Results for "Sébastien Renaux-Petel"
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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 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 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 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 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 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 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 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 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 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 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 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 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 Latt{è}s maps and the interior of the bifurcation locusJan 19 2018Feb 21 2018We show the existence of open sets of bifurcations near Latt{\`e}s maps of sufficiently high degree. In particular, every Latt{\`e}s map has an iterate which is in the closure of the interior of the bifurcation locus. To show this, we design a method ... More A Core Theory of Delay SystemsJul 09 2017We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a practical ... 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 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 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 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 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 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 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 $3$-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 Application of a nudging technique to thermoacoustic tomographyDec 03 2011ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to correct the state ... More A Taxonomy of Daemons in Self-stabilizationOct 03 2011We survey existing scheduling hypotheses made in the literature in self-stabilization, commonly referred to under the notion of daemon. We show that four main characteristics (distribution, fairness, boundedness, and enabledness) are enough to encapsulate ... More Sparse recovery with unknown variance: a LASSO-type approachJan 02 2011Nov 05 2012We address the issue of estimating the regression vector $\beta$ in the generic $s$-sparse linear model $y = X\beta+z$, with $\beta\in\R^{p}$, $y\in\R^{n}$, $z\sim\mathcal N(0,\sg^2 I)$ and $p> n$ when the variance $\sg^{2}$ is unknown. We study two LASSO-type ... More Le droit du numérique : une histoire à préserverOct 12 2012Although the history of informatics is recent, this field poses unusual problems with respect to its preservation. These problems are amplified by legal issues, digital law being in itself a subject matter whose history is also worth presenting in a computer ... More Optimal feeding is optimal swimming for all Péclet numbersSep 01 2011Cells swimming in viscous fluids create flow fields which influence the transport of relevant nutrients, and therefore their feeding rate. We propose a modeling approach to the problem of optimal feeding at zero Reynolds number. We consider a simplified ... More Parameterizable Byzantine Broadcast in Loosely Connected NetworksJan 17 2013Dec 08 2013We consider the problem of reliably broadcasting information in a multihop asynchronous network, despite the presence of Byzantine failures: some nodes are malicious and behave arbitrarly. We focus on non-cryptographic solutions. Most existing approaches ... More Limiting Byzantien Influence in Multihop Asynchronous NetworksJan 27 2012We consider the problem of reliably broadcasting information in a multihop asyn- chronous network that is subject to Byzantine failures. That is, some nodes of the network can exhibit arbitrary (and potentially malicious) behavior. Existing solutions ... More The algorithm of noisy k-meansAug 15 2013In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. ... More Rigidity of square-tiled interval exchange transformationsFeb 20 2017We look at interval exchange transformations defined as first return maps on the set of diagonals of a flow of direction $\theta$ on a square-tiled surface: using a combinatorial approach, we show that, when the surface has at least one true singularity ... More Context-Aware Learning for Neural Machine TranslationMar 12 2019Interest in larger-context neural machine translation, including document-level and multi-modal translation, has been growing. Multiple works have proposed new network architectures or evaluation schemes, but potentially helpful context is still sometimes ... More A corrected quantitative version of the Morse lemmaOct 10 2018There is a gap in the proof of the main theorem in the article [ShCh13a] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [ShCh13a] is correct. We also describe a computer certification ... More Variational Calibration of Computer ModelsOct 29 2018Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model discrepancy ... More Asymptotics of even-even correlations in the Ising modelApr 23 2018Nov 26 2018We consider finite-range ferromagnetic Ising models on $\mathbb{Z}^d$ in the regime $\beta<\beta_c$. We analyze the behavior of the prefactor to the exponential decay of $\mathrm{Cov}(\sigma_A,\sigma_B)$, for arbitrary finite sets $A$ and $B$ of even ... More Morphing for faster computations in transformation opticsJul 07 2014Aug 01 2014We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given ... More Subadditive and Multiplicative Ergodic TheoremsSep 25 2015A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of Karlsson-Ledrappier, ... More Phoretic self-propulsion at finite Péclet numbersMar 14 2014Phoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow ... More On Byzantine Broadcast in Planar GraphsJan 14 2013Dec 07 2013We consider the problem of reliably broadcasting information in a multihop asynchronous network in the presence of Byzantine failures: some nodes may exhibit unpredictable malicious behavior. We focus on completely decentralized solutions. Few Byzantine-robust ... More On Byzantine Broadcast in Loosely Connected NetworksSep 05 2012We consider the problem of reliably broadcasting information in a multihop asynchronous network that is subject to Byzantine failures. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the authentic message ... More