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Your search keyword '"Instituto de Ciencias Matemàticas [Madrid] (ICMAT)"' showing total 7 results
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7 results on '"Instituto de Ciencias Matemàticas [Madrid] (ICMAT)"'

1. On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

Author

Ivan Bardet, Cambyse Rouzé, David Pérez-García, Angelo Lucia, Angela Capel, Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), California Institute of Technology (CALTECH), Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Ivan Bardet is supported by French A.N.R. grant: ANR-14-CE25-0003 'StoQ'. Angela Capel is partially supported by a La Caixa-Severo Ochoa grant (ICMAT Severo Ochoa project SEV-2011-0087, MINECO) and Angela Capel and David Perez Garcia acknowledge support from MINECO (grant MTM2017-88385-P) and from Comunidad de Madrid (grantQUITEMAD-CM, ref. P2018/TCS-4342). Angelo Lucia acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907), and from the BBVA Fundation.This project has received funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation programme (grant agreementNo 648913). Cambyse Rouzé acknowledges financial support from the TUM university Foundation Fellowship and by the DFG cluster of excellence 2111 (Munich Center for Quantum Science and Technology)., Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Security, Cryptology and Transmissions (SECRET), Instituto de Ciencias Matemàticas [Madrid], Consejo Superior de Investigaciones Científicas [Spain] (CSIC), Universidad Complutense de Madrid [Madrid] (UCM), and Technische Universität München [München] (TUM)

Subjects
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Gibbs state, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Entropy (classical thermodynamics), symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, 0101 mathematics, Gibbs measure, Mixing (physics), Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematical physics, Mathematics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 010102 general mathematics, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Sobolev space, symbols, Dissipative system, 010307 mathematical physics, Constant (mathematics), Quantum Physics (quant-ph), Hamiltonian (control theory)
Abstract

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we show that for the heat-bath dynamics for 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy., 28 pages, 4 figures. Included some additional comments and updated results in light of recent advances in the literature

Published
2021
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2. High order variational integrators in the optimal control of mechanical systems

Author

Cédric M. Campos, Emmanuel Trélat, Sina Ober-Blöbaum, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), University of Paderborn, 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), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), Institut des Sciences de la Terre (ISTerre), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Discretization, Computer science, Control variable, Dynamical Systems (math.DS), 010103 numerical & computational mathematics, 01 natural sciences, Convergence (routing), FOS: Mathematics, Discrete Mathematics and Combinatorics, Applied mathematics, Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, 0101 mathematics, Variational integrator, Mathematics - Optimization and Control, Applied Mathematics, Numerical analysis, Numerical Analysis (math.NA), 65P10 (Primary) 65L06, 65K10, 49Mxx (Secondary), Optimal control, 010101 applied mathematics, Mechanical system, Runge–Kutta methods, Optimization and Control (math.OC), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis
Abstract

In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are momentum preserving and symplectic. In this article, we develop two high order variational integrators which distinguish themselves in the dimension of the underling space of approximation and we investigate their application to finite-dimensional optimal control problems posed with mechanical systems. The convergence of state and control variables of the approximated problem is shown. Furthermore, by analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that, for these particular integrators, dualization and discretization commute., 25 pages, 9 figures, 1 table, submitted to DCDS-A

Published
2015
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3. Self-improving properties for abstract Poincaré type inequalities

Author

José María Martell, Frédéric Bernicot, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Ministerio de Economía y Competitividad (España), Martell, José María, and Martell, José María [0000-0001-6788-4769]

Subjects
Generalized Poincar e-Sobolev inequalities, Computer Science::Machine Learning, General Mathematics, Dyadic cubes, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Computer Science::Digital Libraries, 01 natural sciences, semigroups, Statistics::Machine Learning, symbols.namesake, 0103 physical sciences, 46E35, John-Nirenberg inequalities, Direct proof, 0101 mathematics, Lp space, Self-improving properties, Mathematics, BMO and Lipschitz spaces, Conjecture, Euclidean space, Applied Mathematics, 010102 general mathematics, 1. No poverty, Lipschitz continuity, pseudo-Poincaré inequalities, Algebra, Elliptic operator, Pseudo-Poincare inequalities, Mathematics - Classical Analysis and ODEs, Poincaré conjecture, Computer Science::Mathematical Software, symbols, generalized Poincaré-Sobolev inequalities, 010307 mathematical physics
Abstract

We study self-improving properties in the scale of Lebesgue spaces of generalized Poincar e inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain operators (e.g., approximations of the identity, semigroups or mean value operators) that have o -diagonal decay in some range. Our results provide a uni ed theory that is applicable to the classical Poincar e inequalities and furthermore it includes oscillations de ned in terms of semigroups associated with second order elliptic operators as those in the Kato conjecture. In this latter situation we obtain a direct proof of the John-Nirenberg inequality for the associated BMO and Lipschitz spaces of [HMay, HMM], The second author was supported by MINECO Grant MTM2010-16518 and ICMAT Severo Ochoa project SEV-2011-0087

Published
2014
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4. Vertical versus conical square functions

Author

José María Martell, Pascal Auscher, Steve Hofmann, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), University of Missouri [Columbia] (Mizzou), University of Missouri System, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
elliptic operators, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, extrapolation, MSC 2010: 42B25, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Conical surface, 01 natural sciences, Vertical square functions, Square (algebra), Elliptic operator, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 010307 mathematical physics, 0101 mathematics, conical square functions, Analysis of PDEs (math.AP), Mathematics
Abstract

We study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator., Comment: 21 pages

Published
2012
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5. Unfolding the double shuffle structure of q-multiple zeta values

Author

Dominique Manchon, Jaime Castillo-Medina, Kurusch Ebrahimi-Fard, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Pure mathematics, Number theory, 11M32, 39A13, Mathematics - Number Theory, General Mathematics, Regularization (physics), Jackson integral, FOS: Mathematics, Number Theory (math.NT), [MATH]Mathematics [math], 16. Peace & justice, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Mathematics
Abstract

We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin., Comment: Submitted. Added paragraphs (5.2 and 5.3) on handling non-modified qMZVs. Red internal comment removed

Published
2013
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6. Stability estimates for the Radon transform with restricted data and applications

Author

Pedro Caro, David Dos Santos Ferreira, Alberto Ruiz, Department of Mathematics and Statistics [Helsinki], Falculty of Science [Helsinki], University of Helsinki-University of Helsinki, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Mathematics - Analysis of PDEs, Radon transform, Mathematics - Classical Analysis and ODEs, General Mathematics, Norm (mathematics), Mathematical analysis, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inverse, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Mathematics, Analysis of PDEs (math.AP)
Abstract

In this article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the $L^p$ norm of the function itself, under some conditions on the support of the function. We apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data., Comment: 37 pages

Published
2012
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7. On an extension of Knuth's rotation correspondence to reduced planar trees

Author

Dominique Manchon, Kurusch Ebrahimi-Fard, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)

Subjects
Algebra and Number Theory, Binary tree, Mathematics::Combinatorics, Structure (category theory), Extension (predicate logic), Computer Science::Computational Geometry, Hopf algebra, Space (mathematics), Combinatorics, Planar, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Bijection, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), [MATH]Mathematics [math], Rotation (mathematics), Mathematical Physics, Mathematics
Abstract

International audience; We present a bijection from planar reduced trees to planar rooted hypertrees, which extends Knuth's rotation correspondence between planar binary trees and planar rooted trees. The operadic counterpart of the new bijection is explained. Related to this, the space of planar reduced forests is endowed with a combinatorial Hopf algebra structure. The corresponding structure on the space of planar rooted hyperforests is also described.

Published
2012
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