Arc-quasianalytic functionsJan 29 2014We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its restriction to every ... More
Geometry of polynomial mappings at infinity via intersection homologyJul 14 2010For given polynomial map $F:\C^2\to\C^2$ with nonvanishing jacobian we associate a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.
Vanishing homologyJan 14 2008In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$ definable ... More
$L^\infty$ cohomology is intersection cohomologyDec 03 2009Jul 06 2012Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.
On the local geometry of definably stratified setsJan 18 2017We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially ... More
Whitney stratifications and the continuity of local Lipschitz Killing curvaturesJul 05 2015We prove that local Lipschitz Killing curvatures of definable sets in a polynomially bounded o-minimal structure are continuous along strata of Whitney stratifications and locally Lipschitz if the stratifications are (w)- regular.
Flat currents on definable pseudomanifoldsOct 05 2016We show that the cohomology of flat currents on definable pseudomanifolds in polynomially bounded o-minimal structures is isomorphic to its intersection cohomology in the top perversity.
Le problème de Kadison-Singer (The Kadison-Singer problem)Sep 20 2014In 1959, R.V. Kadison and I.M. Singer asked whether each pure state of the algebra of bounded diagonal operators on $\ell^2$, admits a unique state extension to $B(\ell^2)$. The positive answer was given in June 2013 by A. Marcus, D. Spielman and N. Srivastava, ... More
On a singular variety associated to a polynomial mappingDec 28 2012In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping $F : \C^2 \to \C^2$ with nonvanishing jacobian a variety whose homology or intersection homology ... More
A New Large N Expansion for General Matrix-Tensor ModelsSep 21 2017Apr 21 2019We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a half-integer associated ... More
A New Large N Expansion for General Matrix-Tensor ModelsSep 21 2017We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a half-integer associated ... More
On 1-cocycles induced by a positive definite function on a locally compact abelian groupMar 18 2013For $\varphi$ a normalized positive definite function on a locally compact abelian group $G$, we consider on the one hand the unitary representation $\pi_\varphi$ associated to $\varphi$ by the GNS construction, on the other hand the probability measure ... More
Locally compact groups with every isometric action bounded or properMay 02 2017A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine isometric actions ... More
On equivariant embeddings of generalized Baumslag-Solitar groupsDec 30 2012Let G be a group acting cocompactly without inversion on a tree X, with all vertex and edge stabilizers isomorphic to the same free abelian group Z^n. We prove that G has the Haagerup Property if and only if G is weakly amenable, and we give a necessary ... More
Toward an Anthropocentric Approach for Hybrid Control Architectures: Case of a Furniture FactoryDec 14 2018Typology of goods and services' consumption has changed. In order to adapt to this change, it is relevant for a company to turn toward new ways of production and management. Slowly, the concept of industry 4.0 starts to set up in manufacturing companies. ... More
Melonic TurbulenceOct 03 2018We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized perturbations ... More
More on the New Large $D$ Limit of Matrix ModelsOct 19 2017In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases of complex ... More
L^2-Betti numbers and Plancherel measureJul 01 2013We compute $L^2$-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the ... More
Isometric group actions on Hilbert spaces: structure of orbitsApr 03 2006Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.
Unbounded symmetric operators in $K$-homology and the Baum-Connes ConjectureDec 18 2004Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac operator on the ... More
K-homology and K-theory for the lamplighter groups of finite groupsOct 10 2016Oct 15 2016Let $F$ be a finite group. We consider the lamplighter group $L=F\wr\mathbb{Z}$ over $F$. We prove that $L$ has a classifying space for proper actions $\underline{E} L$ which is a complex of dimension two. We use this to give an explicit proof of the ... More
The Euclidean distortion of the lamplighter groupMay 31 2007We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion ${\rm O}(\sqrt{\log n})$. This matches the lower bound proved by Lee, Naor and Peres in \cite{LeeNaoPer}, answering a question posed in that paper. Thus ... More
Comparison of two different extinction laws with Hipparcos observationsMay 04 1998Interstellar absorption in the galactic plane is highly variable from one direction to another. In this paper colour excesses and distances from a new open cluster sample are used to investigate the spatial distribution of the interstellar extinction. ... More
Non-simplifying Graph Rewriting TerminationFeb 26 2013So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly with trees. ... More
A Lefschetz duality intersection homologyDec 13 2010Apr 20 2011We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption and is a generalization ... More
Higgs algebra of curves and loop crystalsMay 20 2010We define the Higgs algebra $\mathcal{H}_\P1$ of the projective line, as a convolution algebra of constructible functions on the global nilpotent cone $\underline{\Lambda}_\P1$, a lagrangian substack of the Higgs bundle $T^*\Coh_\P1$, where $\Coh_\P1$ ... More
A geometric Schur-Weyl duality for quotients of affine Hecke algebrasJan 28 2008Mar 19 2008After establishing a geometric Schur-Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts have nice ideals ... More
A molecular density functional theory to study solvation in waterAug 28 2014A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation functions. Those functions ... More
Bounds on the Principal Frequency of the $p$-LaplacianApr 18 2013Oct 01 2014This paper is concerned with the lower bounds for the principal frequency of the $p$-Laplacian on $n$-dimensional Euclidean domains. In particular, we extend the classical results involving the inner radius of a domain and the first eigenvalue of the ... More
On a characterization of ordered pivotal samplingNov 23 2012When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. Deville and Tille proposed in 2004 a general algorithm to perform balanced sampling, named the cube method. In this paper, we are interested ... More
High-energy factorization and evolution with improved kinematicsSep 02 2011The high-energy factorization and the associated B-JIMWLK or BK evolution equations are presented, using the example of DIS structure functions. The necessity of taking gluon saturation into account is discussed, and also the various approximations underlying ... More
Matricial model for the free multiplicative convolutionFeb 21 2014This paper investigates homomorphisms \`a la Bercovici-Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with measures on the space of Hermitian matrices and on the unitary group. The ... More
Espace des twisteurs d'une variété quaternionique Kähler généraliséeJan 22 2014Jan 15 2016To give an almost quaternionic structure on a 4n-manifold $M$ is equivalent to give its bundle of twistors $Z(Q)\longrightarrow M$. When $Q$ is invariant under a torsion free connection, $Z(Q) $ can be provided with an almost complex structure $ \mathbb ... More
Pseudodifferential calculus on manifolds with fibred corners : the groupoid of phi-calculusOct 24 2013This paper is concerned with pseudodifferential calculus on manifolds with fibred corners. Following work of Connes, Monthubert, Skandalis and Androulidakis, we associate to every manifold with fibred corners a longitudinally smooth groupoid which algebraic ... More
Free Convolution Operators and Free Hall TransformApr 05 2013Jul 15 2013We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free convolution. It also ... More
Universality of QCD traveling-waves with running coupling beyond leading logarithmic accuracyJun 04 2008We discuss the solutions of QCD evolution equations with saturation in the high energy limit. We present a general argument showing that, in the running coupling case, the Next-to-Leading-Logarithmic (NLL) and higher order terms are irrelevant for the ... More
Asymptotics of QCD traveling waves with fluctuations and running coupling effectsAug 27 2007Aug 27 2008Extending independently the Balitsky-Kovchegov (BK) equation to running coupling or to fluctuation effects due to Pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper we study the ... More
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial timeSep 15 2010In this paper we study planar polynomial differential systems of this form: dX/dt=A(X, Y), dY/dt= B(X, Y), where A,B belongs to Z[X, Y], degA \leq d, degB \leq d, and the height of A and B is smaller than H. A lot of properties of planar polynomial differential ... More
Gamma-ray absorption in massive X-ray binariesSep 21 2005Jan 30 2006Gamma-ray emission in the TeV range has been detected by HESS from two X-ray binaries: PSR B1259-63 and LS 5039. In both, the early-type star provides large numbers of target photons for pair-production with TeV gamma-rays. This results in a modulation ... More
Existence condition of strong stationary times for continuous time Markov chains on discrete graphsJul 06 2016Oct 13 2016We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some equivalent condition ... More
Empirical risk minimization is optimal for the convex aggregation problemDec 16 2013Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over $\operatorname {conv}(F)$. ... More
Performances of the NA48 Liquid Krypton calorimeterDec 05 2000The NA48 experiments aims at a precise measurement of direct CP violation in the neutral Kaon system. This puts stringent requirements on the electromagnetic calorimeter used to detect photons of average energy 25 GeV. The choice of NA48 is a quasi homogeneous ... More
Maximal inequality for high-dimensional cubesFeb 25 2009Aug 31 2009We present lower estimates for the best constant appearing in the weak $(1,1)$ maximal inequality in the space $(\R^n,\|\cdot\|_{\iy})$. We show that this constant grows to infinity faster than $(\log n)^{1-o(1)}$ when $n$ tends to infinity. To this end, ... More
Systolic geometry and regularization techniqueJun 25 2015The aim of this text is to present the concept of systole of a compact riemannian manifold and to give an overview of systolic geometry. I will also present the "regularization technique", which leads to major results in systolic geometry. I will detail ... More
Structures conformes asymptotiquement platesOct 14 2008In the first part of this article we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive ... More
Bornes effectives des fonctions d'approximation des solutions formelles d'équations binomialesJan 11 2013The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the Weierstrass Preparation ... More
Veech groups of flat surfaces with polesJun 12 2016Dec 21 2017Flat surfaces that correspond to meromorphic $1$-forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify groups that appear as Veech groups of translation surfaces with poles. ... More
Thurston's cataclysms for Anosov representationsJan 29 2013Apr 30 2013Given an Anosov representation $\rho \colon \pi_1(S) \to \PSL_{n}(\mathbb{R})$ and a maximal geodesic lamination $\lambda$ in a surface $S$, we construct shear deformations along the leaves of the geodesic lamination $\lambda$ endowed with a certain flag ... More
An alternative scaling solution for high-energy QCD saturation with running couplingMar 14 2008A new type of approximate scaling compatible with the Balitsky-Kovchegov equation with running coupling is found, which is different from the previously known running coupling geometric scaling. The corresponding asymptotic traveling wave solution is ... More
Veech groups of flat surfaces with polesJun 12 2016Flat surfaces that correspond to meromorphic $1$-forms or meromorphic quadratic differentials with poles of order no smaller than two are surfaces of infinite area. Therefore, we cannot normalize the area and have to consider the whole action of $GL^{+}(2,\mathbb{R})$ ... More
Gamma-ray binaries: pulsars in disguise ?May 11 2006LS 5039 and LSI +61 303 are unique amongst high-mass X-ray binaries (HMXB) for their spatially-resolved radio emission and their counterpart at >GeV gamma-ray energies, canonically attributed to non-thermal particles in an accretion-powered relativistic ... More
Thin discs, thick discs and transition zonesJun 13 2002Accretion onto a compact object must occur through a disc when the material has some initial angular momentum. Thin discs and the thicker low radiative efficiency accretion flows are solutions to this problem that have been widely studied and applied. ... More
Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''Oct 29 2010In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain ... More
Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard modelSep 25 2009May 20 2010We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define ... More
Multi-component power spectra estimation method for multi-detector observations of the Cosmic Microwave BackgroundNov 13 2003We present a new method for multi-component power spectra estimation in multi-frequency observations of the CMB. Our method is based on matching a model to the cross and auto power spectra of observed maps. All the component power spectra are estimated, ... More
Approximation of a Maximum-Submodular-Coverage problem involving spectral functions, with application to Experimental DesignJul 23 2010Dec 05 2011We study a family of combinatorial optimization problems defined by a parameter $p\in[0,1]$, which involves spectral functions applied to positive semidefinite matrices, and has some application in the theory of optimal experimental design. This family ... More
About the algebraic closure of the field of power series in several variables in characteristic zeroMar 08 2013Mar 27 2015We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the ... More
A short proof of a symmetry identity for the $(q,μ,ν)$-deformed Binomial distributionApr 16 2014We give a short and elementary proof of a $(q, \mu, \nu)$-deformed Binomial distribution identity arising in the study of the $(q, \mu, \nu)$-Boson process and the $(q, \mu, \nu)$-TASEP. This identity found by Corwin in [4] was a key technical step to ... More
Improving the kinematics for low-x QCD evolution equations in coordinate spaceJan 01 2014High-energy evolution equations, such as the BFKL, BK or JIMWLK equations, aim at resumming the high-energy (next-to-)leading logarithms appearing in QCD perturbative series. However, the standard derivations of those equations are performed in a strict ... More
Gamma-ray binaries and related systemsJul 26 2013Sep 05 2013After initial claims and a long hiatus, it is now established that several binary stars emit high (0.1-100 GeV) and very high energy (>100 GeV) gamma rays. A new class has emerged called 'gamma-ray binaries', since most of their radiated power is emitted ... More
Principal frequency of the $p$-Laplacian and the inradius of Euclidean domainsOct 04 2014We study the lower bounds for the principal frequency of the $p$-Laplacian on $N$-dimensional Euclidean domains. For $p>N$, we obtain a lower bound for the first eigenvalue of the $p$-Laplacian in terms of its inradius, without any assumptions on the ... More
The asymptotic number of $12..d$-Avoiding Words with $r$ occurrences of each letter $1,2, ..., n$Dec 18 2014Dec 22 2014Following Ekhad and Zeilberger (The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Dec 5 2014; see also arXiv:1412.2035), we study the asymptotics for large $n$ of the number $A_{d,r}(n)$ of words of length $rn$ having $r$ letters $i$ for ... More
Lojasiewicz inequality over the ring of power series in two variablesJan 11 2013We prove a Lojasiewicz type inequality for a system of polynomial equations with coefficients in the ring of formal power series in two variables. This result is an effective version of the Strong Artin Approximation Theorem. From this result we deduce ... More
Real zeros and size of Rankin-Selberg L-functions in the level aspectFeb 23 2005In this paper, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg L-functions. One of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving ... More
Series de Poincare motiviques geometrique et arithmetique d'un germe d'hypersurface irreductible quasi-ordinaireFeb 10 2005Sep 23 2005We give here a description of the motivic Poincare series in case of irreducible quasi-ordinary hypersurfaces in all dimension. We give an explicit formula in a particular case. Finally, for such singularities, we give a constructive proof of a result ... More
A new combinatorial identity for unicellular maps, via a direct bijective approachJun 25 2010A unicellular map, or one-face map, is a graph embedded in an orientable surface such that its complement is a topological disk. In this paper, we give a new viewpoint to the structure of these objects, by describing a decomposition of any unicellular ... More
Simultaneous approximation of a real number by all conjugates of an algebraic numberJun 07 2007Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree n, and 2) by ... More
Hybrid inverse problems and internal functionalsOct 21 2011This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when they combine high ... More
Simultaneous adaptation to the margin and to complexity in classificationSep 29 2005Oct 19 2007We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and ... More
Topological protection of perturbed edge statesSep 02 2017Aug 14 2018This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a large class ... More
Local topological algebraicity with algebraic coefficients of analytic sets or functionsJun 19 2017May 14 2018We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.
Differential forms and smoothness of quotients by reductive groupsNov 02 2000In this paper we give smoothness criterions for a good quotient Y of a smooth variety X by a reductive group G. Our results partially answer a question raised by J. Fogarty in the case where G is a finite group. They also give a converse to a theorem ... More
Superlevel sets and nodal extrema of Laplace-Beltrami eigenfunctionsSep 24 2014We estimate the volume of superlevel sets of Laplace-Beltrami eigenfunctions on a compact Riemannian manifold. The proof uses the Green's function representation and the Bathtub principle. As an application, we obtain upper bounds on the distribution ... More
Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagationAug 21 2014Apr 01 2015Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence ... More
A formal approach for correct-by-construction system substitutionApr 29 2014May 07 2014The substitution of a system with another one may occur in several situations like system adaptation, system failure management, system resilience, system reconfiguration, etc. It consists in replacing a running system by another one when given conditions ... More
Fast polynomial evaluation and compositionJul 22 2013Jul 26 2013The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as H\"orner, divide and conquer and new ones can be added easily. Notably, a new scheme is introduced ... More
Integrability of weight modules of degree 1Jul 06 2011The aim of this article is to find all weight modules of degree 1 of a simple complex Lie algebra that integrate to a continuous representation of a simply-connected real Lie group on some Hilbert space.
The physical mechanisms that initiate and drive solar eruptionsSep 27 2013Solar eruptions are due to a sudden destabilization of force-free coronal magnetic fields. But the detailed mechanisms which can bring the corona towards an eruptive stage, then trigger and drive the eruption, and finally make it explosive, are not fully ... More
Veech groups of flat surfaces with polesJun 12 2016Oct 12 2016Flat surfaces that correspond to meromorphic $1$-forms or meromorphic quadratic differentials with poles of order no smaller than two are surfaces of infinite area. Therefore, we cannot normalize the area and have to consider the whole action of $GL^{+}(2,\mathbb{R})$ ... More
DIM light on Black Hole X-ray TransientsSep 05 2005The current model for the outburst of stellar-mass black holes X-ray binaries is the disk instability model (DIM). An overview of this model and a discussion of its theoretical and observational challenges are given.
A first step phenomenology for the statistics of non-equilibrium fluctuationsApr 16 2009Jan 30 2012The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical potential leads to ... More
Structures de Weyl ALFNov 12 2010In this paper, we introduce the notions of ALF Weyl connection and of associated mass, and we prouve the positive mass theorem for the ALF Weyl structures.
The amplification method in the context of $GL(n)$ automorphic formsFeb 15 2015Feb 23 2015In \cite{SiVe2} and \cite{BlMa1}, the authors proved the existence of a so-called higher rank amplifier and in \cite{HoRiRo2}, the authors described an explicit version of a $GL(3)$ amplifier. This article provides, for $n\geq 4$, a totally explicit $GL(n)$ ... More
Optimal rates of aggregation in classification under low noise assumptionMar 18 2006Dec 04 2007In the same spirit as Tsybakov (2003), we define the optimality of an aggregation procedure in the problem of classification. Using an aggregate with exponential weights, we obtain an optimal rate of convex aggregation for the hinge risk under the margin ... More
Symplectic and Hamiltonian properties of holomorphic coadjoint orbitsJan 20 2011This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant K\"ahlerian structure. These coadjoint orbits ... More
Higgs bundles on weighted projective lines and loop crystalsDec 20 2013Jun 28 2015We consider the space of nilpotent Higgs bundles on a weighted projective line, as a global analog of the nilpotent cone. We show that it is pure, compute its dimension, and define geometric correspondences between irreducible components. We prove it ... More
Computing Optimal Designs of multiresponse Experiments reduces to Second-Order Cone ProgrammingDec 30 2009Nov 25 2010Elfving's Theorem is a major result in the theory of optimal experimental design, which gives a geometrical characterization of $c-$optimality. In this paper, we extend this theorem to the case of multiresponse experiments, and we show that when the number ... More
Length functions of Hitchin representationsJun 30 2011Apr 11 2013Given a Hitchin representation $\rho \colon \pi_1(S) \to \PSL_n(\mathbb{R})$, we construct $n$ continuous functions $\ell_i^\rho \colon \mathcal \CH(S) \to \mathbb{R}$ defined on the space of H\"older geodesic currents $\CH(S)$ such that, for a closed, ... More
Gravity dual of N=4 SYM theory with fast moving sourcesMar 05 2009Feb 25 2010A family of wave solutions to the full Einstein equations in AdS_5 geometry is derived. These background solutions give by duality the response of N=4 SYM at strong coupling to an arbitrary distribution of fast moving external sources for the energy-momentum ... More
Binaries, microquasars and GLASTApr 04 2007Radio and X-ray observations of the relativistic jets of microquasars show evidence for the acceleration of particles to very high energies. Signatures of non-thermal processes occurring closer in to the compact object can also be found. In addition, ... More
Lower bounds and aggregation in density estimationMar 18 2006In this paper we prove the optimality of an aggregation procedure. We prove lower bounds for aggregation of model selection type of $M$ density estimators for the Kullback-Leiber divergence (KL), the Hellinger's distance and the $L\_1$-distance. The lower ... More
A Howe-type correspondence for the dual pair (sl(2),sl(n)) in sl(2n)Nov 27 2009Feb 22 2010In this article we prove a Howe correspondence for a family of representations of sl(2n), which was introduced by Benkart, Britten, and Lemire.
Homomorphisms of local algebras in positive characteristicDec 08 2006Jan 07 2013We investigate some properties of regularity of homomorphisms of local algebras over positive characteristic fields. We state a result of monomialization of such a homomorphism between algebras of analytic or algebraic power series. From this we deduce ... More
Cauchy problem for Ultrasound Modulated EITJan 04 2012Ultrasound modulation of electrical or optical properties of materials offers the possibility to devise hybrid imaging techniques that combine the high electrical or optical contrast observed in many settings of interest with the high resolution of ultrasound. ... More
Homogenization with large spatial random potentialSep 05 2008We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We characterize ... More
Maximum Likelihood Estimation for Conditionally Heteroscedastic Models when the Innovation Process is in the Domain of Attraction of a Stable LawDec 28 2012We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only suppose that ... More