Author: "Centre for Mathematical Sciences" - Searchworks@Jio Institute Digital Library Search Results

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1,062 results on '"Centre for Mathematical Sciences"'

1. Some properties of a generalized type-1 Dirichlet distribution

Author: MAYAMOL, E. V. and Centre For Mathematical Sciences Pala Campus-Arunapuram P.O., Palai, Kerala
Subjects: lcsh:Statistics, lcsh:HA1-4737
Abstract: This paper deals with a generalization of type-1 Dirichlet density by incorporating partial sums of the component variables. We study various proportions, structural decompositions, connections to random volumes and p-parallelotopes. We will also look into the regression function of xk on x1,...,xk-1, Bayes’ estimates for the probabilities of a multinomial distribution by using this generalized Dirichlet model as the prior density are given. Other results illustrate the importance of the study of variable x1 in this model. It is found that the variable x1 in this model can be represented as the ratio of squares of volumes of two parallelotopes. Under certain conditions, x1 can be used to study the structural representations of the likelihood ratio criteria in MANOVA, MANCOVA etc., Statistica; Vol 70, No 1 (2010); 95-111
Published: 2013

2. Explicit Evaluations of Matrix-Variate Gamma and Beta Integrals in the Real and Complex Cases

Author: Mathai, A. M.; Centre for Mathematical Sciences India, Arunapuram, P.O., Palai, Kerala-686 574, Kerala and Mathai, A. M.; Centre for Mathematical Sciences India, Arunapuram, P.O., Palai, Kerala-686 574, Kerala
Abstract: Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta integrals in the general real and complex situations. The procedure also reveals the structure of these matrix- variate integrals. Apart from the evaluation of matrix-variate gamma and beta integrals, the procedure can also be applied to evaluate such integrals explicitly in similar situations. Various methods described here will be useful to those who are working on integrals involving real-valued scalar functions of matrix argument in general and gamma and beta integrals in particular.
Published: 2016

3. A new fractional D2-brane, G2 holonomy and T-duality

Author: Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA, DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, UK, Center for Theoretical Physics, Texas A&M University, College Station, TX 77843, USA, Ann Arbor, Cvetic, M., Gibbons, G. W., Liu, James T., Lü, H., Pope, C. N., Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA, DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, UK, Center for Theoretical Physics, Texas A&M University, College Station, TX 77843, USA, Ann Arbor, Cvetic, M., Gibbons, G. W., Liu, James T., Lü, H., and Pope, C. N.
Abstract: Recently, a new example of a complete non-compact Ricci-flat metric of G2 holonomy was constructed, which has an asymptotically locally conical structure at infinity with a circular direction whose radius stabilizes. In this paper, we find a regular harmonic 3-form in this metric, which we then use in order to obtain an explicit solution for a fractional D2-brane configuration. By performing a T-duality transformation on the stabilized circle, we obtain the type IIB description of the fractional brane, which now corresponds to a D3-brane with one of its worldvolume directions wrapped around the circle.
Published: 2006

4. A Variational Model Dedicated to Joint Segmentation, Registration, and Atlas Generation for Shape Analysis

Author: Carola-Bibiane Schönlieb, Carole Le Guyader, M. Romanchikova, John A. D. Aston, Fabien Bonardi, Noémie Debroux, Alistair B. Forbes, Institut Pascal (IP), SIGMA Clermont (SIGMA Clermont)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), University of Cambridge [UK] (CAM), Informatique, BioInformatique, Systèmes Complexes (IBISC), Université d'Évry-Val-d'Essonne (UEVE)-Université Paris-Saclay, National Physical Laboratory [Teddington] (NPL), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Statslab, Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, and Apollo - University of Cambridge Repository
Subjects: D m -splines, Computer science, General Mathematics, Population, 02 engineering and technology, Ogden materials, geometric PCA AMS subject classifications. 68U10, 4603 Computer Vision and Multimedia Computation, atlas generation, asymptotic results, symbols.namesake, Segmentation, 46 Information and Computing Sciences, registration, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Potts model, 62H25, Mathematics - Numerical Analysis, education, education.field_of_study, nonlinear elasticity, 65D18, business.industry, Applied Mathematics, Numerical analysis, Linear space, Pattern recognition, Numerical Analysis (math.NA), Computer Science::Computer Vision and Pattern Recognition, Principal component analysis, Jacobian matrix and determinant, symbols, 020201 artificial intelligence & image processing, Artificial intelligence, business, 41A15, Shape analysis (digital geometry)
Abstract: International audience; In medical image analysis, constructing an atlas, i.e. a mean representative of an ensemble of images, is a critical task for practitioners to estimate variability of shapes inside a population, and to characterise and understand how structural shape changes have an impact on health. This involves identifying significant shape constituents of a set of images, a process called segmentation, and mapping this group of images to an unknown mean image, a task called registration, making a statistical analysis of the image population possible. To achieve this goal, we propose treating these operations jointly to leverage their positive mutual influence, in a hyperelasticity setting, by viewing the shapes to be matched as Ogden materials. The approach is complemented by novel hard constraints on the L ∞ norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism. Segmentation is based on the Potts model, which allows for a partition into more than two regions, i.e. more than one shape. The connection to the registration problem is ensured by the dissimilarity measure that aims to align the segmented shapes. A representation of the deformation field in a linear space equipped with a scalar product is then computed in order to perform a geometry-driven Principal Component Analysis (PCA) and to extract the main modes of variations inside the image population. Theoretical results emphasizing the mathematical soundness of the model are provided, among which existence of minimisers, analysis of a numerical method, asymptotic results and a PCA analysis, as well as numerical simulations demonstrating the ability of the model to produce an atlas exhibiting sharp edges, high contrast and a consistent shape.
Published: 2020
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5. On an integral identity

Author: Fernando Chamizo, Mikael Persson Sundqvist, Alin Bostan, Symbolic Special Functions : Fast and Certified (SPECFUN), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidad Autonoma de Madrid (UAM), Centre for Mathematical Sciences, Lund University, Centre for Mathematical Sciences, ANR-19-CE40-0018,DeRerumNatura,Décider l'irrationalité et la transcendance(2019), and Universidad Autónoma de Madrid (UAM)
Subjects: [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Mathematics - Number Theory, Generalization, General Mathematics, 010102 general mathematics, Mathematics::Classical Analysis and ODEs, Irrationality, 010103 numerical & computational mathematics, Bivariate analysis, 16. Peace & justice, Mathematical proof, 01 natural sciences, Algebra, Identity (mathematics), [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Number theory, Mathematics - Classical Analysis and ODEs, Elementary proof, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Computer Science::Symbolic Computation, Number Theory (math.NT), 0101 mathematics, Hypergeometric function, Mathematics
Abstract: We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a generalization together with an equally elementary proof and discuss some consequences., Comment: 6 pages
Published: 2020
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6. High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat

Author: Herbert Spohn, Tomasz Komorowski, Lenya Ryzhik, Stefano Olla, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Department of Mathematics [Stanford], Stanford University, Centre fo Mathematical Sciences (D-MUTU-ZM), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), This work was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund., ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Stanford University [Stanford], Technische Universität München [München] (TUM), ANR-15-CE40-0020,LSD,Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics(2015), CEntre de REcherches en MAthématiques de la DEcision ( CEREMADE ), Université Paris-Dauphine-Centre National de la Recherche Scientifique ( CNRS ), Centre fo Mathematical Sciences ( D-MUTU-ZM ), Technische Universität München [München] ( TUM ), and ANR-15-CE40-0020,LSD,Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics ( 2015 )
Subjects: 82C21, Complex system, FOS: Physical sciences, 01 natural sciences, law.invention, Mathematics (miscellaneous), Chain (algebraic topology), law, Computer Science::Systems and Control, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Wigner distribution, Limit (music), Langevin thermostats, FOS: Mathematics, Wigner distribution function, 0101 mathematics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], energy transport, Harmonic oscillator, Mathematical Physics, Condensed Matter - Statistical Mechanics, Physics, Statistical Mechanics (cond-mat.stat-mech), Scattering, Mechanical Engineering, 010102 general mathematics, Probability (math.PR), [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph], Mathematical Physics (math-ph), High frequency limit, Thermostat, 010101 applied mathematics, Nonlinear Sciences::Chaotic Dynamics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Quantum electrodynamics, Condensed Matter::Statistical Mechanics, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Analysis, Energy (signal processing), Mathematics - Probability
Abstract: International audience; We consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat at the origin. In the high frequency limit, we establish the reflection-transmission coefficients for the wave energy for the scattering of the thermostat. To our surprise, even though the thermostat fluctuations are time-dependent, the scattering does not couple wave energy at various frequencies.
Published: 2020
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7. Regularized Contextual Bandits

Author: Fontaine, Xavier, Berthet, Quentin, Perchet, Vianney, Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Criteo AI Lab, Criteo [Paris], and Fontaine, Xavier
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Machine Learning (stat.ML), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract: We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy which is known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting the context space into bins, and solving simultaneously - and independently - regularized multi-armed bandit instances on each bin. We derive slow and fast rates of convergence, depending on the unknown complexity of the problem. We also consider a new relevant margin condition to get problem-independent convergence rates, ending up in intermediate convergence rates interpolating between the aforementioned slow and fast rates., Comment: AISTATS 2019, 23 pages, 2 figures
Published: 2019

8. Large time behavior of the Vlasov-Navier-Stokes system on the torus

Author: Iván Moyano, Ayman Moussa, Daniel Han-Kwan, Centre de Mathématiques Laurent Schwartz (CMLS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and ANR-19-CE40-0004,SALVE,Singularités dans des limites asymptotiques d'équations de Vlasov(2019)
Subjects: Physics, Mechanical Engineering, Dirac (video compression format), 010102 general mathematics, Mathematical analysis, Complex system, Structure (category theory), Mathematics::Analysis of PDEs, Torus, Type (model theory), 01 natural sciences, Exponential function, 010101 applied mathematics, Mathematics (miscellaneous), Distribution function, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Analysis, Energy (signal processing), Analysis of PDEs (math.AP)
Abstract: International audience; We study the large time behavior of Fujita–Kato type solutions to the Vlasov–Navier–Stokes system set on $\T^3 \times \R^3$. Under the assumption that the initial so-called modulated energy is small enough, we prove that the distribution function converges to a Dirac mass in velocity, with exponential rate. The proof is based on the fine structure of the system and on a bootstrap analysis allowing us to get global bounds on moments.
Published: 2019
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9. Spectral Inequalities for the Schrödinger operator

Author: Lebeau, Gilles, Moyano, Iván, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), and University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)
Subjects: Mathematics - Analysis of PDEs, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Mathematics::Spectral Theory
Abstract: In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schr\"odinger operator in $ \mathbb{R}^d$ \begin{equation*} H_{g,V} = \Delta_g + V(x), \end{equation*} where $\Delta_g$ is the Laplace-Beltrami operator with respect to an analytic metric $g$, which is a perturbation of the Euclidean metric, and $V(x)$ a real valued analytic potential vanishing at infinity.
Published: 2019

10. Quantitative Rates of Convergence to Equilibrium for the Degenerate Linear Boltzmann equation on the Torus

Author: Evans, Josephine, Moyano, Iván, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and ANR-17-CE40-0030,EFI,Entropie, flots, inégalités(2017)
Subjects: Mathematics - Analysis of PDEs, Probability (math.PR), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], FOS: Physical sciences, Mathematical Physics (math-ph), [MATH]Mathematics [math], Mathematical Physics, Mathematics - Probability, Analysis of PDEs (math.AP)
Abstract: We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In \cite{BS13} Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump rate satisfies the geometric control condition of Bardos, Lebeau and Rauch \cite{BLR91}. In \cite{HL15} Han-Kwan and L\'{e}autaud showed a more general result for linear Boltzmann equations under the action of potentials in different geometric contexts, including the case of unbounded velocities. In this paper we obtain quantitative rates of convergence to equilibrium when the geometric control condition is satisfied, using a probabilistic approach based on Doeblin's theorem from Markov chains., Comment: 22 pages
Published: 2019
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11. (dual-frequency)-dependent dynamic functional connectivity analysis of visual working memory capacity

Author: John Aston, Dominique Dehay, Dudek, Anna E., Jean-Marc Freyermuth, Denes Szucs, Lincoln Colling, Freyermuth, Jean-Marc, University of Cambridge [UK] (CAM), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), AGH University of Science and Technology [Krakow, PL] (AGH UST), Aix Marseille Université (AMU), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Published: 2019

12. FINITE-TIME STABILIZATION OF AN OVERHEAD CRANE WITH A FLEXIBLE CABLE

Author: D'Andréa-Novel , Brigitte, Moyano , Iván, Rosier , Lionel, Analyse et synthèse sonores [Paris], Sciences et Technologies de la Musique et du Son ( STMS ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -IRCAM-Centre National de la Recherche Scientifique ( CNRS ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -IRCAM-Centre National de la Recherche Scientifique ( CNRS ), Centre de Robotique ( CAOR ), MINES ParisTech - École nationale supérieure des mines de Paris-PSL Research University ( PSL ), Statistical Laboratory ( DPMMS ), University of Cambridge [UK] ( CAM ), Centre Automatique et Systèmes ( CAS ), MathAmSud project Icops, Centre de Robotique (CAOR), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Sound Systems and Signals: Audio/Acoustics, InstruMents (S3AM), Sciences et Technologies de la Musique et du Son (STMS), Institut de Recherche et Coordination Acoustique/Musique (IRCAM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche et Coordination Acoustique/Musique (IRCAM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and Centre Automatique et Systèmes (CAS)
Subjects: nonlinear feedback law, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], PDE-ODE system, nonlinear semigroups, Finite-time stability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], wave equation, 93C20, 93D15, transparent boundary conditions
Abstract: The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear feedback law inspired by those given by Haimo in [12] for a second-order ODE, we prove that a finite-time stabilization occurs for the full system platform + cable. The global well-posedness of the system is also established by using the theory of nonlinear semigroups.
Published: 2018

13. Comparison between five acellular oxidative potential measurement assays performed with detailed chemistry on PM10 samples from the city of Chamonix (France)

Author: Calas , Aude, Uzu , Gaëlle, Kelly , Frank, Houdier , Stephan, Martins , Jean, Thomas , Fabrice, Molton , Florian, CHARRON , Aurélie, Dunster , Christina, Oliete , Ana, Jacob , Véronique, Besombes , Jean-Luc, Chevrier , Florie, Jaffrezo , Jean-Luc, Institut des Géosciences de l’Environnement (IGE), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut de Recherche pour le Développement (IRD)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), MRC -PHE Centre for Environment & Health, Département de Chimie Moléculaire - Chimie Inorganique Redox Biomimétique (DCM - CIRE ), Département de Chimie Moléculaire (DCM), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Français des Sciences des Transports, de l'Aménagement et des Réseaux (IFSSTAR), IFSSTAR, Laboratoire de Chimie Moléculaire et Environnement (LCME), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut de Recherche pour le Développement (IRD)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Département de Chimie Moléculaire - Chimie Inorganique Redox (DCM - CIRE ), Laboratoire Ecologie Fonctionnelle et Environnement (ECOLAB), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Observatoire Midi-Pyrénées (OMP), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Laboratoire Transports et Environnement (IFSTTAR/AME/LTE), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon, Institut des Géosciences de l’Environnement ( IGE ), Institut de Recherche pour le Développement ( IRD ) -Institut polytechnique de Grenoble - Grenoble Institute of Technology ( Grenoble INP ) -Institut national des sciences de l'Univers ( INSU - CNRS ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Département de Chimie Moléculaire - Chimie Inorganique Redox Biomimétique ( DCM - CIRE ), Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut de Chimie Moléculaire de Grenoble (ICMG)-Centre National de la Recherche Scientifique ( CNRS ), Département de Chimie Moléculaire ( DCM ), Université Joseph Fourier - Grenoble 1 ( UJF ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Institut Français des Sciences des Transports, de l'Aménagement et des Réseaux ( IFSSTAR ), Laboratoire de Chimie Moléculaire et Environnement ( LCME ), Université Grenoble Alpes [Saint Martin d'Hères]-Université Savoie Mont Blanc ( USMB [Université de Savoie] [Université de Chambéry] ), Laboratoire Ecologie Fonctionnelle et Environnement (LEFE), Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Observatoire Midi-Pyrénées (OMP), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université de Toulouse (UT)
Subjects: [ SDE ] Environmental Sciences, [SDE]Environmental Sciences, [CHIM]Chemical Sciences, [ CHIM ] Chemical Sciences, GEOF
Abstract: International audience; Many studies have demonstrated associations between exposure to ambient particulate matter (PM) and adverse health outcomes in humans that can be explained by PM capacity to induce oxidative stress in vivo. Thus, assays have been developed to quantify the oxidative potential (OP) of PM as a more refined exposure metric than PM mass alone. Only a small number of studies have compared different acellular OP measurements for a given set of ambient PM samples. Yet, fewer studies have compared different assays over a year-long period and with detailed chemical characterization of ambient PM. In this study, we report on seasonal variations of the dithiothreitol (DTT), ascorbic acid (AA), electron spin resonance (ESR) and the respiratory tract lining fluid (RTLF, composed of the reduced glutathione (GSH) and ascorbic acid (ASC)) assays over a 1-year period in which 100 samples were analyzed. A detailed PM 10 characterization allowed univariate and multivariate regression analyses in order to obtain further insight into groups of chemical species that drive OP measurements. Our results show that most of the OP assays were strongly intercorrelated over the sampling year but also these correlations differed when considering specific sampling periods (cold vs. warm). All acellular assays are correlated with a significant number of chemical species when considering univariate correlations , especially for the DTT assay. Evidence is also presented of a seasonal contrast over the sampling period with significantly higher OP values during winter for the DTT, AA, GSH and ASC assays, which were assigned to biomass burning species by the multiple linear regression models. The ESR assay clearly differs from the other tests as it did not show seasonal dynamics and presented weaker correlations with other assays and chemical species.
Published: 2018
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14. Diffusion in small time in incomplete sub-Riemannian manifolds

Author: Bailleul, Ismael, Norris, James, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Apollo - University of Cambridge Repository, INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), ANR-16-CE40-0020,SINGULAR,Equations aux dérivées partielles singulières(2016), Division of Medical Chemistry and Natural Products, UNC Eshelman School of Pharmacy, and Center for Integrative Chemical Biology and Drug Discovery
Subjects: Mathematics - Differential Geometry, Numerical Analysis, Applied Mathematics, diffusion, Probability (math.PR), sub-Riemannian, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Analysis of PDEs, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], heat kernel, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], Mathematics - Probability, Analysis, Analysis of PDEs (math.AP)
Abstract: For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and transition probabilities, with optimal constant in the exponent. Under similar conditions, we obtain the small-time logarithmic asymptotics of the heat kernel, and show concentration of diffusion bridge measures near a path of minimal energy. The first condition requires that we consider points whose distance apart is no greater than the sum of their distances to infinity. The second condition requires only that the operator not be too asymmetric., Comment: Accepted version
Published: 2018
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15. Fast and stable schemes for non-linear osmosis filtering

Author: Calatroni, L., Morigi, S., Parisotto, S., Recupero, G. A., Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), and University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)
Subjects: Computational Mathematics, Computational Theory and Mathematics, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Modeling and Simulation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Numerical Analysis, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 68U10, 94A08, 49K20, 65M05, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general scalar function g with suitable properties, which allows to balance the diffusion intensity on the different regions of the image while preventing smoothing artefacts. For the proposed model, conservation properties (intensity and non-negativity) are proved and a variational interpretation is showed for specific choices of g. Upon suitable spatial discretisation, both an explicit and a semi-implicit iterative scheme are considered, for which convergence restrictions and unconditional stability are proved, respectively. To validate the proposed modelling and the computational speed of the numerical schemes considered, we report several results and comparisons for the problem of shadow/light-spot removal and compact data representation, showing that artefact-free and computationally efficient results are obtained in comparison to standard linear and anisotropic models, and state-of-the art approaches., Comment: 25 pages, 14 figures
Published: 2023
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16. Uniform Stability of a Particle Approximation of the Optimal Filter Derivative

Author: Arnaud Doucet, Sumeetpal S. Singh, Pierre Del Moral, Department of Statistics [Oxford], University of Oxford [Oxford], Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), University of Cambridge [UK] (CAM), Inria & Labri, Univ. Bordeaux, Apollo - University of Cambridge Repository, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: FOS: Computer and information sciences, Control and Optimization, Mathematics - Statistics Theory, Statistics Theory (math.ST), Derivative, sequential Monte Carlo, state-space models, Statistics - Computation, Stability (probability), Methodology (stat.ME), FOS: Mathematics, recursive maximum likelihood, Applied mathematics, Computation (stat.CO), Statistics - Methodology, ComputingMilieux_MISCELLANEOUS, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Signal processing, hidden Markov models, Estimation theory, Applied Mathematics, smoothing, Filter (signal processing), Statistics::Computation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, filter derivative, Particle filter, Smoothing
Abstract: Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.
Published: 2015
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17. Diffusivity of a random walk on random walks

Author: Serge Cohen, Thibault Espinasse, James Norris, Emmanuel Boissard, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Random graph, Discrete mathematics, Heterogeneous random walk in one dimension, Applied Mathematics, General Mathematics, Probability (math.PR), Central limit theorem, Loop-erased random walk, Random element, Random walk, 05C81, 60F05, Computer Graphics and Computer-Aided Design, Graph, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Combinatorics, Mathematics::Probability, Lévy flight, FOS: Mathematics, Quantum walk, Mathematics - Probability, ComputingMilieux_MISCELLANEOUS, Software, Self-avoiding walk, Mathematics
Abstract: We consider a random walk Zn1,',ZnK+1∈i¾?K+1 with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor i¾?K2=2K+2 with respect to the case of the classical simple random walk without constraint. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 267-283, 2015
Published: 2014
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18. Lozenge tiling dynamics and convergence to the hydrodynamic equation

Author: Benoit Laslier, Fabio Lucio Toninelli, University of Cambridge [UK] (CAM), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), CNRS PICS grant 'Interfaces al ́eatoires discr`etes et dy-namiques de Glauber, and ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015)
Subjects: Physics, 010102 general mathematics, Probability (math.PR), Inverse, Statistical and Nonlinear Physics, Function (mathematics), 01 natural sciences, Parabolic partial differential equation, Projection (linear algebra), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Bernoulli's principle, FOS: Mathematics, Heat equation, Differentiable function, 0101 mathematics, Langevin dynamics, Mathematical Physics, ComputingMilieux_MISCELLANEOUS, Mathematics - Probability, Mathematical physics
Abstract: We study a reversible continuous-time Markov dynamics of a discrete $(2+1)$-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times L$ torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in [Luby-Randall-Sinclair]: in terms of interlaced particles, a particle jump of length $n$ that preserves the interlacement constraints has rate $1/(2n)$. This dynamics presents special features: the average mutual volume between two interface configurations decreases with time and a certain one-dimensional projection of the dynamics is described by the heat equation. In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as $L\to\infty$ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be $C^2$ differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model [Funaki-Spohn,Nishikawa], here the mobility coefficient turns out to be a non-trivial function of the interface slope., Comment: 35 pages, 7 figures. v3: a few more typos corrected, remark 2.8 added. To appear on Comm. Math. Phys
Published: 2017
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19. Hydrodynamic limit equation for a lozenge tiling Glauber dynamics

Author: Benoît Laslier, Fabio Lucio Toninelli, University of Cambridge [UK] (CAM), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Probabilités, statistique, physique mathématique (PSPM), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)
Subjects: Physics, Nuclear and High Energy Physics, Markov chain, Plane (geometry), Probability (math.PR), 010102 general mathematics, Mathematical analysis, FOS: Physical sciences, Statistical and Nonlinear Physics, Hamming distance, Mathematical Physics (math-ph), 01 natural sciences, Parabolic partial differential equation, Square (algebra), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, Limit (mathematics), 0101 mathematics, Balanced flow, ComputingMilieux_MISCELLANEOUS, Mathematics - Probability, Mathematical Physics
Abstract: We study a reversible continuous-time Markov dynamics on lozenge tilings of the plane, introduced by Luby et al. Single updates consist in concatenations of $n$ elementary lozenge rotations at adjacent vertices. The dynamics can also be seen as a reversible stochastic interface evolution. When the update rate is chosen proportional to $1/n$, the dynamics is known to enjoy especially nice features: a certain Hamming distance between configurations contracts with time on average and the relaxation time of the Markov chain is diffusive, growing like the square of the diameter of the system. Here, we present another remarkable feature of this dynamics, namely we derive, in the diffusive time scale, a fully explicit hydrodynamic limit equation for the height function (in the form of a non-linear parabolic PDE). While this equation cannot be written as a gradient flow w.r.t. a surface energy functional, it has nice analytic properties, for instance it contracts the $\mathbb L^2$ distance between solutions. The mobility coefficient $\mu$ in the equation has non-trivial but explicit dependence on the interface slope and, interestingly, is directly related to the system's surface free energy. The derivation of the hydrodynamic limit is not fully rigorous, in that it relies on an unproven assumption of local equilibrium., Comment: 31 pages, 8 figures. v2: typos corrected, some proofs clarified. To appear on Annales Henri Poincare
Published: 2016
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20. Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

Author: Mariana Haragus, Erik Wahlén, Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Centre for Mathematical Sciences, Lund University, Centre for Mathematical Sciences, and ANR-13-BS01-0009,BoND,Frontières, numérique, dispersion.(2013)
Subjects: Transverse instability, media_common.quotation_subject, FOS: Physical sciences, 35Q53 (Primary) 76B15, 76B25, 35B35, 35P15 (Secondary), Pattern Formation and Solitons (nlin.PS), 01 natural sciences, Instability, Mathematics - Analysis of PDEs, generalized solitary waves, dispersive equations, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Spectral analysis, transverse stability, 0101 mathematics, periodic waves, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical Physics, media_common, Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Order (ring theory), Mathematical Physics (math-ph), Infinity, Nonlinear Sciences - Pattern Formation and Solitons, 010101 applied mathematics, Classical mechanics, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Line (geometry), Mechanical wave, Analysis, Longitudinal wave, Analysis of PDEs (math.AP)
Abstract: We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators., To appear in Journal of Differential Equations
Published: 2016

21. From the seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994. Gibbs random fields on the lattice. Definitions, existence, uniqueness

Author: Yuri Suhov, Semen Bensionovich Shlosman, S. A. Pirogov, Robert Minlos, Eugene Pechersky, Inst. of the Information Transmission Problems (IITP RAS), Russian Academy of Sciences [Moscow] (RAS), CPT - E5 Physique statistique et systèmes complexes, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), and University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)
Subjects: Physics, Gibbs random fields, Lattice (order), [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], 010102 general mathematics, 0103 physical sciences, General Physics and Astronomy, 010307 mathematical physics, Uniqueness, Statistical physics, 0101 mathematics, 01 natural sciences, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2012
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22. A note on dimers and T-graphs

Author: Berestycki, Nathanael, Laslier, Benoît, Ray, Gourab, University of Cambridge [UK] (CAM), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and Laslier, Benoit
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Probability
Abstract: The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation between the dimer model on the heaxgonal lattice with a given slope, and the behaviour of the uniform spanning tree on the associated T-graph. Together with the main result of the companion paper \cite{BLR16}, the results here show Gaussian free field fluctuations for the height function in some dimer models.
Published: 2016
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23. Simple regret for infinitely many armed bandits

Author: Alexandra Carpentier, Valko, M., Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Sequential Learning (SEQUEL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and ANR-14-CE24-0010,ExTra-Learn,Extraction et transfert de connaissances dans l'apprentissage par renforcement(2014)
Subjects: FOS: Computer and information sciences, Computer Science::Machine Learning, Computer Science - Learning, Statistics::Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract: We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous algorithms for this setting were designed for minimizing the cumulative regret of the learner. In this paper, we propose an algorithm aiming at minimizing the simple regret. As in the cumulative regret setting of infinitely many armed bandits, the rate of the simple regret will depend on a parameter $\beta$ characterizing the distribution of the near-optimal arms. We prove that depending on $\beta$, our algorithm is minimax optimal either up to a multiplicative constant or up to a $\log(n)$ factor. We also provide extensions to several important cases: when $\beta$ is unknown, in a natural setting where the near-optimal arms have a small variance, and in the case of unknown time horizon., Comment: in 32th International Conference on Machine Learning (ICML 2015)
Published: 2015

24. On a Bubble algorithm for the cubic Nonlinear Schrödinger equation

Author: Faou, Erwan, Le Henaff, Yoann, Raphaël, Pierre, Multi-scale numerical geometric schemes (MINGUS), École normale supérieure - Rennes (ENS Rennes)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes (IRMAR), Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and PI ERC/UKRI advanced grant SWAT,Associated team INRIA-University of Cambridge: Bubbles
Subjects: Mathematics - Analysis of PDEs, Soliton, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Bubbles, numerical Dirac-Frenkel, Schrödinger, dynamical system, 35C08, 65M22, 37M15, 35Q41, Analysis of PDEs (math.AP)
Abstract: Based on very recent and promising ideas, stemming from the use of bubbles, we discuss an algorithm for the numerical simulation of the cubic nonlinear Schr{\"o}dinger equation with harmonic potential (cNLS) in any dimension, that could easily be extended to other polynomial nonlinearities. This algorithm consists in discretizing the initial function as a sum of modulated complex gaussian functions (the bubbles), each one having its own set of parameters, and then updating the parameters according to cNLS. Numerically, we solve exactly the linear part of the equation and use the Dirac-Frenkel-MacLachlan principle to approximate the nonlinear part. We then obtain a grid free algorithm in any dimension whose efficiency compared with spectral methods is illustrated by numerical examples.
Published: 2023

25. Extreme bandits

Author: Alexandra Carpentier, Valko, M., Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Sequential Learning (SEQUEL), Laboratoire d'Informatique Fondamentale de Lille (LIFL), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), and Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)
Subjects: [STAT.ML]Statistics [stat]/Machine Learning [stat.ML]
Abstract: International audience; In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under limited feedback. While sequential design of experiments is well studied in bandit theory, the most commonly optimized property is the regret with respect to the maximum mean reward. However, in other problems such as network intrusion detection, we are interested in detecting the most extreme value output by the sources. Therefore, in our work we study extreme regret which measures the efficiency of an algorithm compared to the oracle policy selecting the source with the heaviest tail. We propose the ExtremeHunter algorithm, provide its analysis, and evaluate it empirically on synthetic and real-world experiments.
Published: 2014

26. Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes

Author: Chambolle, Antonin, Delplancke, Claire, Ehrhardt, Matthias, Schönlieb, Carola-Bibiane, Tang, Junqi, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), EDF R&D (EDF R&D), EDF (EDF), Department of Mathematical Sciences [Bath], University of Bath [Bath], Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), School of Mathematics [Birmingham], University of Birmingham [Birmingham], MJE acknowledges support from the EPSRC (EP/S026045/1, EP/T026693/1, EP/V026259/1) and the Leverhulme Trust (ECF-2019-478)., and CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC advanced career fellowship EP/V029428/1, EPSRC grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute.
Subjects: 47N10, 49J40, 65D18, 65K10, 90C06, 90C15, 90C25, 92C55, 94A08, Optimization and Control (math.OC), FOS: Mathematics, [MATH]Mathematics [math], Mathematics - Optimization and Control
Abstract: In this work we propose a new primal-dual algorithm with adaptive step-sizes. The stochastic primal-dual hybrid gradient (SPDHG) algorithm with constant step-sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step-sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step-sizes is critical in applications. Up-to-now there is no systematic and successful way of selecting the primal and dual step-sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms, and prove their convergence under weak assumptions. We also propose concrete parameters-updating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes., 28 pages, 8 figures
Published: 2023

27. Stochastic Simultaneous Optimistic Optimization

Author: Valko, M., Alexandra Carpentier, Munos, R., Sequential Learning (SEQUEL), Laboratoire d'Informatique Fondamentale de Lille (LIFL), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), European Project: 270327,EC:FP7:ICT,FP7-ICT-2009-6,COMPLACS(2011), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: [STAT.ML]Statistics [stat]/Machine Learning [stat.ML]
Abstract: International audience; We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.
Published: 2013

28. Nonexplosion criteria for relativistic diffusions

Author: Jacques Franchi, Ismael Bailleul, Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Agence Nationale de la Recherche, n° ANR-09-BLAN-0364-01, et EPSRC grant EP/E01772X/1., I. Bailleul - J. Franchi, and ProbaGeo, ANR-09-BLAN-0364-01,ProbaGeo, ANR-09-BLAN-0364-01
Subjects: Statistics and Probability, 83C99, General relativity, 83C10, Lorentz transformation, FOS: Physical sciences, nonexplosion criterion, Curvature, 01 natural sciences, Volume growth, 010104 statistics & probability, symbols.namesake, Mathematics::Probability, FOS: Mathematics, Covariant transformation, 0101 mathematics, Mathematical Physics, Mathematical physics, Mathematics, Primary 58J65, secondary 53C50, 83C10, 83C99, Probability (math.PR), 53C50, 010102 general mathematics, Subriemannian minimal time, Mathematical Physics (math-ph), 58J65, Physics::History of Physics, Manifold, Non-explosion criterion, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Relativistic diffusions, symbols, Statistics, Probability and Uncertainty, Mathematics - Probability, Stochastic completeness
Abstract: Some general Lorentz covariant operators, associated to the so-called \Theta (or \Xi)-relativistic diffusions and making sense in any Lorentzian manifold, have been introduced by Franchi and Le Jan [Comm. Pure Appl. Math. 60 (2007) 187-251], Franchi and Le Jan [Curvature diffusions in general relativity (2010). Unpublished manuscript]. Only a few examples have been studied so far. We provide in this work some nonexplosion criteria for these diffusions, which can be used in generic cases., Comment: Published in at http://dx.doi.org/10.1214/11-AOP672 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Published: 2012
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29. Online allocation and homogeneous partitioning for piecewise constant mean-approximation

Author: Maillard, Odalric-Ambrym, Carpentier, Alexandra, Montanuniversität Leoben (MUL), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and Maillard, Odalric-Ambrym
Subjects: Active sampling, Histograms, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Multi-armed bandits, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML]
Abstract: 22; In the setting of active learning for the multi-armed bandit, where the goal of a learner is to estimate with equal precision the mean of a finite number of arms, recent results show that it is possible to derive strategies based on finite-time confidence bounds that are competitive with the best possible strategy. We here consider an extension of this problem to the case when the arms are the cells of a finite partition P of a continuous sampling space X \subset \Real^d. Our goal is now to build a piecewise constant approximation of a noisy function (where each piece is one region of P and P is fixed beforehand) in order to maintain the local quadratic error of approximation on each cell equally low. Although this extension is not trivial, we show that a simple algorithm based on upper confidence bounds can be proved to be adaptive to the function itself in a near-optimal way, when |P| is chosen to be of minimax-optimal order on the class of \alpha-Hölder functions.
Published: 2012

30. Some discussions of D. Fearnhead and D. Prangle's Read Paper 'Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation'

Author: Christophe Andrieu, Simon Barthelme, Nicolas Chopin, Julien Cornebise, Arnaud Doucet, Mark Girolami, Ioannis Kosmidis, Ajay Jasra, Anthony Lee, Jean-Michel Marin, Pierre Pudlo, Christian Robert, Mohammed Sedki., Singh, Sumeetpal S., Department of Mathematics [Bristol], University of Bristol [Bristol]-University Walk, Technische Universität Berlin (TU), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), Department of Statistical Science, University College of London [London] (UCL), Department of Computing [London], Biomedical Image Analysis Group [London] (BioMedIA), Imperial College London-Imperial College London, Department of Statistics [Oxford], University of Oxford [Oxford], Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and Robert, Christian
Subjects: stat.CO, Methodology (stat.ME), FOS: Computer and information sciences, [STAT.ME] Statistics [stat]/Methodology [stat.ME], stat.ME, [STAT.CO]Statistics [stat]/Computation [stat.CO], [STAT.CO] Statistics [stat]/Computation [stat.CO], [STAT.ME]Statistics [stat]/Methodology [stat.ME], Statistics - Computation, Computation (stat.CO), Statistics - Methodology
Abstract: This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors., 10 pages
Published: 2012

31. From the seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994. Contour technics

Author: E. Dinaburg, Semen Bensionovich Shlosman, S. A. Pirogov, Eugene Pechersky, Yuri Suhov, Inst. of the Information Transmission Problems (IITP RAS), Russian Academy of Sciences [Moscow] (RAS), CPT - E5 Physique statistique et systèmes complexes, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), and University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)
Subjects: Physics, 010104 statistics & probability, 010102 general mathematics, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Calculus, General Physics and Astronomy, State (computer science), 0101 mathematics, 01 natural sciences, Engineering physics, History of science, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2012
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32. SCOTCH and SODA: A Transformer Video Shadow Detection Framework

Author: Liu, Lihao, Prost, Jean, Zhu, Lei, Papadakis, Nicolas, Liò, Pietro, Schönlieb, Carola-Bibiane, Aviles-Rivero, Angelica I, Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Electronic and Computer Engineering Department [Hong Kong] (ECE), Hong Kong University of Science and Technology (HKUST), and European Project: 777826,NoMADS(2018)
Subjects: FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]
Abstract: Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliu-cambridge.github.io/scotch_and_soda/, Accepted to CVPR 2023
Published: 2022

33. Microscopic observation of two-level systems in a metallic glass model

Author: Felix C. Mocanu, Ludovic Berthier, Simone Ciarella, Dmytro Khomenko, David R. Reichman, Camille Scalliet, Francesco Zamponi, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Laboratoire Charles Coulomb (L2C), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Dipartimento di Fisica [Roma La Sapienza], Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome] (UNIROMA), Columbia University [New York], Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), and European Project: 723955,GlassUniversality
Subjects: [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], General Physics and Astronomy, FOS: Physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Disordered Systems and Neural Networks (cond-mat.dis-nn), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Physical and Theoretical Chemistry, Computational Physics (physics.comp-ph), Condensed Matter - Disordered Systems and Neural Networks, Physics - Computational Physics
Abstract: The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements., 17 pages, 12 figures
Published: 2022
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34. A Historical Law of Large Numbers for the Marcus-Lushnikov Process

Author: Stéphanie Jacquot, Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), INRIA Bordeaux - Sud-Ouest, and SESSION 03 : Processus de branchement en dynamique des populations
Subjects: Statistics and Probability, 60B10, Distribution (number theory), Smoluchowski coagulation equation, tightness, 01 natural sciences, Combinatorics, 010104 statistics & probability, symbols.namesake, 60J25, Law of large numbers, 60B05, Statistical physics, Limit (mathematics), coupling, Physics::Chemical Physics, 0101 mathematics, Marcus-Lushnikov process on trees, Mathematics, Particle system, limit measure on trees, 010102 general mathematics, Empirical distribution function, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, Particle, historical trees, 60F15, Tree (set theory), Statistics, Probability and Uncertainty
Abstract: The Marcus-Lushnikov process is a finite stochastic particle system, in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$. Under certain assumptions, this process converges to the solution to the Smoluchowski coagulation equation, as the number of particles increases to infinity. The Marcus-Lushnikov process gives at each time the distribution of masses of the particles present in the system, but does not retain the history of formation of the particles. In this paper, we set up a historical analogue of the Marcus-Lushnikov process (built according to the rules of construction of the usual Markov-Lushnikov process) each time giving what we call the historical tree of a particle. The historical tree of a particle present in the Marcus-Lushnikov process at a given time t encodes information about the times and masses of the coagulation events that have formed that particle. We prove a law of large numbers for the empirical distribution of such historical trees. The limit is a natural measure on trees which is constructed from a solution to the Smoluchowski coagulation equation.
Published: 2010
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35. Almost All F-Free Graphs Have The Erdos-Hajnal Property

Author: Bruce Reed, Stéphan Thomassé, Martin Loebl, Alex Scott, Andrew Thomason, Department of Applied Mathematics (KAM) (KAM), Univerzita Karlova v Praze, Mathematical Institute [Oxford] (MI), University of Oxford, Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Algorithmes, Graphes et Combinatoire (ALGCO), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), University of Oxford [Oxford], Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), and École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL)
Subjects: Discrete mathematics, 010102 general mathematics, Induced subgraph, 0102 computer and information sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 16. Peace & justice, 01 natural sciences, Degeneracy (graph theory), Combinatorics, Rado graph, 010201 computation theory & mathematics, Graph power, Triangle-free graph, Split graph, 0101 mathematics, Forbidden graph characterization, Mathematics, Universal graph
Abstract: International audience; Erdős and Hajnal conjectured that, for every graph H, there exists a constant ɛ(H) > 0 such that every H-free graph G (that is, not containing H as an induced subgraph) must contain a clique or an independent set of size at least |G|ɛ( H). We prove that there exists ɛ(H) such that almost every H-ïvee graph G has this property, meaning that, amongst the if-free graphs with n vertices, the proportion having the property tends to one as n → ∞.
Published: 2010
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36. Prospects for GRB Science with the Fermi Large Area Telescope

Author: R. M. Kippen, Brenda Dingus, Sinéad McGlynn, Takashi Shimokawabe, Carmelo Sgrò, E. Moretti, Jonathan Granot, F. Kuehn, J. P. Norris, M. N. Mazziotta, P. D. Smith, R. E. Hughes, Nicola Omodei, M. Kuss, James Chiang, J. J. Russell, Felix Ryde, Jeffrey D. Scargle, P. Lubrano, N. Gehrels, E. Do Couto E Silva, P. Spinelli, Guido Barbiellini, Ryo Yamazaki, F. Longo, Brian L Winer, G. Bogaert, V. Pelassa, S. Cutini, V. Connaughton, F. Piron, Robert D. Preece, Matthew G. Baring, Takeshi Nakamori, Gerald J. Fishman, T. Kamae, N. Giglietto, Masanori Ohno, M. Razzano, P. M. Saz Parkinson, David L. Band, M. Olivo, Johann Cohen-Tanugi, F. de Palma, Magnus Axelsson, A. Galli, Gloria Spandre, Julie McEnery, Luca Baldini, Sylvain Guiriec, J. Bonnel, Elisabetta Bissaldi, M. Battelino, Denis Bastieri, Ronaldo Bellazzini, M. Stamatikos, N. Komin, Department of Zoology, University of Gothenburg (GU), CNR Institute of Atmospheric Sciences and Climate (ISAC), Consiglio Nazionale delle Ricerche (CNR), Astrophysique Interprétation Modélisation (AIM (UMR_7158 / UMR_E_9005 / UM_112)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Leprince-Ringuet (LLR), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Joint Center for Astrophysics/Physics Department University of Maryland, University of Maryland [College Park], University of Maryland System-University of Maryland System, Laboratoire de Physique Théorique et Astroparticules (LPTA), Université Montpellier 2 - Sciences et Techniques (UM2)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Bureau d'Économie Théorique et Appliquée (BETA), Institut National de la Recherche Agronomique (INRA)-Université de Strasbourg (UNISTRA)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Hansen Experimental Physics Laboratory (HEPL), Stanford University [Stanford], Kavli Institute for Particle Astrophysics and Cosmology (KIPAC), Stanford Linear Accelerator Center (SLAC), Institut d'Informatique et de Mathématiques Appliquées de Grenoble (IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Department of Chemistry [Waterloo], University of Waterloo [Waterloo], Statistical Laboratory (DPMMS), University of Cambridge [UK] (CAM), Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (INFN, Sezione di Trieste), National Institute for Nuclear Physics (INFN), Lunar and Planetary Laboratory [Tucson] (LPL), University of Arizona, NASA Goddard Space Flight Center (GSFC), Center for Research and Exploration in Space Science and Technology [GSFC] (CRESST), Stockholm Observatory Department of Astronomy, Stockholm University, Istituto Nazionale di Fisica Nucleare [Pisa] (INFN), Istituto Nazionale di Fisica Nucleare (INFN), Dipartimento di Fisica [Trieste], Università degli studi di Trieste = University of Trieste, Department of Physics and Astronomy [Houston], Rice University [Houston], Istituto Nazionale di Fisica Nucleare, Sezione di Padova (INFN, Sezione di Padova), Dipartimento di Fisica 'G. Galilei', Università degli Studi di Padova = University of Padua (Unipd), Department of Physics, Royal Institute of Technology (KTH), Max-Planck-Institut für Extraterrestrische Physik (MPE), Stanford University, SLAC National Accelerator Laboratory (SLAC), Hansen Experimental Physics Lab [Stanford] (HEPL), University of Alabama in Huntsville (UAH), Agenzia Spaziale Italiana (ASI), Istituto Nazionale di Fisica Nucleare, sezione di Bari (INFN, sezione di Bari), Dipartimento di Fisica 'M. Merlin' dell'Università e del Politecnico di Bari, Politecnico di Bari, Los Alamos National Laboratory (LANL), NASA Marshall Space Flight Center (MSFC), Istituto di Astrofisica Spaziale e Fisica cosmica - Roma (IASF-Roma), Istituto Nazionale di Astrofisica (INAF), University of Maryland System, Centre for Astrophysics Research [Hatfield], University of Hertfordshire [Hatfield] (UH), Department of Physics, Ohio State University, Laboratoire Aimé Cotton (LAC), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (INFN, Sezione di Perugia), Tokyo Institute of Technology [Tokyo] (TITECH), Department of Physics [Tokyo], Rikkyo University [Tokyo], Department of Physics and Astronomy [Denver], University of Denver, Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency [Sagamihara] (JAXA), Santa Cruz Institute for Particle Physics (SCIPP), University of California [Santa Cruz] (UC Santa Cruz), University of California (UC)-University of California (UC), NASA Ames Research Center (ARC), Center for Cosmology & AstroParticle Physics, Ohio State University [Columbus] (OSU), Department of Physics, The Ohio State University, Hiroshima Astrophysical Science Center, Hiroshima University, Department of Physical Sciences [Higashi-Hiroshima], The Fermi LAT Collaboration acknowledges support from a number of agencies and institutes for both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support from the Istituto Nazionale di Astrofisica in Italy for science analysis during the operations phase is also gratefully acknowledged., Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Université de Lorraine (UL)-Université de Strasbourg (UNISTRA)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), D. L., Band, M., Axelsson, L., Baldini, BARBIELLINI AMIDEI, Guido, M. G., Baring, D., Bastieri, M., Battelino, R., Bellazzini, Bissaldi, Elisabetta, G., Bogaert, J., Bonnell, J., Chiang, J., Cohen Tanugi, V., Connaughton, S., Cutini, F. d., Palma, B. L., Dingu, E. D. E., Silva, G., Fishman, A., Galli, N., Gehrel, N., Giglietto, J., Granot, S., Guiriec, R. E., Hughe, T., Kamae, N., Komin, F., Kuehn, M., Ku, Longo, Francesco, P., Lubrano, R. M., Kippen, M. N., Mazziotta, J. E., Mcenery, S., Mcglynn, Moretti, Elena, T., Nakamori, J. P., Norri, M., Ohno, M., Olivo, N., Omodei, V., Pelassa, F., Piron, R., Preece, M., Razzano, J. J., Russell, F., Ryde, P. M. S., Parkinson, J. D., Scargle, C., Sgro, T., Shimokawabe, P. D., Smith, G., Spandre, P., Spinelli, M., Stamatiko, B. L., Winer, and R., Yamazaki
Subjects: [PHYS.ASTR.HE]Physics [physics]/Astrophysics [astro-ph]/High Energy Astrophysical Phenomena [astro-ph.HE], [PHYS.ASTR.IM]Physics [physics]/Astrophysics [astro-ph]/Instrumentation and Methods for Astrophysic [astro-ph.IM], gamma rays: bursts, Astrophysics::High Energy Astrophysical Phenomena, FOS: Physical sciences, Fermi satellite, Astrophysics, 7. Clean energy, 01 natural sciences, High Energy Gamma-ray Astronomy, law.invention, Telescope, law, 0103 physical sciences, 010306 general physics, Instrumentation and Methods for Astrophysics (astro-ph.IM), 010303 astronomy & astrophysics, High Energy Astrophysical Phenomena (astro-ph.HE), Physics, Bursts, Spacecraft, business.industry, [SDU.ASTR.HE]Sciences of the Universe [physics]/Astrophysics [astro-ph]/High Energy Astrophysical Phenomena [astro-ph.HE], Detector, Gamma rays, Astrophysics::Instrumentation and Methods for Astrophysics, Astronomy and Astrophysics, Afterglow, [SDU.ASTR.IM]Sciences of the Universe [physics]/Astrophysics [astro-ph]/Instrumentation and Methods for Astrophysic [astro-ph.IM], Space and Planetary Science, Gamma-ray Bursts, business, Gamma-ray burst, Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Instrumentation and Methods for Astrophysics, Fermi Gamma-ray Space Telescope
Abstract: The LAT instrument on the Fermi mission will reveal the rich spectral and temporal gamma-ray burst phenomena in the > 100 MeV band. The synergy with Fermi's GBM detectors will link these observations to those in the well explored 10-1000 keV range; the addition of the > 100 MeV band observations will resolve theoretical uncertainties about burst emission in both the prompt and afterglow phases. Trigger algorithms will be applied to the LAT data both onboard the spacecraft and on the ground. The sensitivity of these triggers will differ because of the available computing resources onboard and on the ground. Here we present the LAT's burst detection methodologies and the instrument's GRB capabilities., Accepted by ApJ
Published: 2009
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37. A stochastic min-driven coalescence process and its hydrodynamical limit

Author: Anne-Laure Basdevant, Clément Rau, Philippe Laurençot, James Norris, Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Subjects: Statistics and Probability, Stochastic modelling, stochastic coalescence, 82C22, 60K35, 60H10, 34A34, 34C11, Binary number, 01 natural sciences, hydrodynamical limit, 010104 statistics & probability, 82C22, 60K35, 60H10, 34A34, 34C11, FOS: Mathematics, Statistical physics, 0101 mathematics, Mathematics, Coalescence (physics), Probability (math.PR), 010102 general mathematics, Time evolution, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], min-driven clustering, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract: International audience; A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalised version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.
Published: 2009
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38. New quasidilaton theory in partially constrained vielbein formalism

Author: Tanahashi, Norihiro [Department of Applied Mathematics and Theoretical Physics,Centre for Mathematical Sciences, University of Cambridge,Wilberforce Road, Cambridge CB3 0WA (United Kingdom)]
Published: 2016
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39. The speed of Galileon gravity

Author: Davis, Anne-Christine [DAMTP, Centre for Mathematical Sciences, University of Cambridge, CB3 0WA (United Kingdom)]
Published: 2016
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40. Multiple coexisting states of liquid rope coiling

Author: Daniel Bonn, Herbert E. Huppert, Neil M. Ribe, Mehdi Habibi, Mark A. Hallworth, Institut de Physique du Globe de Paris (IPGP), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-IPG PARIS-Université Paris Diderot - Paris 7 (UPD7)-Université de La Réunion (UR)-Centre National de la Recherche Scientifique (CNRS), Institute of Theoretical Geophysics [Cambridge] (ITG), Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Department of Earth Sciences [Cambridge, UK], University of Cambridge [UK] (CAM), Institute for Advanced Studies in Basic Sciences, Institute for advanced Studies in Basic Sciences, Laboratoire de Physique Statistique de l'ENS (LPS), Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Institut des Neurosciences Cellulaires et Intégratives (INCI), Université Louis Pasteur - Strasbourg I-Centre National de la Recherche Scientifique (CNRS), University of Amsterdam Van der Waals-Zeeman Institute (VAN DER WAALS-ZEEMAN INSTITUTE), University of Amsterdam [Amsterdam] (UvA), Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institute for Advanced Studies in Basic Sciences (IASBS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université de La Réunion (UR)-Institut de Physique du Globe de Paris (IPG Paris)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and Soft Matter (WZI, IoP, FNWI)
Subjects: Physics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Mechanical Engineering, Bending, Viscous liquid, Condensed Matter Physics, Rotation, 01 natural sciences, Instability, String (physics), 010305 fluids & plasmas, Gravitation, Classical mechanics, Mechanics of Materials, 0103 physical sciences, Life Science, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Atomic physics, 010306 general physics, Falling (sensation), ComputingMilieux_MISCELLANEOUS, Rope
Abstract: A thin ‘rope’ of viscous fluid falling from a sufficient height onto a surface forms a series of regular coils. Here we investigate theoretically and experimentally a curious feature of this instability: the existence of multiple states with different frequencies at a fixed value of the fall height. Using a numerical model based on asymptotic ‘thin rope’ theory, we determine curves of coiling frequency Ω vs. fall height H as functions of the fluid viscosity ν, the diameter d of the injection hole, the volumetric injection rate Q, and the acceleration due to gravity g. In addition to the three coiling modes previously identified (viscous, gravitational and inertial), we find a new multivalued ‘inertio-gravitational’ mode that occurs at heights intermediate between gravitational and inertial coiling. In the limit when the rope is strongly stretched by gravity and Π1 ≡ (ν 5 /gQ 3 ) 1/5 � 1, inertio-gravititational coiling occurs in the height range O(Π −1/6 1 ) H (g/ν 2 ) 1/3 O(Π −5/48 1 ). The frequencies of the individual branches are proportional to (g/H) 1/2 , and agree closely with the eigenfrequencies of a whirling liquid string with negligible resistance to bending and twisting. The number of coexisting branches scales as Π 5/32 1 . The predictions of the numerical model are in excellent agreement with laboratory experiments performed by two independent groups using different apparatus and working fluids. The experiments further show that interbranch transitions in the inertio-gravitational regime occur via an intermediate state with a ‘figure of eight’ geometry that changes the sense of rotation of the coiling.
Published: 2006
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41. Large deviations for the Yang-Mills measure on a compact surface

Author: James Norris, Thierry Lévy, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Surface (mathematics), Mathematics - Differential Geometry, High Energy Physics::Lattice, FOS: Physical sciences, Yang–Mills existence and mass gap, 01 natural sciences, Measure (mathematics), General Relativity and Quantum Cosmology, High Energy Physics::Theory, Large deviation principle, Simple (abstract algebra), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Mathematics::Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Limit (mathematics), 0101 mathematics, Sobolev connections, Yang-Mills measure, Mathematical Physics, Mathematics, MSC 60F10, 81T13, 58D20, 010102 general mathematics, Mathematical analysis, Probability (math.PR), Statistical and Nonlinear Physics, Mathematical Physics (math-ph), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear Sciences::Exactly Solvable and Integrable Systems, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Large deviations theory, 010307 mathematical physics, Rate function, Energy (signal processing), Mathematics - Probability
Abstract: We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energy.
Published: 2004
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42. Modelling Incentives for Collaboration in Mobile Ad Hoc Networks

Author: Richard J. Gibbens, Jon Crowcroft, Frank Kelly, Sven Östring, Inria Sophia Antipolis-Méditerranée / I3s, Service Ist, Computer Laboratory [Cambridge], University of Cambridge [UK] (CAM), Statistical Laboratory [Cambridge], Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)-Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), and Session 04 : Game models for cooperation in Ad-hoc networks (T. Basar)
Subjects: Delay-tolerant networking, Computer Networks and Communications, Computer science, Wireless ad hoc network, 02 engineering and technology, [INFO.INFO-MC]Computer Science [cs]/Mobile Computing, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-MC] Computer Science [cs]/Mobile Computing, [INFO.INFO-PF] Computer Science [cs]/Performance [cs.PF], Computer Science::Networking and Internet Architecture, 0202 electrical engineering, electronic engineering, information engineering, Vehicular ad hoc network, Adaptive quality of service multi-hop routing, [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI], business.industry, 020206 networking & telecommunications, Mobile ad hoc network, Ad hoc wireless distribution service, [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF], Optimized Link State Routing Protocol, Hardware and Architecture, Geocast, Modeling and Simulation, 020201 artificial intelligence & image processing, Telecommunications, business, Software, Computer network
Abstract: International audience; This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send trafic. The paper explores consequences of the model by means of fluid-level simulations of a network and illustrates the way in which network resources are allocated to users according to their geographical position.
Published: 2003

43. Semidefinite programming lower bounds on the squashed entanglement

Author: Fawzi, Hamza, Fawzi, Omar, Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Traitement optimal de l'information avec des dispositifs quantiques (QINFO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 851716,ERC-2019-STG,AlgoQIP(2021), Fawzi, Omar, and Beyond Shannon: Algorithms for optimal information processing - AlgoQIP - 2021-01-01 - 2025-12-31 - 851716 - VALID
Subjects: Quantum Physics, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Physics::Space Physics, FOS: Physical sciences, TheoryofComputation_GENERAL, Quantum Physics (quant-ph), [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Physics::Geophysics
Abstract: The squashed entanglement is a widely used entanglement measure that has many desirable properties. However, as it is based on an optimization over extensions of arbitrary dimension, one drawback of this measure is the lack of good algorithms to compute it. Here, we introduce a hierarchy of semidefinite programming lower bounds on the squashed entanglement., 10 pages, comments welcome
Published: 2022

44. Non-canonical inflation coupled to matter

Author: Davis, Anne-Christine [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)]
Published: 2015
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45. Distinguishing modified gravity models

Author: Davis, Anne-Christine [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WA (United Kingdom)]
Published: 2015
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46. Symmetric polynomials in information theory: Entropy and subentropy

Author: Mitchison, Graeme [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)]
Published: 2015
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47. Device-independent lower bounds on the conditional von Neumann entropy

Author: Brown, Peter, Fawzi, Hamza, Fawzi, Omar, Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Traitement optimal de l'information avec des dispositifs quantiques (QINFO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria), Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), European Project: 851716,ERC-2019-STG,AlgoQIP(2021), Fawzi, Omar, and Beyond Shannon: Algorithms for optimal information processing - AlgoQIP - 2021-01-01 - 2025-12-31 - 851716 - VALID
Subjects: Quantum Physics, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], FOS: Physical sciences, [INFO]Computer Science [cs], [INFO] Computer Science [cs], Quantum Physics (quant-ph), [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Computer Science::Cryptography and Security
Abstract: The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascu\'es-Pironio-Ac\'in hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering all known tight analytical bounds up to several decimal places. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security., Comment: 21 (+8) pages, 4 (+2) figures. V2: improved numerics and restructured article
Published: 2022

48. A subpolynomial-time algorithm for the free energy of one-dimensional quantum systems in the thermodynamic limit

Author: Fawzi, Hamza, Omar, Fawzi, Scalet, Samuel, Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Traitement optimal de l'information avec des dispositifs quantiques (QINFO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 851716,ERC-2019-STG,AlgoQIP(2021), and Apollo - University of Cambridge Repository
Subjects: Quantum Physics, One-dimensional quantum systems, Physics and Astronomy (miscellaneous), Statistical Mechanics (cond-mat.stat-mech), Theory of computation → Design and analysis of algorithms, FOS: Physical sciences, Mathematical Physics (math-ph), Theory of computation → Quantum complexity theory, Atomic and Molecular Physics, and Optics, Theory of computation → Quantum information theory, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Free energy, Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics, Mathematical Physics
Abstract: We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T = 0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed temperature T > 0 in subpolynomial time, i.e., in time O((1/ε)^c) for any constant c > 0 where ε is the additive approximation error. Previously, the best known algorithm had a runtime that is polynomial in 1/ε where the degree of the polynomial is exponential in the inverse temperature 1/T. Our algorithm is also particularly simple as it reduces to the computation of the spectral radius of a linear map. This linear map has an interpretation as a noncommutative transfer matrix and has been studied previously to prove results on the analyticity of the free energy and the decay of correlations. We also show that the corresponding eigenvector of this map gives an approximation of the marginal of the Gibbs state and thereby allows for the computation of various thermodynamic properties of the quantum system., LIPIcs, Vol. 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023), pages 49:1-49:6
Published: 2022
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49. Optimal L2-approximation of occupation and local times for symmetric stable processes

Author: Altmeyer, Randolf, Guével, Ronan Le, Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM), Université de Rennes (UR), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Université de Rennes (UNIV-RENNES)
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Statistics and Probability, local time, Lévy process, Probability (math.PR), FOS: Mathematics, Statistics, Probability and Uncertainty, lower bound, Mathematics - Probability, occupation time, stable process
Abstract: The L2-approximation of occupation and local times of a symmetric $\alpha$-stable L{\'e}vy process from high frequency discrete time observations is studied. The standard Riemann sum estimators are shown to be asymptotically efficient when 0 < $\alpha$ $\le$ 1, but only rate optimal for 1 < $\alpha$ $\le$ 2. For this, the exact convergence of the L2-approximation error is proven with explicit constants.
Published: 2022
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50. α-z-Rényi relative entropies

Author: Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB (United Kingdom)]
Published: 2015
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