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Gravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation methodJul 10 2019By listening to gravity in the low frequency band, between 0.1 mHz and 1 Hz, the future space-based gravitational-wave observatory LISA will be able to detect tens of thousands of astrophysical sources from cosmic dawn to the present. The detection and ... More

Dealing with missing data: An inpainting application to the MICROSCOPE space missionDec 01 2015Missing data are a common problem in experimental and observational physics. They can be caused by various sources, either an instrument's saturation, or a contamination from an external event, or a data loss. In particular, they can have a disastrous ... More

Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise dataDec 16 2016The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10^-15 precision. To reach this performance requires an accurate and robust data analysis method, especially since the possible WEP violation ... More

Exponential shapelets: basis functions for data analysis of isolated featuresMar 14 2019We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics with elegant ... More

Gaussian regression and power spectral density estimation with missing data: The MICROSCOPE space mission as a case studyAug 30 2016We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging, based on the ... More

Stabilizing a Molecular Switch at Solid Surfaces: A Density-Functional Theory Study of Azobenzene at Cu(111), Ag(111), and Au(111)Mar 05 2009We present a density-functional theory trend study addressing the binding of the trans-cis conformational switch azobenzene (C6H5-N=N-C6H5) at three coinage metal surfaces. From the reported detailed energetic, geometric, and electronic structure data ... More

Optimal Testing for Planted Satisfiability ProblemsJan 09 2014Feb 08 2015We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the study of the number ... More

A bridge bewteen U-frequent hypercyclicity and frequent hypercyclicityApr 09 2019Given $\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\sum_{n=0}^{\infty} a_n$ diverges, we show that the supremum on $\mathcal{A}$ of lower weighted densities coincides with the unweighted upper density and that ... More

A new proof of Raynaud-Gruson's flattening theoremJan 03 2018Mar 27 2018We give a new proof of Raynaud-Gruson's theorem regarding flattening by blow-ups. The proof is direct, by working directly on the inverse limit of admissible blow-ups, which is a valuative space similar to the classical Zariski-Riemann space. These valuatives ... More

Lower bounds for k-distance approximationMar 21 2013Consider a set P of N random points on the unit sphere of dimension $d-1$, and the symmetrized set S = P union (-P). The halving polyhedron of S is defined as the convex hull of the set of centroids of N distinct points in S. We prove that after appropriate ... More

On the ramified class field theory of relative curvesApr 06 2018May 29 2019We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.

A better bound for ordinary trianglesMay 17 2018Jun 26 2018Let $P$ be a finite set of points in the plane. A c-ordinary triangle is a set of three non-collinear points of $P$ such that each line spanned by the points contains at most $c$ points of $P$. We show that if $P$ is not contained in the union of two ... More

Singular measure traveling waves in an epidemiological model with continuous phenotypesOct 06 2017Sep 13 2018We consider the reaction-diffusion equation \begin{equation*} u_t=u_{xx}+\mu\left(\int_\Omega M(y,z)u(t,x,z)dz-u\right) + u\left(a(y)-\int_\Omega K(y,z) u(t,x,z)dz\right) , \end{equation*} where $ u=u(t,x,y) $ stands for the density of a theoretical population ... More

On Modular Functions with a Cuspidal DivisorSep 13 2016The aim of this paper is the generalization of the following equivalence due to Kohnen: Let f be a modular function of integral weight with respect to Gamma_0(N), N square-free. Then f has a cuspidal divisor (i.e. zeros and poles supported at the cusps) ... More

Composite dark matter and direct-search experimentsDec 18 2015We reinterpret the results of the direct searches for dark matter in terms of composite dark matter, i.e. dark matter particles that form neutral bound states, generically called dark atoms, either with ordinary particles, or with other dark matter particles. ... More

Milli-interacting dark matter interpretation of the direct-search experimentsJan 21 2014Jan 24 2014We reinterpret the results of the direct searches for dark matter in terms of milli-interacting dark particles. The model reproduces the positive results from DAMA/LIBRA and CoGeNT and is consistent with the absence of signal in the XENON100, CDMS-II/Ge ... More

On the ramified class field theory of relative curvesApr 06 2018We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.

Size of the medial axis and stability of Federer's curvature measuresJan 18 2010In this article, we study the (d-1)-volume and the covering numbers of the medial axis of a compact set of the Euclidean d-space. In general, this volume is infinite; however, the (d-1)-volume and covering numbers of a filtered medial axis (the mu-medial ... More

Strong renewal theorems and local large deviations for multivariate random walks and renewalsJul 10 2018Apr 17 2019We study a random walk $\mathbf{S}_n$ on $\mathbb{Z}^d$ ($d\geq 1$), in the domain of attraction of an operator-stable distribution with index $\boldsymbol{\alpha}=(\alpha_1,\ldots,\alpha_d) \in (0,2]^d$: in particular, we allow the scalings to be different ... More

Existence of common hypercyclic subspaces for the derivative operator and the translation operatorsNov 25 2016We show that the non-zero multiples of the derivative operator and the non-zero multiples of non-trivial translation operators on the space of entire functions share a common hypercyclic subspace, i.e. a closed infinite-dimensional subspace in which each ... More

Geometric local epsilon factorsFeb 18 2019May 29 2019Inspired by the work of Laumon on $\varepsilon$-factors and by Deligne's $1974$ letter to Serre, we give an explicit cohomological definition of $\varepsilon$-factors for $\ell$-adic Galois representations over henselian discrete valuation fields of positive ... More

Review of gas and dust in debris discsNov 21 2016This proceeding summarises a talk given on the state-of-the-art of debris disc modelling. We first review the basics of debris disc physics, which is followed by a short overview of the state-of-the-art in terms of modelling dust and gas in debris disc ... More

A Theorem for Distinct Zeros of L-FunctionsApr 24 2015Apr 30 2015In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered in the particular ... More

Milli-interacting Dark MatterJul 29 2013We present a dark matter model reproducing well the results from DAMA/LIBRA and CoGeNT and having no contradiction with the negative results from XENON100 and CDMS-II/Ge. Two new species of fermions F and G form hydrogen-like atoms with standard atomic ... More

Search for extra dimensions in the diphoton final state with ATLASJan 23 2012The large difference between the Planck scale and the electroweak scale, known as the hierarchy problem, has been addressed in some models through the existence of extra spatial dimensions. A search for evidence of extra spatial dimensions has been performed, ... More

Strong renewal theorems and local large deviations for multivariate random walks and renewalsJul 10 2018We study a random walk $\mathbf{S}_n$ on $\mathbb{Z}^d$ ($d\geq 1$), in the domain of attraction of an operator-stable distribution with index $\boldsymbol{\alpha}=(\alpha_1,\ldots,\alpha_d) \in (0,2]^d$: in particular, we allow the scalings to be different ... More

On generalized modular forms with a cuspidal divisorSep 13 2016Apr 03 2019In [6], Kohnen proves that if $\Gamma=\Gamma_0(N)$ where $N$ is a square-free integer, then any modular function of weight $0$ for $\Gamma$ having a divisor supported at the cusps is an $\eta$-product. Under the condition of having rational Fourier coefficients, ... More

Geometric local epsilon factorsFeb 18 2019Inspired by the work of Laumon on $\varepsilon$-factors and by Deligne's $1974$ letter to Serre, we give an explicit cohomological definition of $\varepsilon$-factors for $\ell$-adic Galois representations over henselian discrete valuation fields of positive ... More

An extension of Macdonald's identity for $\mathfrak{sl}_n$Apr 23 2019May 10 2019Let $n$ be an odd positive integer. In this short elementary note, we slightly extend the Macdonald identity for $\mathfrak{sl}_{n}$ into a two-variables identity in the spirit of Jacobi forms. The peculiarity of this work lies in its proof which uses ... More

A new proof of Raynaud-Gruson's flattening theoremJan 03 2018May 29 2019We give a new proof of Raynaud-Gruson's theorem regarding flattening by blow-ups. The proof is direct, by working directly on the inverse limit of admissible blow-ups, which is a valuative space similar to the classical Zariski-Riemann space. These valuative ... More

On generalized modular forms with a cuspidal divisorSep 13 2016Apr 24 2019In [6], Kohnen proves that if $\Gamma=\Gamma_0(N)$ where $N$ is a square-free integer, then any modular function of weight $0$ for $\Gamma$ having a divisor supported at the cusps is an $\eta$-product. Under the condition of having rational Fourier coefficients, ... More

Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian EnvironmentJan 22 2013Nov 06 2013We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a>0. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and we discuss ... More

Notes on Random Walks in the Cauchy Domain of AttractionJun 24 2017Nov 13 2018The goal of these notes is to fill some gaps in the literature about random walks in the Cauchy domain of attraction, which has been in many cases left aside because of its additional technical difficulties. We prove here several results in that case: ... More

A bridge between U-frequent hypercyclicity and frequent hypercyclicityApr 09 2019Apr 11 2019Given $\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\sum_{n=0}^{\infty} a_n$ diverges, we show that the supremum on $\mathcal{A}$ of lower weighted densities coincides with the unweighted upper density and that ... More

Pinning model in random correlated environment: appearance of an infinite disorder regimeMar 12 2013Oct 09 2013We study the influence of a correlated disorder on the localization phase transition in the pinning model. When correlations are strong enough, a strong disorder regime arises: large and frequent attractive regions appear in the environment. We present ... More

OpenCFU, a New Free and Open-Source Software to Count Cell Colonies and Other Circular ObjectsOct 18 2012Nov 26 2012Counting circular objects such as cell colonies is an important source of information for biologists. Although this task is often time-consuming and subjective, it is still predominantly performed manually. The aim of the present work is to provide a ... More

An identity for the number of partitions (mod l) of nApr 23 2019Let $p(n)$ denotes the number of partitions of $n$ and let $\ell\geq 5$ be a prime number. Let also $\delta$ denotes $(\ell^2-1)/24$. For $n<\ell^2$, we prove a surprising identity $(\text{mod}~\ell)$ between $p(n-\delta)$ and the number of points in ... More

Homology Classes of Semi-Algebraic Sets and Mass MinimizationApr 18 2014Nov 06 2014We associate to any compact semi-algebraic set $X \subset \mathbb R^n$ a chain complex of currents $S_\ast (X)$ generated by integration along semi-algebraic submanifolds and we analyze the corresponding homology groups. In particular, we show that these ... More

Hypercyclic subspaces and weighted shiftsAug 24 2012We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T and show a ... More

Hypercyclic subspaces on Fréchet spaces without continuous normFeb 26 2013Oct 03 2013Known results about hypercyclic subspaces concern either Fr\'echet spaces with a continuous norm or the space \omega. We fill the gap between these spaces by investigating Fr\'echet spaces without continuous norm. To this end, we divide hypercyclic subspaces ... More

Linear chaos and frequent hypercyclicityOct 27 2014We answer one of the main current questions in Linear Dynamics by constructing a chaotic operator on $\ell^1$ which is not $\mathcal{U}$-frequently hypercyclic and thus not frequently hypercyclic. This operator also gives us an example of a chaotic operator ... More

Quantum correlations by four-wave-mixing in atomic vapor. Theory and ExperimentsJan 26 2011We study both theoretically and experimentally the generation of quantum correlations in the continuous variable regime by way of four-wave mixing in a hot atomic vapor. Two theoretical approaches have been developed. On one side, we study the four-wave ... More

On the mean field approximation of many-boson dynamicsSep 20 2016We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in infinite dimensional ... More

Anosov AdS representations are quasi-FuchsianOct 02 2007Let Gamma be a cocompact lattice in SO(1,n). A representation rho: Gamma \to SO(2,n) is quasi-Fuchsian if it is faithfull, discrete, and preserves an acausal subset in the boundary of anti-de Sitter space - a particular case is the case of Fuchsian representations, ... More

Inverse of $\mathcal{U}$-frequently hypercyclic operatorsApr 16 2019We show that there exists an invertible $\mathcal{U}$-frequently hypercyclic operator on $\ell^p(\mathbb{N})$ ($1\le p <\infty$) whose the inverse is not $\mathcal{U}$-frequently hypercyclic.

An extension of Macdonald's identity for $\mathfrak{sl}_n$Apr 23 2019Jul 01 2019Let $n$ be an odd positive integer. In this short elementary note, we slightly extend Macdonald's identity for $\mathfrak{sl}_{n}$ into a two-variables identity in the spirit of Jacobi forms. The peculiarity of this work lies in its proof which uses Wronskians ... More

Hereditarily hypercyclic subspacesDec 20 2013We say that a sequence of operators $(T_n)$ possesses hereditarily hypercyclic subspaces along a sequence $(n_k)$ if for any subsequence $(m_k)\subset(n_k)$, the sequence $(T_{m_k})$ possesses a hypercyclic subspace. While so far no characterization of ... More

Existence and non-existence of frequently hypercyclic subspaces for weighted shiftsAug 17 2013Aug 29 2013We study the existence and the non-existence of frequently hypercyclic subspaces in Banach spaces. In particular, we give an example of a weighted shift on lp possessing a frequently hypercyclic subspace and an example of a frequently hypercyclic weighted ... More

Inverse of $\mathcal{U}$-frequently hypercyclic operatorsApr 16 2019May 22 2019We show that there exists an invertible $\mathcal{U}$-frequently hypercyclic operator on $\ell^p(\mathbb{N})$ ($1\le p <\infty$) whose inverse is not $\mathcal{U}$-frequently hypercyclic.

The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of $Ω\mathcal{M}_{g}$Mar 11 2015The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian differentials. ... More

On Galois groups of strongly normal extensionsDec 18 2015We show that the differential Galois groups of strongly normal extensions, under the hypothesis that the subfield of constants has a model complete theory, are isomorphic to interpretable groups in the subfield of constants. We find a partial correspondence ... More

Local Lorentz-Symmetry Breaking and GravitySep 17 2013The lagrangian-based Standard-Model Extension framework offers a broad description of possible gravitational effects from local Lorentz violation. In this talk, I review the status of the theoretical and phenomenological work in this area. The extension ... More

Is dark matter made of mirror matter? Evidence from cosmological dataNov 22 2012Jan 20 2014We present new fast numerical simulations of cosmic microwave background and large scale structure in the case in which the cosmological dark matter is made entirely or partly of mirror matter. We consider scalar adiabatic primordial perturbations at ... More

Gravity Couplings in the Standard-Model ExtensionAug 02 2010The Standard-Model Extension (SME) is an action-based expansion describing general Lorentz violation for known matter and fields, including gravity. In this talk, I will discuss the Lorentz-violating gravity couplings in the SME. Toy models that match ... More

Testing Lorentz Symmetry with GravitySep 15 2007In this talk, results from the gravitational sector of the Standard-Model Extension (SME) are discussed. The weak-field phenomenology of the resulting modified gravitational field equations is explored. The application of the results to a variety of modern ... More

Gravity Sector of the SMEJul 25 2016In this talk, the gravity sector of the effective field theory description of local Lorentz violation is discussed, including minimal and nonminimal curvature couplings. Also, recent experimental and observational analyses including solar-system ephemeris ... More

Optimal component labeling algorithms for mesh-connected computers and VLSIFeb 05 2015Given an undirected graph $G$ of $n$ weighted edges, stored one edge per processor in a square mesh of $n$ processors, we show how to determine the connected components and a minimal spanning forest in $\Theta(\sqrt{n})$ time. More generally, we show ... More

Lorentz-violating gravitoelectromagnetismMay 10 2010Sep 07 2010The well-known analogy between a special limit of General Relativity and electromagnetism is explored in the context of the Lorentz-violating Standard-Model Extension (SME). An analogy is developed for the minimal SME that connects a limit of the CPT-even ... More

Lorentz Violation and GravityNov 10 2009In the last decade, a variety of high-precision experiments have searched for miniscule violations of Lorentz symmetry. These searches are largely motivated by the possibility of uncovering experimental signatures from a fundamental unified theory. Experimental ... More

Investigation of resonances in gravity-capillary wave turbulenceMay 13 2016We report experimental results on nonlinear wave coupling in surface wave turbulence on water at scales close to the crossover between surface gravity waves and capillary waves. We study 3-wave correlations either in the frequency domain or in wavevector ... More

Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetriesJun 12 2007We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing angles; on the other ... More

Estimation of smooth densities in Wasserstein distanceFeb 05 2019Feb 06 2019The Wasserstein distances are a set of metrics on probability distributions supported on $\mathbb{R}^d$ with applications throughout statistics and machine learning. Often, such distances are used in the context of variational problems, in which the statistician ... More

A Proof Theory for Model Checking: An Extended AbstractJan 18 2017While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the emphasis of model ... More

Dimension improvement in Dhar's refutation of the Eden conjectureMay 23 2017Jan 31 2018We consider the Eden model on the d-dimensional hypercubical unoriented lattice , for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate ... More

Transient events in bright debris discs: Collisional avalanches revisitedNov 17 2017A collisional avalanche is set off by the breakup of a large planetesimal, releasing small unbound grains that enter a debris disc located further away from the star, triggering there a collisional chain reaction that can potentially create detectable ... More

Is there more than meets the eye? Presence and role of submicron grains in debris discsApr 10 2019The presence of submicron grains has been inferred in several debris discs, despite the fact that these particles should be blown out by stellar radiation pressure on very short timescales. So far, no fully satisfying explanation has been found for this ... More

Recent Developments in Spacetime-Symmetry tests in GravityJun 20 2019We summarize theoretical and experimental work on tests of CPT and local Lorentz symmetry in gravity. Recent developments include extending the effective field theory framework into the nonlinear regime of gravity.

Recent Developments in Spacetime-Symmetry tests in GravityJun 20 2019Jun 25 2019We summarize theoretical and experimental work on tests of CPT and local Lorentz symmetry in gravity. Recent developments include extending the effective field theory framework into the nonlinear regime of gravity.

The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptoticsJul 29 2010We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a random walk ... More

A combinatorial approach to Rauzy-type dynamics II: the labelling method and a second proof of the KZB classification theoremJan 18 2018Feb 19 2018Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact ... More

Existence and qualitative properties of travelling waves for an epidemiological model with mutationsDec 19 2014In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other with a certain ... More

Anisotropic cubic curvature couplingsJul 31 2016To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied ... More

Time-delay and Doppler tests of the Lorentz symmetry of gravityApr 02 2009Aug 12 2009Modifications to the classic time-delay effect and Doppler shift in General Relativity (GR) are studied in the context of the Lorentz-violating Standard-Model Extension (SME). We derive the leading Lorentz-violating corrections to the time-delay and Doppler ... More

Simple strategies for Banach-Mazur games and fairly correct systemsApr 19 2013Jul 17 2013In 2006, Varacca and V\"olzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try ... More

Semi-Microscopical Description of the Scission Configuration in the Cold Fission of $^{252}$CfJun 03 1999The cold(neutronless) fission of $^{252}$Cf is studied in the frame of a molecular model in which the scission configuration is described by two aligned fragments interacting by means of Coulomb (+ nuclear) forces. The study is carried out for different ... More

Probabilistic Asynchronous Arbitrary Pattern FormationAug 15 2015Sep 20 2017We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operates inthe ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinatesystems of robots (the robots do not share a common ... More

Special Functions and Gauss-Thakur Sums in Higher Rank and DimensionMar 18 2019Anderson generating functions have received a growing attention in function field arithmetic in the last years. Despite their introduction by Anderson in the 80s where they were at the heart of comparison isomorphisms, further important applications e.g. ... More

Resource Allocation for Statistical EstimationDec 20 2014Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the effectiveness of ... More

Axions and anomalous $U(1)$'sSep 21 2018Inspired by recent studies of high-scale decay constant or flavorful QCD axions, we review and clarify their existence in effective string models with anomalous $U(1)$ gauge groups. We find that such models, when coupled to charged scalars getting vacuum ... More

A framework for proof certificates in finite state explorationJul 31 2015Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in computer models ... More

The high-temperature behavior for the directed polymer in dimension 1+2Jun 30 2015We investigate the high-temperature behavior of the directed polymer model in dimension $1+2$. More precisely we study the difference $\Delta \mathtt{F}(\beta)$ between the quenched and annealed free energies for small values of the inverse temperature ... More

Sharp critical behavior for pinning model in random correlated environmentApr 26 2011This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition ... More

Optimal link prediction with matrix logistic regressionMar 19 2018We consider the problem of link prediction, based on partial observation of a large network, and on side information associated to its vertices. The generative model is formulated as a matrix logistic regression. The performance of the model is analysed ... More

Existence of common and upper frequently hypercyclic subspacesSep 03 2014We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic subspaces and ... More

Special Functions and Gauss-Thakur Sums in Higher Rank and DimensionMar 18 2019Apr 15 2019Anderson generating functions have received a growing attention in function field arithmetic in the last years. Despite their introduction by Anderson in the 80s where they were at the heart of comparison isomorphisms, further important applications e.g. ... More

On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEsFeb 22 2016Sep 13 2016In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective aspects and a probabilistic representation of the solutions. It extends ... More

Lorentz-Violating ElectromagnetostaticsNov 10 2005In this talk, the stationary limit of Lorentz-violating electrodynamics is discussed. As illustrated by some simple examples, the general solution includes unconventional mixing of electrostatic and magnetostatic effects. I discuss a high-sensitivity ... More

L infinity Isotonic Regression for Linear, Multidimensional, and Tree OrdersJul 08 2015Algorithms are given for determining $L_\infty$ isotonic regression of weighted data where the independent set is n vertices in multidimensional space or in a rooted tree. For a linear order, or, more generally, a grid in multidimensional space, an optimal ... More

Differential Galois Theory in the class of formally real fieldsApr 13 2014We study strongly normal extensions within the class of formally real fields. Assuming that the constant field is real closed, we show that the differential Galois groups are semi-algebraic. We prove a partial Galois correspondence.

A Multiple-Valued Plateau ProblemJul 07 2015Aug 27 2015The existence of Dirichlet minimizing multiple-valued functions for given boundary data has been known since pioneering work of F. Almgren. Here we prove a multiple-valued analogue of the classical Plateau problem of the existence of area-minimizing mappings ... More

On differential Galois groups of strongly normal extensionsApr 13 2014May 16 2017We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ... More

Mean field limit for Bosons with compact kernels interactions by Wigner measures transportationFeb 18 2014We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner ... More

Pulsating fronts for Fisher-KPP systems with mutations as models in evolutionary epidemiologyJul 05 2016We consider a periodic reaction diffusion system which, because of competition between $u$ and $v$, does not enjoy the comparison principle. It also takes into account mutations, allowing $u$ to switch to $v$ and vice versa. Such a system serves as a ... More

Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shiftMar 25 2015Apr 08 2015The effect of disorder for pinning models is a subject which has attracted much attention in theoretical physics and rigorous mathematical physics. A peculiar point of interest is the question of coincidence of the quenched and annealed critical point ... More

Kinetic equations and self-organized band formationsJan 14 2019Self-organization is an ubiquitous phenomenon in nature which can be observed in a variety of different contexts and scales, with examples ranging from fish schools, swarms of birds or locusts, to flocks of bacteria. The observation of such global patterns ... More

Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space missionMar 04 2015The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving ... More

State and Parameter Estimation of Partially Observed Linear Ordinary Differential Equations with Deterministic Optimal ControlOct 28 2014Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give unsatisfactory results because ... More

A Tracking Approach to Parameter Estimation in Linear Ordinary Differential EquationsOct 28 2014Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data. Classical statistical ... More

Optimal detection of sparse principal components in high dimensionFeb 23 2012Sep 19 2013We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete ... More

Nonlocal resonances in weak turbulence of gravity-capillary wavesMar 13 2015We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve 3-wave resonant interactions. ... More