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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.

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.

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

$L^1$ 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

$L^\infty$ 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.

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

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.

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

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

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

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

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

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

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

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

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

Property (T), finite-dimensional representations, and generic representationsNov 13 2017Let $G$ be a discrete group with property (T). It is a standard fact that, in a unitary representation of $G$ on a Hilbert space $\mathcal{H}$, almost invariant vectors are close to invariant vectors, in a quantitative way. We begin by showing that, if ... 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

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

Logarithmic mathematical morphology: a new framework adaptive to illumination changesJun 08 2018Nov 26 2018A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics of acquisition ... More

Gamma-ray emission from binaries in contextJul 03 2015More than a dozen binary systems are now established as sources of variable, high energy (HE, 0.1-100 GeV) gamma rays. Five are also established sources of very high energy (VHE, >100 GeV) gamma rays. The mechanisms behind gamma-ray emission in binaries ... 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.

Theoreme d'approximation cylindrique dans le cas des anneaux analytiquesFeb 20 2003Oct 02 2003This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

Continuous bulk and interface description of topological insulatorsAug 23 2018We analyze continuous partial differential models of topological insulators in the form of systems of Dirac equations. We describe the bulk and interface topological properties of the materials by means of indices of Fredholm operators constructed from ... More

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

The structure of unicellular maps, and a connection between maps of positive genus and planar labelled treesApr 03 2008Mar 05 2009A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of fixed genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the case of labelled ... More

Feuilletage lisse de $S^5$ par surfaces complexesMar 23 2010In 2002 Meersseman-Verjovsky [2] constructed a smooth, codimension-one, foliation on 5-sphere by complex surfaces with two compact leaves. The aim of this note is to improve their construction in order to give a smooth foliation on 5-sphere by complex ... More

On the number of saddle connections in translation surfaces with polesMar 22 2016Oct 12 2016Translation surfaces with poles correspond to meromorphic differentials on compact Riemann surfaces. They appear in compactifications of strata of the moduli space of Abelian differentials and in the study of stability conditions. Such structures have ... 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

Higgs boson measurements at the LHCNov 26 2018Measurements of the Higgs boson production and decay performed at the Large Hadron Collider by the ATLAS and CMS experiments are reviewed. These measurements are based on proton-proton collision data at $\sqrt{s}$=~13~TeV, corresponding to integrated ... More

Modular bootstrap agrees with path integral in the large moduli limitMay 24 2018Based on the rigorous path integral formulation of Liouville Conformal Field Theory initiated by David-Kupiainen-Rhodes-Vargas on the Riemann sphere and David-Rhodes-Vargas on the torus of modulus $\tau$, we give the exact asymptotic behaviour of the ... More

LARNN: Linear Attention Recurrent Neural NetworkAug 16 2018The Linear Attention Recurrent Neural Network (LARNN) is a recurrent attention module derived from the Long Short-Term Memory (LSTM) cell and ideas from the consciousness Recurrent Neural Network (RNN). Yes, it LARNNs. The LARNN uses attention on its ... More

A quantitative fourth moment theorem in free probability theoryMar 26 2018Mar 29 2018A quantitative "fourth moment theorem" is provided for any self-adjoint element in a homogeneous Wigner chaos: the Wasserstein distance is controlled by the distance from the fourth moment to two. The proof uses the free counterpart of the Stein discrepancy. ... More

Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributionsAug 22 2017The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $\sigma^{\gamma^*}_{T}$ and $\sigma^{\gamma^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. ... More

The James construction and $π_4(\mathbb{S}^3)$ in homotopy type theoryOct 27 2017In the first part of this paper we present a formalization in Agda of the James construction in homotopy type theory. We include several fragments of code to show what the Agda code looks like, and we explain several techniques that we used in the formalization. ... More

Chamber structure of modular curves $X_{1}(N)$Oct 23 2017Feb 04 2019Modular curves $X_{1}(N)$ parametrize elliptic curves with a point of order $N$. They can be identified with connected components of projectivized strata $\mathbb{P}\mathcal{H}(a,-a)$ of meromorphic differentials. As strata of meromorphic differentials, ... More

The Fyodorov-Bouchaud formula and Liouville conformal field theoryOct 18 2017Apr 30 2018In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of (sub-critical) Gaussian multiplicative chaos (GMC) associated to the Gaussian free field (GFF) on the unit circle. In this paper we ... More

On the interior motive of certain Shimura varieties : the case of Picard varietiesMay 09 2017The aim of this article is the construction of the interior motive of a Picard variety. Those are Shimura varieties of PEL type. Our result is an application of the strategy developed by Wildeshaus to construct a Hecke-invariant motive whose realizations ... More

Prior knowledge and Markov parameters of linear time-invariant modelsJun 27 2016In many practical cases, the engineer has access to prior knowledge like rough values of the DC-gain or the main time constant of the system. In order to improve the accuracy of subspace-based identification techniques using the model Markov parameters, ... More

Conjectures about the structure of strong- and weak-coupling expansions of a few ground-state observables in the Lieb-Liniger and Yang-Gaudin modelsJul 09 2019In this paper, we apply experimental number theory to two integrable quantum models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi gas with contact interactions. We identify patterns in weak- and strong-coupling series expansions ... More

Hybrid inverse problems and redundant systems of partial differential equationsOct 01 2012Nov 23 2013Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step that is not considered ... 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

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

Approximation diophantienne dans les corps de series en plusieurs variablesMay 31 2005Sep 23 2005We give here a result of diophantine approximation between $\O_N$, the ring of power series in several variables, and the completion of the valuation ring that dominates $\O_N$ for the $\m$-adic topology. We deduce from this that the Artin function of ... 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

Optimal oracle inequality for aggregation of classifiers under low noise conditionMar 22 2006We consider the problem of optimality, in a minimax sense, and adaptivity to the margin and to regularity in binary classification. We prove an oracle inequality, under the margin assumption (low noise condition), satisfied by an aggregation procedure ... More

About the algebraic closure of the field of power series in several variables in characteristic zeroMar 08 2013Mar 07 2017We 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

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

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

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

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

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

Existence condition of strong stationary times for continuous time Markov chains on discrete graphsJul 06 2016Feb 15 2017We 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

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.

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

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

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

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

Distribution of short sums of classical Kloosterman sums of prime powers moduliJul 03 2019Corentin Perret-Gentil proved, under some very general conditions, that short sums of $\ell$-adic trace functions over finite fields of varying center converges in law to a Gaussian random variable or vector. The main inputs are P.~Deligne's equidistribution ... More

Wolf-Keller theorem for Neumann eigenvaluesJul 27 2010The classical Szego-Weinberger inequality states that among bounded planar domains of given area, the first nonzero Neumann eigenvalue is maximized by a disk. Recently, it was shown by Girouard, Nadirashvili and Polterovich that, for simply connected ... 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.

Counting saddle connections in flat surfaces with poles of higher orderJun 12 2016Dec 06 2017Flat surfaces that correspond to $k$-differentials on compact Riemann surfaces are of finite area provided there is no pole of order $k$ or higher. We denote by \textit{flat surfaces with poles of higher order} those surfaces with flat structures defined ... 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

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

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

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

Convergence to SPDEs in Stratonovich formSep 05 2008We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to ... 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

A recombination algorithm for the decomposition of multivariate rational functionsNov 03 2010In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study the complexity ... More

Nearly Optimal Algorithms for the Decomposition of Multivariate Rational Functions and the Extended Lüroth's TheoremApr 29 2010The extended L\"uroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)$ is equal to $\KK(f)$. In this paper ... More

Counting saddle connections in flat surfaces with poles of higher orderJun 12 2016Oct 08 2016Flat surfaces that correspond to $k$-differentials on compact Riemann surfaces are of finite area provided there is no pole of order $k$ or higher. We denote by \textit{flat surfaces with poles of higher order} those surfaces with flat structures defined ... More

The gamma-ray binaries LS 5039, LS I +61 303 and PSR B1259-63Aug 12 2006Three binaries are now established sources of emission at very high energies (>1e11 eV). They are composed of a massive star and a compact object. The emission can be due to the interaction of the relativistic wind from a young ms pulsar with the stellar ... More