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On the Morse Index of Branched Willmore Spheres in $3$-SpaceMay 14 2019We develop a general method to compute the Morse index of branched Willmore spheres and show that for immersions the Morse index is equal to a certain matrix whose dimension is equal to the number of end of the dual minimal surface. As a corollary, we ... More

Higher Regularity of Weak Limits of Willmore Immersions IIApr 22 2019We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a consequence, out of the twelve families of non-planar minimal surfaces in $\mathbb{R}^3$ ... More

Morse Index of Willmore spheres in $S^3$Mar 30 2016We obtain an upper bound for the Morse index of Willmore spheres $\Sigma\subset S^3$ coming from an immersion of $S^2$. The quantization of Willmore energy shows that there exists an integer $m$ such that $\mathscr{W}(\Sigma)=4\pi m$. Then we show that ... More

On the Morse Index of Critical Points in the Viscosity MethodJun 25 2018We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences of critical points of these approximations satisfying the expected Morse index bounds as in Lazer-Solimini's theory, together ... More

On the Moduli Space of Null Curves in Klein's QuadricMay 13 2019We study the moduli space of null curves in Klein's quartic in the four-dimensional (complex) projective plane using methods developed by Robert Bryant. As a consequence, we show that minimal surfaces with $9$ embedded planar ends do not exist and formulate ... More

Morse Index Estimates of Min-Max Willmore SurfacesAug 23 2018We show that the sum of the Morse indices of the Willmore spheres realising the width of Willmore type sweep-outs is bounded by the number of the parameters of the min-max. As an application, we deduce that among the true Willmore spheres realising the ... More

Computer-assisted proof of the main theorem of 'The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphere'Nov 28 2017Dec 04 2017We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main theorem 4.11 of our paper 'The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphere' (arXiv:1706.01405), ... More

Higher Regularity of Weak Limits of Willmore Immersions IApr 09 2019Apr 23 2019We obtain in arbitrary codimension a removability result on the order of singularity of weak limits and bubbles of Willmore immersions measured by the second residue. This permits to reduce significantly the number of possible bubbling scenarii. As a ... More

The Classification of Branched Willmore Spheres in the $3$-Sphere and the $4$-SphereJun 05 2017Apr 23 2019We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to variational branched Willmore spheres $S^3$ and show that they are inverse stereographic projections of complete minimal surfaces with finite total curvature in $\mathbb{R}^3$ ... More

The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphereJun 05 2017Nov 28 2017We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to true branched Willmore spheres and show that non-completely umbilic variational branched Willmore spheres in $S^3$ are inverse stereographic projections of complete minimal ... More

A Viscosity Method for the Min-Max Construction of Closed GeodesicsNov 14 2015We present a viscosity approach to the min-max construction of closed geodesics on compact Riemannian manifolds of arbitrary dimension. We also construct counter-examples in dimension $1$ and $2$ to the $\varepsilon$-regularity in the convergence procedure. ... More

Higher Regularity of Weak Limits of Willmore Immersions IApr 09 2019We obtain in arbitrary codimension a removability result on the order of singularity of weak limits and bubbles of Willmore immersions measured by the second residue. This permits to reduce significantly the number of possible bubbling scenarii. As a ... More

Computer-Assisted Proof of the Main Theorem of 'The Classification of Branched Willmore Spheres in the $3$-Sphere and the $4$-Sphere'Nov 28 2017Apr 23 2019We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main Theorem 4.11 of our paper 'The Classification of Branched Willmore spheres in the $3$-Sphere and the $4$-Sphere' (arXiv:1706.01405), ... More

Bound states for rapidly oscillating Schrödinger operators in dimension 2Sep 02 2016Oct 18 2016We study the eigenvalues of Schr\"odinger operators on $\mathbb{R}^2$ with rapidly oscillating potential $V(x) = W(x,x/\varepsilon)$, where $W(x,y) \in C^\infty_0(\mathbb{R}^2 \times \mathbb{T}^2)$ satisfies $\int_{\mathbb{T}^2} W(x,y) dy =0$. We show ... More

Global Stability analyses of a cellular model of Hepatitis C Virus infection under treatmentJan 28 2019In this paper, we present the global analysis of a HCV model under therapy. We prove that the solutions with positive initial values are global, positive, bounded and not display periodic orbits. In addition, we show that the model is globally asymptotically ... More

A singular limit in a fractional reaction-diffusion equation with periodic coefficientsApr 26 2018Dec 13 2018We provide an asymptotic analysis of a non-local Fisher-KPP type equation in periodic media and with a non-local stable operator of order $\alpha$ $\in$ (0, 2). We perform a long time-long range scaling in order to prove that the stable state invades ... More

Aerial Drop of Robots and Sensors for Optimal Area CoverageNov 28 2017The problem of rapid optimal coverage through the distribution a team of robots or static sensors via means of aerial drop is the topic of this work. Considering a nonholonomic (fixed-wing) aerial robot that corresponds to the carrier of a set of small ... More

Einstein-Scalar Field System with a cosmological constant on the type I Bianchi space-timeFeb 19 2017In many cases a scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject particularly on type I Bianchi space-time. In this paper, global existence to the coupled Einstein-scalar field ... More

Existence and non-existence of extremizers for certain $k$-plane transform inequalitiesDec 16 2014Nov 07 2016We provide sharp forms of $k$-plane transform inequalities on the $d$-dimensional sphere $\mathbb{S}^d$ and the $d$-dimensional hyperbolic space $\mathbb{H}^d$. In particular, we prove that extremizers do not exist for $\mathbb{H}^d$. This work is a natural ... More

Limit sets of stable Cellular AutomataJan 16 2013We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere steady factor map ... More

Apodized phase mask coronagraphs for arbitrary aperturesDec 26 2012Phase masks coronagraphs can be seen as linear systems that spatially redistribute, in the pupil plane, the energy collected by the telescope. Most of the on-axis light must ideally be rejected outside the aperture to be blocked with a Lyot stop, while ... More

A Rotating Charged Black Hole Solution in f(R) GravityAug 31 2011In the context of f(R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. The new metric is obtained by solving the field equations and we show that the behavior of it is typical ... More

Approximate inference via variational samplingMay 08 2011Oct 14 2013A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model by minimizing ... More

Exposing the Gas Braking Mechanism of the beta Pictoris DiskJan 20 2011Ever since the discovery of the edge-on circumstellar disk around beta Pictoris, a standing question has been why the gas observed against the star in absorption is not rapidly expelled by the strong radiation pressure from the star. A solution to the ... More

Performing Hybrid Recommendation in Intermodal Transportation-the FTMarket System's Recommendation ModuleSep 12 2009Diverse recommendation techniques have been already proposed and encapsulated into several e-business applications, aiming to perform a more accurate evaluation of the existing information and accordingly augment the assistance provided to the users involved. ... More

On the First Law of Thermodynamics for (2+1) Dimensional Charged BTZ Black Hole and Charged de Sitter SpaceJul 16 2007In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional ... More

Traversable Wormholes Construction in (2+1) GravityJul 06 2007Jul 16 2007Wormholes have been always an interesting object in gravity theories. In this paper we make a little review of the principal properties of these objects and the exotic matter they need to exist. Then, we obtain two specific solutions in the formalism ... More

The maximum of the local time of a diffusion process in a drifted Brownian potentialApr 04 2006Nov 18 2015We consider a one-dimensional diffusion process $X$ in a $(-\kappa/2)$-drifted Brownian potential for $\kappa\neq 0$. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from ... More

Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic OscillatorJan 08 2006Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$ ($\Delta\mu_n=\mu_n-\mu_n^0+o(n^{-1/4})$, ... More

T Tauri Multiple SystemsSep 17 2003New high-resolution adaptive optics systems provide an unprecedentedly detailed view of nearby star forming regions. In particular, young nearby T Tauri stars can be probed at much smaller physical scales (a few AU) than possible just a decade ago (several ... More

Aproximacion Discreta de la Relatividad GeneralJun 09 2003Jul 16 2007These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.

Thermodynamics of Charged BTZ Black Holes and Effective String TheoryOct 09 2007In this paper we study the first law of thermodynamics for the (2+1) dimensional charged BTZ black hole considering a pair of thermodinamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the ... More

Systèmes interactifs sensibles aux émotions : architecture logicielleOct 03 2007We propose a software architecture for interactive systems which allows integrating the user's emotion. Emotion can be involved in interaction at several levels. In our application case - ballet dance - emotions is explicitely manipulated by the interactive ... More

Agujeros de Gusano en Gravedad (2+1)Jun 08 2007Jul 16 2007Traversable wormholes are objects that present a lot of interest in the last years because of their geometric features and their relation with exotic matter. In this paper we presnt a review of the principal characteristics of traversable Morris-Thorne ... More

Charm Mixing and Lifetimes at BabarMay 21 2002Preliminary limits on the D^0 mixing parameter y = \Delta \Gamma / 2 \Gamma are obtained using about 57.8 fb^-1 of data collected by BaBar in 2000 and 2001:y = (1.4 \pm 1.0 (stat.) +0.6 -0.7 (syst.))%. y is extracted, provided that CP is conserved, by ... More

The bulk-edge correspondence for continuous honeycomb latticesJan 18 2019We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals $2$ or $-2$, with sign depending on nearby Dirac points and on the magnetic field. We then prove the existence ... More

Bound states for rapidly oscillating Schrödinger operators in dimension 2Sep 02 2016We study the eigenvalues of Schr\"odinger operators on $\mathbb{R}^2$ with rapidly oscillating potential $V(x) = W(x,x/\varepsilon)$, where $W(x,y) \in C^\infty_0(\mathbb{R}^2 \times \mathbb{T}^2)$ satisfies $\int_{\mathbb{T}^2} W(x,y) dy =0$. We show ... More

Thermodynamics of the (2+1)-dimensional Black Hole with non linear Electrodynamics and without Cosmological Constant from the Generalized Uncertainly PrincipleDec 22 2008Jan 23 2009In this paper, we study the thermodynamical properties of the (2+1)dimensional black hole with a non-linear electrodynamics and without cosmological constant using the Generalized Uncertainty Principle (GUP). This approach shows that there is a maximum ... More

Results in Charm Physics from Babar ExperimentJun 04 2004Recent measurements in the charm sector at BaBar are reviewed. The scope of the presentation includes the observation of two new narrow mesons in the D+(s)pi0 and D+(s)pi0gamma final states as well as the measurement of D0-D0bar mixing parameters by means ... More

Involutory Hopf group-coalgebras and flat bundles over 3-manifoldsJun 24 2002Given a group G, we use involutary Hopf G-coalgebras to define a scalar invariant of flat G-bundles over 3-manifolds. When G=1, this invariant equals to the one of 3-manifolds constructed by Kuperberg from involutary Hopf algebras. We give examples which ... More

The bulk-edge correspondence for continuous dislocated systemsOct 24 2018Jan 29 2019We study topological aspects of defect modes for a family of operators $\{\mathscr{P}(t)\}_{t \in [0,2\pi]}$ on $L^2(\mathbb{R})$. $\mathscr{P}(t)$ is a periodic Schr\"odinger operator $P_0$ perturbed by a dislocated potential. This potential is periodic ... More

Pollicott-Ruelle resonances via kinetic Brownian motionJul 13 2016Jul 22 2016The kinetic Brownian motion on the cosphere bundle of a Riemannian manifold $\mathbb{M}$ is a stochastic process that models the geodesic equation perturbed by a random white force of size $\varepsilon$. When $\mathbb{M}$ is a compact negatively curved ... More

Composite Bayesian inferenceDec 24 2015May 03 2016This paper revisits the concept of composite likelihood from the perspective of probabilistic inference, and proposes a generalization called super composite likelihood for sharper inference in multiclass problems. It is argued that, beside providing ... More

Resonances for random highly oscillatory potentialsMar 23 2017We study discrete spectral quantities associated to Schr\"odinger operators of the form $-\Delta_{\mathbb{R}^d}+V_N$, $d$ odd. The potential $V_N$ models a highly disordered crystal; it varies randomly at scale $N^{-1} \ll 1$. We use perturbation analysis ... More

Composite Bayesian inferenceDec 24 2015Apr 17 2019We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This perspective gives ... More

Note de lecture: 'Climat: 15 vérités qui dérangent'Apr 07 2014This is a critical review of the book 'Climat: 15 v\'erit\'es qui d\'erangent', under the scientific supervision of Pr Itsvan Mark\'o, and co-authored by Anne Debeil, Ludovic Delory, Samuel Furfari, Drieu Godefridi, Henri Masson, Lars Myren, and Alain ... More

Expansions of MSO by cardinality relationsOct 30 2013Dec 04 2013We study expansions of the Weak Monadic Second Order theory of (N,<) by cardinality relations, which are predicates R(X1,...,Xn) whose truth value depends only on the cardinality of the sets X1, ...,Xn. We first provide a (definable) criterion for definability ... More

Global existence of solutions to the Einstein-massive scalar field equations with a cosmological constant for a perfect fluid on the flat Robertson-Walker space-timeAug 31 2013In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled Einstein-massive scalar ... More

Area Spectrum of a Rotating Charged Black Hole Solution of Heterotic String TheoryApr 04 2012The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of black holes in string theory. We use the period of motion of an outgoing wave, which is shown to be related to ... More

Best constant and value of extremizers for a k-plane transform inequalityNov 21 2011Jan 11 2012The k-plane transform acting on test functions on R^d satisfies a dilation-invariant L^p to L^q inequality for some exponents p,q. We will explicit some extremizers and the value of the best constant for any value of k and d, solving the limit case of ... More

Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocityMay 16 2007In this short note, we give a link between the regularity of the solution $u$ to the 3D Navier-Stokes equation, and the behavior of the direction of the velocity $u/|u|$. It is shown that the control of $\Div (u/|u|)$ in a suitable $L_t^p(L_x^q)$ norm ... More

Graded quantum groupsDec 17 2003Starting from a Hopf algebra endowed with an action of a group G by Hopf automorphisms, we construct (by a twisted double method) a quasitriangular Hopf G-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular Hopf G-coalgebras ... More

Kirby elements and quantum invariantsDec 17 2003Dec 17 2003We define the notion of a Kirby element of a ribbon category C (not necessarily semisimple). Kirby elements lead to 3-manifolds invariants. We characterize (in terms of the structure maps of some categorical Hopf algebra) a set of Kirby elements of C ... More

Quantitative form of certain k-plane transform inequalitiesMay 15 2012Nov 18 2014Let d > 1 and 0 < k < d. The k-plane transform satisies some Lp to Lq dilation-invariant inequality. In this case the best constant and the extremizers are explicitly known. We give a quantitative form of the inequality with respect to these extremizers, ... More

Area Spectrum of BTZ Black Holes from the Periodicity in Euclidean TimeApr 05 2012Apr 23 2012The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of three dimensional black holes. We use the period of motion of an outgoing wave which is shown to be related to ... More

Dimension des fibres de Springer affines pour les groupesMar 05 2012Sep 03 2014Following Steinberg, we construct an adjoint quotient for the Vinberg semi-group and a section to this quotient. Then, after Ng\^o, we show the existence of a regular centralizer on it and use it to compute the affine Springer fibers for groups.

Entropy Corrections for a Charged Black Hole of String TheoryMar 11 2010Mar 16 2010We study the entropy of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole, originated from the effective action that emerges in the low-energy of string theory, beyond semiclassical approximations. Applying the properties of exact ... More

Entanglement Entropy for the Charged BTZ Black HoleFeb 18 2010Feb 26 2010Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking ... More

Stringy Generalization of the First Law of Thermodynamics for Rotating BTZ Black Hole with a Cosmological Constant as State ParameterOct 31 2007In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to be used at the two ... More

Theta line bundles and the determinant of the Hodge bundleApr 25 1996Nov 14 1996In this note we examine the question of expressing the determinant of the push forward of a symmetric line bundle on an abelian fibration in terms of the pull back of the relative dualizing sheaf via the zero section.

Observation of two narrow mesons in the D+_s pi^0 and D+_s pi^0 gamma final states. Results from BaBar, Belle and CLEONov 15 2003The BaBar experiment has discovered a narrow state, denoted as D*_{sJ}(2317)+, near 2.32 GeV/c^2 in the D+s pi^0 invariant mass distribution from inclusive $e^{+}e^{-}$ interactions at center-of-mass energies near 10.6 GeV. The same experiment has hinted ... More

On numerical approximation schemes for expectation propagationNov 14 2016Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of variational sampling ... More

On a deformation of the nonlinear Schrödinger equationJul 09 2015Aug 20 2015We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm equation. Although ... More

On a Lagrangian reduction and a deformation of completely integrable systemsJan 12 2015Apr 05 2016We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm $H^1$ ... More

Le capo du troupeau des séries de FourierNov 16 2012Jun 10 2013A glimpse at $\sum{{\sin(kx)}\over{k}}$ gives a few lines exposition of Fourier series's quadratic mean convergence for square integrable functions and Dirichlet's convergence theorem of the Fourier serie of a piecewise differentiable function with integrable ... More

Structure preserving noise and dissipation in the Toda latticeApr 10 2018In this paper, we use Flaschka's change of variables of the open Toda lattice and its interpretation in term of the group structure of the LU factorisation as a coadjoint motion on a certain dual of Lie algebra to implement a structure preserving noise ... More

A quantitative version of Hawking radiationOct 08 2015We present a proof of the existence of the Hawking radiation for massive bosons in the Schwarzchild-de Sitter metric. It provides estimates for the rates of decay of the initial quantum state to the Hawking thermal state. The arguments in the proof include ... More

Scattering resonances for highly oscillatory potentialsSep 14 2015Oct 01 2016We study resonances of compactly supported potentials $ V_\varepsilon = W ( x, x/\varepsilon ) $ where $ W : \mathbb{R}^d \times \mathbb{R}^d / ( 2\pi \mathbb{Z}) ^d \to \mathbb{C} $, $ d $ odd. That means that $ V_\varepsilon $ is a sum of a slowly varying ... More

Dynamics of the four kinds of Trapping Horizons and Existence of Hawking RadiationMay 27 2015We work with the notion of apparent/trapping horizons for spherically symmetric, dynamical spacetimes: these are quasi-locally defined, simply based on the behaviour of congruence of light rays. We show that the sign of the dynamical Hayward-Kodama surface ... More

Quarkonium production and polarization in pp collisions with the CMS detectorSep 15 2014The studies of heavy quarkonium inclusive production and polarization at LHC are becoming crucial to solve the puzzle of hadron formation. The results by CMS and the other LHC experiments are compactly presented for the five S-wave states J/Psi, Psi(2S) ... More

Persistence of some additive functionals of Sinai's walkFeb 10 2014Mar 09 2015We are interested in Sinai's walk $(S\_n)\_{n\in\mathbb{N}}$. We prove that the annealed probability that $\sum\_{k=0}^n f(S\_k)$ is strictly positive for all $n\in[1,N]$ is equal to $1/(\log N)^{\frac{3-\sqrt{5}}{2}+o(1)}$, for a large class of functions ... More

Geodesic Structure of the Noncommutative Schwarzschild Anti-de Sitter Black Hole I: Timelike GeodesicsOct 04 2011By considering particles as smeared objects, we investigate the effects of space noncommutativity on the geodesic structure in Schwarzschild-AdS spacetime. By means of a detailed analysis of the corresponding effective potentials for particles, we find ... More

EM algorithm and variants: an informal tutorialMay 07 2011Sep 07 2012The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM variants, suggesting ... More

Réalisation de de Rham des motifs de VoevodskySep 29 2009After reviewing some basic facts about pure and mixed motives, we explain, following Deligne-Goncharov, how to construct a de Rham realisation functor from the category of geometric mixed motives to the category of bifiltered vector spaces.

An Application of the Feferman-Vaught Theorem to Automata and Logics for<br> Words over an Infinite AlphabetJan 16 2008Mar 25 2008We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical characterizations. ... More

Thermodynamical Analogy Between BTZ Black Holes and Effective String TheorySep 26 2007Oct 09 2007In this paper we study the first law of thermodynamics for the (2+1) dimensional BTZ rotating black hole considering a pair of thermodinamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the ... More

Global Stability analysis of a cellular model of Hepatitis C Virus infection under treatmentJan 28 2019May 07 2019In this paper, we present the global analysis of a HCV model under therapy. We prove that the solutions with positive initial values are global, positive, bounded and not display periodic orbits. In addition, we show that the model is globally asymptotically ... More

Realizing the Aerial Robotic Worker for Inspection OperationsMar 08 2017This report overviews a set of recent contributions in the field of path planning that were developed to enable the realization of the autonomous aerial robotic worker for inspection operations. The specific algorithmic contributions address several fundamental ... More

Technical Report: Optimal Surveillance of Dynamic Parades using Teams of Aerial RobotsDec 30 2016This technical report addresses the problem of optimal surveillance of the route followed by a dynamic parade using a team of aerial robots. The dynamic parade is considered to take place within an urban environment, it is discretized and at every iteration, ... More

On massless dyadic forms and no minimal coupling theoremOct 10 2016Oct 12 2016We use the spinor helicity formalism in order to derive the dyadic forms for massless fields of various spins. We also give an iterated form of this approach in case higher spin theories are under study. This reduces calculations at hard and soft scattering ... More

Bound states for rapidly oscillatory Schrödinger operators in dimension 2Sep 02 2016Jan 11 2017We study the eigenvalues of Schr\"odinger operators on $\mathbb{R}^2$ with rapidly oscillatory potential $V(x) = W(x,x/\varepsilon)$, where $W(x,y) \in C^\infty_0(\mathbb{R}^2 \times \mathbb{T}^2)$ satisfies $\int_{\mathbb{T}^2} W(x,y) dy =0$. We show ... More

Estimates of parabolic cylinder functions on the real axisOct 12 2005We estimate simple combination of the parabolic cylinder functions and their derivatives. These estimates are important for the spectral analysis of non-analytically perturbed quantum harmonic oscillator. The estimates are valid in rather complicated ... More

Some properties of the rate function of quenched large deviations for random walk in random environmentFeb 15 2005In this paper, we are interested in some questions of Greven and den Hollander about the rate function $I\_{\eta}^q$ of quenched large deviations for random walk in random environment. By studying the hitting times of RWRE, we prove that in the recurrent ... More

Introduction to Bosonic String TheoryJun 15 2003Jul 16 2007Introductory Notes in Bosonic String Theory and its Canonical Quantization.

Thermodynamic Interpretation of the Field Equations of BTZ Charged Black Hole near the HorizonJun 12 2007Jul 16 2007As is already known, a spacetime horizon acts like a boundary of a thermal system an we can associate with it notions as temperature and entropy. Following the work of M. Akbar, in this paper we will show how it is possible to interpret the field equation ... More

Almost sure asymptotics for a diffusion process in a drifted Brownian potentialNov 02 2005We study a one-dimensional diffusion process in a drifted Brownian potential. We characterize the upper functions of its hitting times in the sense of Paul L\'evy, and determine the lower limits in terms of an iterated logarithm law.

Time Delay in Gravitational Lensing by a Charged Black Hole of String TheorySep 23 2003Jul 16 2007We calculate the time delay between different relativistic images formed by the gravitational lensing produced by the Gibbons-Maeda-Garfinkle-Horowitz-Stromiger (GMGHS) charged black hole of heterotic string theory. Modeling the supermassive central objects ... More

Cohomologie des fibrés en droites sur les compactifications des groupes réductifsMar 11 2003On s'int\'eresse aux compactifications \'equivariantes d'un groupe r\'eductif quelconque, $G$, vu comme espace homog\`ene pour $G \times G$. Pour un rev\^etement fini $\widetilde{G}$ de $G$, les groupes de cohomologie des fibr\'es en droites sur ces compactifications ... More

Characterization of edge states in perturbed honeycomb structuresNov 20 2018This paper is a mathematical analysis of conduction effects at interfaces between insulators. Motivated by work of Haldane-Raghu , we continue the study of a linear PDE initiated in papers of Fefferman-Lee-Thorp-Weinstein. This PDE is induced by a continuous ... More

Cohomologie des fibrés en droites sur les variétés magnifiques de rang minimalJul 28 2005Dec 08 2005The Borel-Weil-Bott theorem describes the cohomology of line bundles over flag varieties. Here, one generalizes this theorem to a wider class of projective varieties : the wonderful varieties of minimal rank.

Hopf group-coalgebrasDec 11 2000We study algebraic properties of Hopf group-coalgebras, recently introduced by Turaev. We show the existence of integrals and traces for such coalgebras, and we generalize the main properties of quasitriangular and ribbon Hopf algebras to the setting ... More

Représentations irréductibles de certaines algèbres d'opérateurs différentielsJan 23 2010For a projective variety $X$ and a line bundle $L$ over $X$, one considers the $L-$twisted global differential operator algebra $\call{D}_L(X)$ which naturally operates on the space of global sections $H^0(X,L)$. In the case where $X$ is the wonderful ... More

Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneitiesJul 20 2018We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau-Lifshitz-Maxwell (LLM) equation, ... More

Probabilities of causation of climate changesNov 30 2017Multiple changes in Earth's climate system have been observed over the past decades. Determining how likely each of these changes are to have been caused by human influence, is important for decision making on mitigation and adaptation policy. Here we ... More

Contractions of group representations via geometric quantisationFeb 09 2018Dec 17 2018We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a representation is expressed via cocycles on coadjoint orbits. This condition ... More

Enumeration of Carlitz MultipermutationsFeb 14 2017Feb 16 2017A multipermutation with $k$ copies each of $1\ldots n$ is Carlitz if neighbours are different. We enumerate these objects for $k=2,3,4$ and derive recurrences. In particular, we prove and improve a conjectured recurrence for $k=3$, stated in OEIS, the ... More

Localization and number of visited valleys for a transient diffusion in random environmentNov 25 2013Mar 09 2015We consider a transient diffusion in a $(-\kappa/2)$-drifted Brownian potential $W\_{\kappa}$ with $0\textless{}\kappa\textless{}1$. We prove its localization at time $t$ in the neighborhood of some random points depending only on the environment, which ... More

Distribution of High-Mass X-ray Binaries in the Milky WayDec 21 2012Feb 07 2013Observations of the high energy sky, particularly with the INTEGRAL satellite, have quadrupled the number of supergiant X-ray Binaries observed in the Galaxy, and revealed new populations of previously hidden High Mass X-ray Binaries (HMXBs), raising ... More

Multifractal random walks with fractional Brownian motion via Malliavin calculusSep 21 2012We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence of this object ... More

On the graded center of graded categoriesAug 28 2012We study the G-centers of G-graded monoidal categories where G is an arbitrary group. We prove that for any spherical G-fusion category C over an algebraically closed field such that the dimension of the neutral component of C is non-zero, the G-center ... More