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Aspects of massive gravityDec 23 2015We report here on two works on Lorentz invariant massive gravity. In the first part, we derive the decoupling limit of massive gravity on de Sitter, relying on embedding de Sitter into an higher dimensional Minkowski spacetime. This enables us to identify ... More

Primordial non-Gaussianities after Planck 2015: an introductory reviewAug 27 2015Deviations from Gaussian statistics of the cosmological density fluctuations, so-called primordial non-Gaussianities (NG), are one of the most informative fingerprints of the origin of structures in the universe. Indeed, they can probe physics at energy ... More

Non-Gaussian inflationary shapes in $G^3$ theories beyond HorndeskiJul 27 2014Sep 03 2014We consider the possible signatures of a recently introduced class of healthy theories beyond Horndeski models on higher-order correlators of the inflationary curvature fluctuation. Despite the apparent large number and complexity of the cubic interactions, ... More

Geometrical Destabilization of InflationOct 05 2015Sep 20 2016We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary ... More

On reaching the adiabatic limit in multi-field inflationMay 23 2014Dec 29 2014We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account ... More

Perturbations in generalized multi-field inflationJan 07 2008May 31 2008We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis ... More

Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of soundMay 31 2018Nov 06 2018Inflationary perturbations in multi-field theories can exhibit a transient tachyonic instability as a consequence of their non-trivial motion in the internal field space. When an effective single-field description is applicable, the resulting theory is ... More

Geometrical destabilization, premature end of inflation and Bayesian model selectionJun 06 2017Nov 03 2017By means of Bayesian techniques, we study how a premature ending of inflation, motivated by geometrical destabilization, affects the observational evidences of typical inflationary models. Large field models are worsened, and inflection point potentials ... More

A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow RollJul 02 2012Oct 02 2012We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the ... More

Multifield Cosmological Perturbations at Third Order and the Ekpyrotic TrispectrumJun 02 2009Sep 14 2009Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields. We use these equations to calculate the trispectrum of ... More

Inflationary stochastic anomaliesJun 26 2018Feb 25 2019The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability ... More

Revisiting non-Gaussianity in multifield inflation with curved field spaceJul 24 2019Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit ... More

Primordial fluctuations and non-Gaussianities in sidetracked inflationApr 30 2018Jul 27 2018Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space ... More

On backreaction effects in geometrical destabilisation of inflationJan 29 2019We study the geometrical instability arising in multi-field models of inflation with negatively-curved field space. We analyse how the homogeneous background evolves in presence of geometrical destabilisation, and show that, in simple models, a kinematical ... More

On backreaction effects in geometrical destabilisation of inflationJan 29 2019Apr 30 2019We study the geometrical instability arising in multi-field models of inflation with negatively-curved field space. We analyse how the homogeneous background evolves in presence of geometrical destabilisation, and show that, in simple models, a kinematical ... More

Hyper non-Gaussianities in inflation with strongly non-geodesic motionFeb 08 2019Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble ... More

Nonlinear perturbations of cosmological scalar fields with non-standard kinetic termsOct 14 2008Dec 09 2008We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation ... More

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflationAug 01 2011Jan 03 2012We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane ... More

Massive Gravity on de Sitter and Unique Candidate for Partially Massless GravityJun 15 2012Jan 10 2013We derive the decoupling limit of Massive Gravity on de Sitter in an arbitrary number of space-time dimensions d. By embedding d-dimensional de Sitter into d+1-dimensional Minkowski, we extract the physical helicity-1 and helicity-0 polarizations of the ... More

Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraintsFeb 17 2009We study multi-field Dirac-Born-Infeld (DBI) inflation models, taking into account the NS-NS and R-R bulk fields present in generic flux compactifications. We compute the second-order action, which governs the behaviour of linear cosmological perturbations, ... More

Spectral distortions in the cosmic microwave background polarizationDec 16 2013Mar 21 2014We compute the spectral distortions of the Cosmic Microwave Background (CMB) polarization induced by non-linear effects in the Compton interactions between CMB photons and cold intergalactic electrons. This signal is of the $y$-type and is dominated by ... More

Primordial fluctuations and non-Gaussianities in multi-field DBI inflationApr 19 2008We study Dirac-Born-Infeld (DBI) inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, ... More

Primordial perturbations and non-Gaussianities in DBI and general multi-field inflationJun 02 2008We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multi-field extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing ... More

Neveu-Schwarz and operators algebras II: Unitary series and charactersOct 01 2010Oct 07 2010This paper is the second of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we give a unitary complete proof of the classification of the unitary series of the Neveu-Schwarz algebra, ... More

On rotarily transitive graphsMay 19 2016From the point of view of discrete geometry, the class of locally finite transitive graphs is a wide and important one. The subclass of Cayley graphs is of particular interest, as testifies the development of geometric group theory. Recall that Cayley ... More

Ergodicity and indistinguishability in percolation theoryOct 04 2012Nov 13 2014This paper explores the link between the ergodicity of the clus-ter equivalence relation restricted to its infinite locus and the indis-tinguishability of infinite clusters. It is an important element of the dictionary connecting orbit equivalence and ... More

Asymptotic Analysis of a Non-Linear Non-Local Integro-Differential Equation Arising from Bosonic Quantum Field DynamicsDec 19 2012We introduce a one parameter family of non-linear, non-local integro-differential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show ... More

Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive FieldOct 16 2018We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is $c\|x\|^{-(d-1)/2}$. The proof is based on the development in the random current representation of a "modern" Ornstein-Zernike ... More

Topology optimization in the framework of the linear Boltzmann equation - a method for designing optimal nuclear equipment and particle opticsOct 02 2018Oct 09 2018In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize the transport ... More

A fictitious domain approach for a mixed finite element method solving the two-phase Stokes problem with surface tension forcesJul 25 2018Apr 01 2019In this article we study a mixed finite element formulation for solving the Stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor, on an interface that splits the domain into two subdomains. Equality of ... More

A fast Monte-Carlo method with a Reduced Basis of Control Variates applied to Uncertainty Propagation and Bayesian EstimationFeb 03 2012The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Leli\`evre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation of many parametrized expected values at many parameter values. We provide ... More

Induction of $\mathbb{Z}^2$-actions and of partitions of the 2-torusJun 03 2019Sturmian sequences are the most simple aperiodic sequences. A result of Morse, Hedlund (1940) and Coven, Hedlund (1970) is that a biinfinite binary sequence is sturmian if and only if it is obtained as the coding of an irrational rotation on the circle ... More

On geometric aspects of the SUSY Fokas-Gel'fand immersion formulaJun 20 2017Mar 09 2018In this paper, we develop a new geometric characterization for the supersymmetric versions of the Fokas--Gel'fand formula for the immersion of soliton supermanifolds with two bosonic and two fermionic independent variables into Lie superalgebras. In order ... More

Neveu-Schwarz and operators algebras I: Vertex operators superalgebrasOct 01 2010Oct 07 2010This paper is the first of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we present an elementary, progressive and self-contained approch to vertex operator superalgebra. We then build ... More

Chern-Simons Invariants of Torus LinksMar 15 2010Jan 03 2011We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus ... More

On the coldness of the local Hubble flow: the role of baryonsFeb 24 2010Jun 14 2010(Abridged) Our aim is to investigate whether the presence of baryons can have any significant influence on the properties of the local Hubble flow which has proved to be "cold". We use two cosmological zoom simulations in the standard LCDM cosmology with ... More

A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random fieldJul 05 2011Jun 25 2012In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric ... More

Low energy scales of Kondo lattices: mean-field perspectiveMar 11 2009A review of the low temperature properties of Kondo lattice systems is presented within the mean-field approximation, focusing on the different characteristic energy scales. The Kondo temperature, T_K, and the Fermi liquid coherence energy, T_0, are analyzed ... More

Johnson-Segalman -- Saint-Venant equations for viscoelastic shallow flows in the elastic limitNov 25 2016The shallow-water equations of Saint-Venant, often used to model the long-wave dynamics of free-surface flows driven by inertia and hydrostatic pressure, can be generalized to account for the elongational rheology of non-Newtonian fluids too. We consider ... More

On coprime percolation, the visibility graphon, and the local limit of the GCD profileApr 17 2018Feb 03 2019Colour an element of $\mathbb{Z}^d$ white if its coordinates are coprime and black otherwise. What does this colouring look like when seen from a "uniformly chosen" point of $\mathbb{Z}^d$? More generally, label every element of $\mathbb{Z}^d$ by its ... More

Directed Diffusion-Limited AggregationNov 13 2014Dec 22 2015In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volume. We obtain bounds on the speed of propagation of information in infinite ... More

Sparsity regret bounds for individual sequences in online linear regressionJan 05 2011Apr 12 2013We consider the problem of online linear regression on arbitrary deterministic sequences when the ambient dimension d can be much larger than the number of time rounds T. We introduce the notion of sparsity regret bound, which is a deterministic online ... More

Variational and non-Archimedean aspects of the Yau--Tian--Donaldson conjectureMay 08 2018We survey some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature K\"ahler metrics to the algebro-geometric notion of K-stability. The emphasis is put on the use of pluripotential ... More

A self-similar aperiodic set of 19 Wang tilesFeb 09 2018Jul 24 2018We define a Wang tile set $\mathcal{U}$ of cardinality 19 and show that the set $\Omega_\mathcal{U}$ of all valid Wang tilings $\mathbb{Z}^2\to\mathcal{U}$ is self-similar, aperiodic and is a minimal subshift of $\mathcal{U}^{\mathbb{Z}^2}$. Thus $\mathcal{U}$ ... More

A Greedy Algorithm to Cluster SpecialistsSep 13 2016Several recent deep neural networks experiments leverage the generalist-specialist paradigm for classification. However, no formal study compared the performance of different clustering algorithms for class assignment. In this paper we perform such a ... More

Searching for New High Mass Phenomena Decaying to Muon Pairs using Proton-Proton Collisions at $\sqrt{s}$ = 13 TeV with the ATLAS Detector at the LHCAug 09 2017We present a search for new high mass phenomena using the latest data collected by the ATLAS detector at the LHC, corresponding to 36.1 fb$^{-1}$ at $\sqrt{s}$ = 13 TeV. The search is conducted for both resonant and non-resonant new phenomena in dimuon ... More

A counterexample to a question of Hof, Knill and SimonJul 05 2013In this article, we give a negative answer to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes. Proven for the binary alphabet by B. Tan in 2007, ... More

A note on matrices mapping a positive vector onto its element-wise inverseAug 21 2017For any primitive matrix $M\in\mathbb{R}^{n\times n}$ with positive diagonal entries, we prove the existence and uniqueness of a positive vector $\mathbf{x}=(x_1,\dots,x_n)^t$ such that $M\mathbf{x}=(\frac{1}{x_1},\dots,\frac{1}{x_n})^t$. The contribution ... More

Conditional Moments of Anticipative $α$-Stable Markov ProcessesMay 14 2018The anticipative $\alpha$-stable autoregression of order 1 (AR(1)) is a stationary Markov process undergoing explosive episodes akin to bubbles in financial time series data. Although featuring infinite variance, integer conditional moments up to order ... More

Some properties of meta-stable supersymmetry-breaking vacua in Wess-Zumino modelsJul 24 2006As a contribution to the current efforts to understand supersymmetry-breaking by meta-stable vacua, we study general properties of supersymmetry-breaking vacua in Wess-Zumino models: we show that tree-level degeneracy is generic, explore some constraints ... More

Torus Knots in Lens Spaces & Topological StringsAug 26 2013Jun 22 2014We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the paper, we propose ... More

A fictitious domain approach for a mixed finite element method solving the two-phase Stokes problem with surface tension forcesJul 25 2018In this article we study a mixed finite element formulation for solving the Stokes problem with general boundary forces that induce a jump of the normal trace of the stress tensor, on an interface that splits the domain into two subdomains. Equality of ... More

Substitutive structure of Jeandel-Rao aperiodic tilingsAug 23 2018We describe the substitutive structure of Jeandel-Rao aperiodic Wang tilings $\Omega_0$. We introduce twelve sets of Wang tiles $\{\mathcal{T}_{i}\}_{1\leq i\leq 12}$ together with their associated Wang shifts $\{\Omega_{i}\}_{1\leq i\leq 12}$. Using ... More

Weak Mixing and Analyticity of the Pressure in the Ising ModelMay 30 2019Jun 20 2019We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on $\mathbb{Z}^d$ is analytic as a function of both the inverse temperature $\beta$ and the magnetic field $h$ whenever the model has the exponential weak mixing ... More

Cellular automata on a $G$-setMay 26 2011We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition also allows ... More

Searches for new phenomena in leptonic final states using the ATLAS detectorSep 28 2018Many theories beyond the Standard Model predict new phenomena which decay to well isolated, high-$p_{\text{T}}$ leptons. Searches for new physics with these signatures are performed using the ATLAS experiment at the LHC. The results reported here use ... More

Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized systemMar 27 2013Jan 02 2014This paper is the first part of a work which consists in proving the stabilization to zero of a fluid-solid system, in dimension 2 and 3. The considered system couples a deformable solid and a viscous incompressible fluid which satisfies the incompressible ... More

Existence of 3D strong solutions for a system modeling a deformable solid inside a viscous incompressible fluidMar 01 2013Jul 07 2014In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the incompressible ... More

Neveu-Schwarz and operators algebras III: Subfactors and Connes fusionOct 01 2010Oct 07 2010This paper is the third of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we introduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtain Jones-Wassermann subfactors ... More

Almost sure invariance principle for dynamical systems by spectral methodsJul 08 2009Feb 09 2011We prove the almost sure invariance principle for stationary R^d--valued processes (with dimension-independent very precise error terms), solely under a strong assumption on the characteristic functions of these processes. This assumption is easy to check ... More

Martin boundary of random walks with unbounded jumps in hyperbolic groupsFeb 21 2013Nov 03 2015Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is known since ... More

Higher order terms for the quantum evolution of a Wick observable within the Hepp methodFeb 19 2011The Hepp method is the coherent state approach to the mean field dynamics for bosons or to the semiclassical propagation. A key point is the asymptotic evolution of Wick observables under the evolution given by a time-dependent quadratic Hamiltonian. ... More

Improved bounds for reduction to depth 4 and depth 3Apr 21 2013May 16 2014Koiran showed that if a $n$-variate polynomial of degree $d$ (with $d=n^{O(1)}$) is computed by a circuit of size $s$, then it is also computed by a homogeneous circuit of depth four and of size $2^{O(\sqrt{d}\log(d)\log(s))}$. Using this result, Gupta, ... More

Bringing Information Credibility Back Into Transparency: The Case for a Global Monitoring System Of Green House Gas EmissionsJul 07 2016The goal of climate change governance is to stabilize greenhouse gas concentrations. This requires the reduction of anthropogenic global net emissions. In the pursuit of such a reduction, knowledge of greenhouse gas sources and sinks is critical to define ... More

Viscoelastic flows with conservation lawsAug 09 2019We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of quasilinear PDEs ... More

A Markov partition for Jeandel-Rao aperiodic Wang tilingsMar 14 2019We define a Markov partition for a $\mathbb{Z}^2$-rotation on the 2-dimensional torus whose associated symbolic dynamical system is a minimal and aperiodic Wang shift defined by 19 Wang tiles. We define another partition for another $\mathbb{Z}^2$-rotation ... More

Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}Nov 07 2016We show that there exists a polynomial automorphism $f$ of $\mathbb{C}^{3}$ of degree 5 such that for every automorphism $g$ sufficiently close to $f$, $g$ admits a tangency between the stable and unstable laminations of some hyperbolic set. As a consequence, ... More

Convex Optimization: Algorithms and ComplexityMay 20 2014Nov 16 2015This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization ... More

Analyticity of the entropy and the escape rate of random walks in hyperbolic groupsSep 23 2015We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible probability measures ... More

Growth of normalizing sequences in limit theorems for conservative mapsMar 30 2018We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an additional ... More

Derivation and numerical approximation of hyperbolic viscoelastic flow systems: Saint-Venant 2D equations for Maxwell fluidsDec 12 2017We pursue here the development of models for complex (viscoelastic) fluids in shallow free-surface gravity flows which was initiated by [Bouchut-Boyaval, M3AS (23) 2013] for 1D (translation invariant) cases. The models we propose are hyperbolic quasilinear ... More

A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluidsJan 17 2017Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Upper-Convected Maxwell (UCM) fluids was proposed in [Bouchut \& Boyaval, 2013], ... More

Locally infinite graphs and symmetriesJan 05 2017When one studies geometric properties of graphs, local finiteness is a common implicit assumption, and that of transitivity a frequent explicit one. By compactness arguments, local finiteness guarantees several regularity properties. It is generally easy ... More

The set of connective constants of Cayley graphs contains a Cantor spaceAug 11 2016Aug 14 2016The purpose of this note is to prove that the set of connective constants of Cayley graphs contains a Cantor space.

Weak Mixing and Analyticity of the Pressure in the Ising ModelMay 30 2019We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on $\mathbb{Z}^d$ is analytic as a function of both the inverse temperature $\beta$ and the magnetic field $h$ whenever the model has the exponential weak mixing ... More

Path prediction of aggregated $α$-stable moving averages using semi-norm representationsSep 10 2018For $(X_t)$ a two-sided $\alpha$-stable moving average, this paper studies the conditional distribution of future paths given a piece of observed trajectory when the process is far from its central values. Under this framework, vectors of the form $\boldsymbol{X}_t=(X_{t-m},\ldots,X_t,X_{t+1},\ldots,X_{t+h})$, ... More

Substitutive structure of Jeandel-Rao aperiodic tilingsAug 23 2018Apr 11 2019We describe the substitutive structure of Jeandel-Rao aperiodic Wang tilings $\Omega_0$. We introduce twelve sets of Wang tiles $\{\mathcal{T}_{i}\}_{1\leq i\leq 12}$ together with their associated Wang shifts $\{\Omega_{i}\}_{1\leq i\leq 12}$. Using ... More

A self-similar aperiodic set of 19 Wang tilesFeb 09 2018Jul 10 2019We define a Wang tile set $\mathcal{U}$ of cardinality 19 and show that the set $\Omega_\mathcal{U}$ of all valid Wang tilings $\mathbb{Z}^2\to\mathcal{U}$ is self-similar, aperiodic and is a minimal subshift of $\mathcal{U}^{\mathbb{Z}^2}$. Thus $\mathcal{U}$ ... More

Supersymmetric and R symmetric vacua in Wess-Zumino modelsAug 16 2007In the context of supersymmetric Wess-Zumino models with an R symmetry, we find some simple conditions on the R-charge content of the theory that imply the presence or absence of supersymmetric and R-symmetric vacua. The main result of this work is that ... More

Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear systemMar 27 2013Jan 02 2014In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the self-propelled ... More

$3$-dimensional Continued Fraction Algorithms Cheat SheetsNov 26 2015Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider multidimensional continued ... More

On integrability aspects of the supersymmetric sine-Gordon equationMar 23 2017In this paper we study certain integrability properties of the supersymmetric sine-Gordon equation. We construct Lax pairs with their zero-curvature representations which are equivalent to the supersymmetric sine-Gordon equation. From the fermionic linear ... More

Inkjet-printed vertically emitting solid-state organic lasersMay 25 2016In this paper, we show that Inkjet Printing can be successfully applied to external-cavity vertically-emitting thin-film organic lasers, and can be used to generate a diffraction-limited output beam with an output energy as high as 33.6 uJ with a slope ... More

Optimal functional supervised classification with separation conditionJan 10 2018We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its worst-case excess ... More

A Scalable Byzantine GridOct 17 2012Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each ... More

Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinityMar 04 2012Jul 19 2013We study constant mean curvature 1/2 surfaces in H2xR that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H2 admits a structure of infinite dimensional manifold with local control ... More

The complexity of Shortest Common Supersequence for inputs with no identical consecutive lettersSep 02 2013Jan 08 2015The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and Johnson] is NP-complete. ... More

Entropic CLT and phase transition in high-dimensional Wishart matricesSep 10 2015Sep 13 2015We consider high dimensional Wishart matrices $\mathbb{X} \mathbb{X}^{\top}$ where the entries of $\mathbb{X} \in {\mathbb{R}^{n \times d}}$ are i.i.d. from a log-concave distribution. We prove an information theoretic phase transition: such matrices ... More

Dynamical properties and characterization of gradient drift diffusionsDec 14 2006We study the dynamical properties of the Brownian diffusions having $\sigma {\rm Id}$ as diffusion coefficient matrix and $b=\nabla U$ as drift vector. We characterize this class through the equality $D^2_+=D^2_-$, where $D_{+}$ (resp. $D_-$) denotes ... More

Invertibility of random submatrices via tail decoupling and a Matrix Chernoff InequalityMar 15 2011Mar 19 2012Let $X$ be a $n\times p$ matrix with coherence $\mu(X)=\max_{j\neq j'} |X_j^tX_{j'}|$. We present a simplified and improved study of the quasi-isometry property for most submatrices of $X$ obtained by uniform column sampling. Our results depend on $\mu(X)$, ... More

Electron-phonon scattering in topological insulatorsMar 01 2011We formulate and apply a theory of electron-phonon interactions for the surface state of a strong topological insulator. Phonons are modelled using an isotropic elastic continuum theory with stress-free boundary conditions and interact with the Dirac ... More

Stabilizing Maximal Independent Set in Unidirectional Networks is HardMar 18 2009A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. In this paper, we consider ... More

A Chaining Algorithm for Online Nonparametric RegressionFeb 26 2015Jul 01 2015We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive ... More

Refined Lower Bounds for Adversarial BanditsMay 24 2016Feb 27 2017We provide new lower bounds on the regret that must be suffered by adversarial bandit algorithms. The new results show that recent upper bounds that either (a) hold with high-probability or (b) depend on the total lossof the best arm or (c) depend on ... More

An Invariant Linear Quadratic Gaussian controller for a simplified carJun 06 2014Jun 18 2014In this paper, we consider the problem of tracking a reference trajectory for a simplified car model based on unicycle kinematics, whose position only is measured, and where the control input and the measurements are corrupted by independent Gaussian ... More

Reasons and Means to Model Preferences as IncompleteJan 05 2018Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the ... More

A Bayesian Clearing Mechanism for Combinatorial AuctionsDec 14 2017Nov 16 2018We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and ... More

Safe Reinforcement Learning Using Robust MPCJun 10 2019Reinforcement Learning (RL) has recently impressed the world with stunning results in various applications. While the potential of RL is now well-established, many critical aspects still need to be tackled, including safety and stability issues. These ... More

Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré AlgorithmApr 16 2014The Arnoux-Rauzy-Poincar\'e multidimensional continued fraction algorithm is obtained by combining the Arnoux-Rauzy and Poincar\'e algorithms. It is a generalized Euclidean algorithm. Its three-dimensional linear version consists in subtracting the sum ... More

A note on Lang's conjecture for quotients of bounded domainsSep 07 2018Dec 13 2018It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this conjecture for projective manifolds whose universal cover carries a bounded, ... More