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1. How Apply Mathematics in Engineering Fields

Author: Aye Aye Aung and New Thazin WaiMathematics Or Particularly Applied Mathematics Is Widely Used In Every Engineering Fields. In This Paper, Several Examples Of Applications Of Mathematics In Civil, Mechanical, Electrical And Architectural Engineering Are Discussed. The Role Of Mathematics In Engineering Education Is One Of These Opportunities. There Has Been Much Recent Debate On What Mathematical Skills Are Needed For The Engineers Of Tomorrow, And How And When These Might Best Be Acquired. We Conclude That The Value Of Mathematics In Engineering Remains A Central Problem, And Argue That Mathematics Should Be A Fundamental Concern In The Design And Practice Of Engineering. Aye Aye Aung | New Thazin Wai \\'How Apply Mathematics In Engineering Fields\\' Published In International Journal Of Trend In Scientific Research And Development (Ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: Https://Www.Ijtsrd.Com/Papers/Ijtsrd27950.Pdf
Subjects: Applied Mathematics, FOS: Mathematics, MathematicsofComputing_GENERAL, civil, mechanical, architectural, electrical
Abstract: Mathematics or particularly applied mathematics is widely used in every engineering fields. In this paper, several examples of applications of mathematics in civil, mechanical, electrical and architectural engineering are discussed. The role of mathematics in engineering education is one of these opportunities. There has been much recent debate on what mathematical skills are needed for the engineers of tomorrow, and how and when these might best be acquired. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of engineering. Aye Aye Aung | New Thazin Wai "How Apply Mathematics in Engineering Fields" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27950.pdf
Published: 2019
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2. The DFT operational Sum Calculus Method for Solving Difference Equations with Boundary Conditions

Author: Abdul j. Jerri ∗ This paper is dedicated to
Subjects: Algebra and Number Theory, Applied Mathematics, Multivariable calculus, Sum rule in integration, Calculus, medicine, Time-scale calculus, Boundary value problem, medicine.disease, Analysis, Calculus (medicine), Mathematics
Published: 1997

3. Results of a survey of elevator interlocks and an analysis of elevator accident statistics

Author: C.E. Oakes, J.A. Dickinson, and Technologic Paper
Subjects: Computer Networks and Communications, Control and Systems Engineering, Applied Mathematics, Signal Processing
Published: 1921

4. Computing Riemann-Roch spaces via Puiseux expansions

Author: Simon Abelard, Elena Berardini, Alain Couvreur, Grégoire Lecerf, Thales SIX GTS France, Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Geometry, arithmetic, algorithms, codes and encryption (GRACE), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-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), This paper is part of a project of École polytechnique, that has received funding from the French 'Agence de l'innovation de défense'. Simon Abelard was partially funded by this grant, when he was hosted at École polytechnique, Institut Polytechnique de Paris (91120 Palaiseau, France), from October 2019 to the end of December 2020., École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), and This paper is part of a project of École polytechnique, that has received funding from the French 'Agence de l'innovation de défense'. Simon Abelard was partially funded by this grant, when he was hosted at École polytechnique, Institut Polytechnique de Paris (91120 Palaiseau, France), from October 2019 to the end of December 2020. Elena Berardini has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 899987.
Subjects: Statistics and Probability, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Numerical Analysis, Control and Optimization, Algebra and Number Theory, Applied Mathematics, General Mathematics, Algebraic curves, Complexity, Riemann-Roch spaces, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Puiseux expansions, Algorithms
Abstract: International audience; Computing large Riemann-Roch spaces for plane projective curves still constitutes a major algorithmic and practical challenge. Seminal applications concern the construction of arbitrarily large algebraic geometry error correcting codes over alphabets with bounded cardinality. Nowadays such codes are increasingly involved in new areas of computer science such as cryptographic protocols and "interactive oracle proofs". In this paper, we design a new probabilistic algorithm of Las Vegas type for computing Riemann-Roch spaces of smooth divisors, in characteristic zero, and with expected complexity exponent 2.373 (a feasible exponent for linear algebra) in terms of the input size.
Published: 2021

5. Distance-Aware Relay Selection in an Energy-Efficient Discovery Protocol for 5G D2D Communication

Author: Nadège Varsier, Cesar Vargas Anamuro, Jean Schwoerer, Xavier Lagrange, Advanced technologies for operated networks (ADOPNET), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES (IRISA-D2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Bretagne Sud (UBS)-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)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Orange Labs [Meylan], Orange Labs, Département Systèmes Réseaux, Cybersécurité et Droit du numérique (IMT Atlantique - SRCD), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), This paper is part of and thereby supported by the Horizon 2020 project ONE5G (ICT-760809) receiving funds from the European Union., European Project: ICT-760809,ONE5G(2017), Université de Rennes (UR)-IMT Atlantique (IMT Atlantique), 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 Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and IMT Atlantique (IMT Atlantique)
Subjects: Computer science, stochastic geometry, 02 engineering and technology, law.invention, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-MC]Computer Science [cs]/Mobile Computing, Base station, Relay, law, Telecommunications link, 0202 electrical engineering, electronic engineering, information engineering, Path loss, Electrical and Electronic Engineering, business.industry, Applied Mathematics, energy-efficient, 020206 networking & telecommunications, Energy consumption, relay selection, Computer Science Applications, User equipment, D2D relaying, Cellular network, mMTC, business, Efficient energy use, Computer network
Abstract: International audience; Massive machine-type communications (mMTC) is one of the main services delivered by the fifth Generation (5G) mobile network. The traditional cellular architecture where all devices connect to the base station is not energy efficient. For this reason, the use of device-to-device (D2D) communications is considered to reduce the energy consumption of mMTC devices. The main idea is to use nearby user equipment (UE) as a relay and establish with it D2D communication. However, the relay selection process also consumes energy, and this consumption can be significant compared to the energy consumed during the data transmission phase. In this paper, we propose a distributed energy-efficient D2D relaying mechanism for mMTC applications. This mechanism favors the selection of the UEs with low path loss with the mMTC device. Through mathematical analysis and simulations, we show that our mechanism allows a reduction of the total energy consumption of mMTC devices (up to 75% compared to direct transmission) when they have an unfavorable link budget. Moreover, our mechanism achieves almost constant energy consumption for a large range of UE densities and distances between the mMTC device and the base station.
Published: 2021

6. Stability of optimal traffic plans in the irrigation problem

Author: Antoine Prouff, Antonio De Rosa, Andrea Marchese, Maria Colombo, Paul Pegon, Ecole Polytechnique Fédérale de Lausanne (EPFL), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Department of mathematics/Dipartimento di Matematica [Univ. Trento], Università degli Studi di Trento (UNITN), 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), 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)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), Maria Colombo was partially supported by the Swiss National Science Foundation grant 200021_182565. Antonio De Rosa has been supported by the NSF DMS Grant No. 1906451. Andrea Marchese acknowledges partial support from GNAMPA-INdAM., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University [Milan, Italy], Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, M. C. was partially supported by the Swiss National Science Foundation grant 200021_182565. A. D. R. has been supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. A. M. acknowledges partial support from GNAMPA-INdAM. A.P. was supported by the Fondation Mathématiques Jacques Hadamard. P.P and A.P. both acknowledge EPFL for hosting them during the semester this paper was prepared., Inria de Paris, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
Subjects: BRANCHED TRANSPORT, Mathematical optimization, Irrigation, TRAFFIC PLANS, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, Stability (probability), symbols.namesake, Mathematics - Analysis of PDEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Computer Science::Networking and Internet Architecture, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Limit (mathematics), 0101 mathematics, Mathematics - Optimization and Control, Mathematics, TRANSPORTATION NETWORK, BRANCHED TRANSPORT, IRRIGATION PROBLEM, TRAFFIC PLANS, STABILITY, STABILITY, IRRIGATION PROBLEM, Applied Mathematics, TRANSPORTATION NETWORK, 010102 general mathematics, Eulerian path, Flow network, 010101 applied mathematics, Optimization and Control (math.OC), Mathematics - Classical Analysis and ODEs, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis, Lagrangian, Analysis of PDEs (math.AP)
Abstract: We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.
Published: 2022

7. CTET+: A Beyond-Birthday-Bound Secure Tweakable Enciphering Scheme Using a Single Pseudorandom Permutation

Author: Benoît Cogliati, Jordan Ethan, Virginie Lallemand, Byeonghak Lee, Jooyoung Lee, Marine Minier, Helmholtz Center for Information Security [Saarbrücken] (CISPA), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Korea Advanced Institute of Science and Technology (KAIST), We would like to thank the anonymous reviewers for their valuable suggestions that helped improving the paper. This work was carried out in the framework of the French-German-Center for Cybersecurity, a collaboration of CISPA and LORIA and was partly supported by the french PIA project 'Lorraine Université d’Excellence', reference ANR-15 IDEX-04-LUE. Jooyoung was supported by Institute for Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (No.2019-0-01343, Regional strategic industry convergence security core talent training business). Part of this work was written while Benoît Cogliati was employed by the University of Luxembourg., Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: TK7885-7895, Computer engineering. Computer hardware, Computational Mathematics, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], Applied Mathematics, tweakable enciphering mode, beyond-birthday-bound security, SPN, Software, Computer Science Applications
Abstract: International audience; In this work, we propose a construction of 2-round tweakable substitution permutation networks using a single secret S-box. This construction is based on non-linear permutation layers using independent round keys, and achieves security beyond the birthday bound in the random permutation model. When instantiated with an n-bit block cipher with ωn-bit keys, the resulting tweakable block cipher, dubbed CTET+, can be viewed as a tweakable enciphering scheme that encrypts ωκ-bit messages for any integer ω ≥ 2 using 5n + κ-bit keys and n-bit tweaks, providing 2n/3-bit security. Compared to the 2-round non-linear SPN analyzed in [CDK+18], we both minimize it by requiring a single permutation, and weaken the requirements on the middle linear layer, allowing better performance. As a result, CTET+ becomes the first tweakable enciphering scheme that provides beyond-birthday-bound security using a single permutation, while its efficiency is still comparable to existing schemes including AES-XTS, EME, XCB and TET. Furthermore, we propose a new tweakable enciphering scheme, dubbed AES6-CTET+, which is an actual instantiation of CTET+ using a reduced round AES block cipher as the underlying secret S-box. Extensive cryptanalysis of this algorithm allows us to claim 127 bits of security.Such tweakable enciphering schemes with huge block sizes become desirable in the context of disk encryption, since processing a whole sector as a single block significantly worsens the granularity for attackers when compared to, for example, AES-XTS, which treats every 16-byte block on the disk independently. Besides, as a huge amount of data is being stored and encrypted at rest under many different keys in clouds, beyond-birthday-bound security will most likely become necessary in the short term.
Published: 2021

8. Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation

Author: Aurélien Alfonsi, Rafaël Coyaud, Virginie Ehrlacher, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Mathematical Risk Handling (MATHRISK), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), MATHematics for MatERIALS (MATHERIALS), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC), The Labex Bézout is acknowledged for funding the PhD thesis of Rafaël Coyaud. Aurélien Alfonsi benefited from the support of the 'Chaire Risques Financiers', Fondation du Risque. We are very grateful to Gero Friesecke, Daniela Vögler, Tony Lelièvre, Gabriel Stoltz and Pierre Monmarché for stimulating discussions, as well as Mathieu Lewin for precious comments on the paper. This publication is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme – Grant Agreement n◦ 810367., European Project: 810367,EMC2(2019), and École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris
Subjects: Applied Mathematics, Modeling and Simulation, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), [MATH]Mathematics [math]
Abstract: The Strictly Correlated Electrons (SCE) limit of the Levy–Lieb functional in Density Functional Theory (DFT) gives rise to a symmetric multi-marginal optimal transport problem with Coulomb cost, where the number of marginal laws is equal to the number of electrons in the system, which can be very large in relevant applications. In this work, we design a numerical method, built upon constrained overdamped Langevin processes to solve Moment Constrained Optimal Transport (MCOT) relaxations (introduced in [A. Alfonsi, R. Coyaud, V. Ehrlacher and D. Lombardi, Approximation of optimal transport problems with marginal moments constraints, Math. Comp. 90 (2021) 689–737; C. Villani, Optimal Transport: Old and New (Springer Science & Business Media, 2008)]) of symmetric multi-marginal optimal transport problems with Coulomb cost. Some minimizers of such relaxations can be written as discrete measures charging a low number of points belonging to a space whose dimension, in the symmetrical case, scales linearly with the number of marginal laws. We leverage the sparsity of those minimizers in the design of the numerical method and prove that there is no strict local minimizer to the resulting problem. We illustrate the performance of the proposed method by numerical examples which solves MCOT relaxations of 3D systems with up to 100 electrons.
Published: 2021

9. The DGDD Method for Reduced-Order Modeling of Conservation Laws

Author: Angelo Iollo, Charbel Farhat, Sebastian Grimberg, Michel Bergmann, Sébastien Riffaud, 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), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), 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)-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)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Aeronautics and Astronautics [Stanford] (AA Stanford), Stanford University, Department of Mechanical Engineering [Stanford], Institute for Computational and Mathematical Engineering [Stanford] (ICME), This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement N° 872442. Experiments presented in this paper were carried out using the PlaFRIM experimental testbed, supported by Inria, CNRS (LABRI and IMB), Université de Bordeaux, Bordeaux INP and Conseil Régional d’Aquitaine (see https://www.plafrim.fr/)., Plafrim, MEMPHIS, European Project: 872442,ARIA, European Project: 872442,ARIA(2019), 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), 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)-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)-Inria Bordeaux - Sud-Ouest
Subjects: ECSW method, Polynomial, Physics and Astronomy (miscellaneous), Proper Orthogonal Decomposition, 010103 numerical & computational mathematics, 01 natural sciences, symbols.namesake, Discontinuous Galerkin method, Applied mathematics, Domain decomposition, 0101 mathematics, Representation (mathematics), Parametric statistics, Mathematics, Numerical Analysis, Conservation law, Applied Mathematics, Domain decomposition methods, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Euler equations, 010101 applied mathematics, Reduced-order model, Computational Mathematics, Modeling and Simulation, symbols, Reduction (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; The discontinuous Galerkin domain decomposition (DGDD) method couples subdomains of high-fidelity polynomial approximation to regions of low-dimensional resolution for the numerical solution of systems of conservation laws. In the low-fidelity regions, the solution is approximated by empirical modes constructed by Proper Orthogonal Decomposition and a reduced-order model is used to predict the solution. The high-dimensional model instead solves the system of conservation laws only in regions where the solution is not amenable to a low-dimensional representation. The coupling between the high-dimensional and the reduced-order models is then performed in a straightforward manner through numerical fluxes at discrete cell boundaries. We show results from application of the proposed method to parametric problems governed by the quasi-1D and 2D compressible Euler equations. In particular, we investigate the prediction of unsteady flows in a converging-diverging nozzle and over a NACA0012 airfoil in presence of shocks. The results demonstrate the stability and the accuracy of the proposed method and the significant reduction of the computational cost with respect to the high-dimensional model.
Published: 2021

10. A well balanced finite volume scheme for general relativity

Author: Gaburro, Elena, Castro, Manuel, Dumbser, Michael, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), 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)-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)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidad de Málaga [Málaga] = University of Málaga [Málaga], University of Trento [Trento], E. G gratefully acknowledges the support received from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Individual Fellowship SuPerMan, grant agreement No. 101025563. E. G. has been also supported by a national mobility grant for young researchers in Italy funded by GNCS-INdAM, and she received funding from the University of Trento via the Strategic Initiative Starting Grant Giovani Ricercatori 2019. Moreover, the research presented in this paper has been partially funded by the European Union’s Horizon 2020 Research and Innovation Programme under the project ExaHyPE, grant No. 671698 (call FETHPC-1-2014).M. D. also acknowledges the ﬁnancial support received from the Italian Ministry of Education, University and Research (MIUR) in the frame of the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant 605 L. 232/2016) and in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial diﬀerential equations and applications. Furthermore, M. D. has also received funding from the University of Trento via the Strategic Initiative Modeling and Simulation. The research of M.J. Castro was partially supported by the Spanish Government (SG), the European Regional Development Fund (ERDF), the Regional Government of Andalusia (RGA), and the University of Malaga(UMA) through the projects of references RTI2018-096064-B-C21 (SG-ERDF), UMA18-Federja-161 (RGA-ERDF-613 UMA), and P18-RT-3163 (RGA-ERDF)., 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)-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)-Inria Bordeaux - Sud-Ouest
Subjects: 010308 nuclear & particles physics, Applied Mathematics, FOS: Physical sciences, Well balanced schemes 23 (WB), General Relativity and Quantum Cosmology (gr-qc), Numerical Analysis (math.NA), 01 natural sciences, General Relativity and Quantum Cosmology, General relativistic magnetohydrodynamics (GRMHD), TOV neutron star, AMS subject classiﬁcations. 35L40, 65M08, 83C05, 83C10, 85-08, 85-10, 85A30, Computational Mathematics, 0103 physical sciences, FOS: Mathematics, Michel accretion disk, Mathematics - Numerical Analysis, [MATH]Mathematics [math], 010306 general physics, Frst order conformal and covariant 24 reformulation of the Einstein ﬁeld equations (FO-CCZ4), Fnite volume schemes (FV), First order hyperbolic systems
Abstract: International audience; In this work we present a novel second order accurate well balanced (WB) finite volume (FV) scheme for the solution of the general relativistic magnetohydrodynamics (GRMHD) equations and the first order CCZ4 formulation (FO-CCZ4) of the Einstein field equations of general relativity, as well as the fully coupled FO-CCZ4 + GRMHD system. These systems of first order hyperbolic PDEs allow to study the dynamics of the matter and the dynamics of the space-time according to the theory of general relativity. The new well balanced finite volume scheme presented here exploits the knowledge of an equilibrium solution of interest when integrating the conservative fluxes, the nonconservative products and the algebraic source terms, and also when performing the piecewise linear data reconstruction. This results in a rather simple modification of the underlying second order FV scheme, which, however, being able to cancel numerical errors committed with respect to the equilibrium component of the numerical solution, substantially improves the accuracy and long-time stability of the numerical scheme when simulating small perturbations of stationary equilibria. In particular, the need for well balanced techniques appears to be more and more crucial as the applications increase their complexity. We close the paper with a series of numerical tests of increasing difficulty, where we study the evolution of small perturbations of accretion problems and stable TOV neutron stars. Our results show that the well balancing significantly improves the long-time stability of the finite volume scheme compared to a standard one.
Published: 2021
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11. A graph cellular automaton with relation-based neighbourhood describing the impact of peer influence on the consumption of marijuana among college-aged youths

Author: Muhammad Zaid Dauhoo, Laurent Dumas, Yusra Bibi Ruhomally, Université de Maurice, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), University of Mauritius, UoM, and We would like to acknowledge the assistance of Mr Maheshsingh Mungur from the University of Mauritius in the preparation of this work. This work has been conducted under the HEC (Higher Education Commission Mauritius) MPhil/PhD scholarship. The authors would also like to thank the reviewers for their constructive and valuable comments, which led to the improvement of the paper.
Subjects: Statistics and Probability, 050402 sociology, Relation (database), media_common.quotation_subject, targeted campaigns of prevention, [SDV]Life Sciences [q-bio], Population, 02 engineering and technology, relation-based, 0504 sociology, 0202 electrical engineering, electronic engineering, information engineering, Set (psychology), education, Recreation, Neighbourhood (mathematics), media_common, Consumption (economics), education.field_of_study, peer influence, Applied Mathematics, Addiction, 05 social sciences, Marijuana, Modeling and Simulation, graph cellular automaton, Graph (abstract data type), 020201 artificial intelligence & image processing, Psychology, Social psychology
Abstract: International audience; A novel approach depicting the dynamics of marijuana usage to gauge the effects of peer influence in a school population, is the site of investigation. Consumption of drug is considered as a contagious social epidemic which is spread mainly by peer influences. A relation-based graph-CA (r-GCA) model consisting of 4 states namely, Nonusers (N), Experimental users (E), Recreational users (R) and Addicts (A), is formulated in order to represent the prevalence of the epidemic on a campus. The r-GCA model is set up by local transition rules which delineates the proliferation of marijuana use. Data available in [4] is opted to verify and validate the r-GCA. Simulations of the r-GCA system are presented and discussed. The numerical results agree quite accurately with the observed data. Using the model, the enactment of campaigns of prevention targeting N, E and R states respectively were conducted and analysed. The results indicate a significant decline in marijuana consumption on the campus when a campaign of prevention targeting the latter three states simultaneously, is enacted.
Published: 2021

12. Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles

Author: Emmanuel Maitre, Mourad E. H. Ismail, Arnaud Sengers, Thibaut Metivet, ModELisation de l'apparence des phénomènes Non-linéaires (ELAN), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] (DYFCOM-LIPhy ), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Most of the computations presented in this paper were performed using the Froggy platform of the GRICAD infrastructure (https://gricad.univ-grenoble-alpes.fr), which is supported by the Rhône-Alpes region (GRANT CPER07_13 CIRA) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, and the Atlas cluster from the Research Institute in Advanced Mathematics (IRMA - UMR7501)., ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] [2020-….] (DYFCOM-LIPhy [2020-….]), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] [2020-….] (LIPhy [2020-….]), and Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)
Subjects: Volume and area preserving, Vol- ume and area preserving, Diffusion generated motion, Physics and Astronomy (miscellaneous), Computer science, Interface (Java), and phrases: Diffusion generated motion, Signed distance function, Clifford torus, 010103 numerical & computational mathematics, Willmore flow, 01 natural sciences, Level set, Dimension (vector space), FOS: Mathematics, Applied mathematics, Mathematics - Numerical Analysis, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Diffusion (business), [MATH]Mathematics [math], High-order geometrical flow, Numerical Analysis, Level set (data structures), Applied Mathematics, Numerical Analysis (math.NA), Thresholding, Computer Science Applications, 010101 applied mathematics, Computational Mathematics, Flow (mathematics), Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus.
Published: 2020

13. The fast iterated bootstrap

Author: Mirza Trokic, Russell Davidson, McGill University = Université McGill [Montréal, Canada], Centre interuniversitaire de recherche en économie quantitative (CIREQ), Aix-Marseille Sciences Economiques (AMSE), École des hautes études en sciences sociales (EHESS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), IHS Markit, and This research was supported by the Canada Research Chair program (Chair in Economics, McGill University), and by grants from the Social Sciences and Humanities Research Council of Canada and the Fonds de Recherche du QuebecSociete Culture, Canada. We are grateful to seminar participants at the Third French Econometric Conference, the Singapore Management University, the Hong Kong University of Science and Technology, and the University of Sydney, for useful comments. We also thank our discussant Matt Webb for insightful comments at the 2017 CESG. Our thanks go to three anonymous referees and a guest co-editor for insightful comments that helped us improve the paper.
Subjects: Economics and Econometrics, Series (mathematics), Computer science, Applied Mathematics, 05 social sciences, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C12 - Hypothesis Testing: General, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C10 - General, Sense (electronics), [SHS.ECO]Humanities and Social Sciences/Economics and Finance, 01 natural sciences, Power (physics), Bootstrap iteration Fast iterated bootstrap, 010104 statistics & probability, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling, Null (SQL), Iterated function, Distortion, 0502 economics and business, bootstrap iteration, fast iterated bootstrap, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C15 - Statistical Simulation Methods: General, 0101 mathematics, Algorithm, 050205 econometrics
Abstract: International audience; The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suffers from less size distortion under the null with no accompanying loss of power.
Published: 2020

14. Multidimensional inequality and inframodular order

Author: Alain Chateauneuf, Zaier Aouani, Department of economics, University of Kansas, University of Kansas [Lawrence] (KU), IPAG Business School, Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), This paper is part of the research project ANR ‘‘Mesure des inégalités ordinales et multidimensionnelles’’ (ORDINEQ) of the French National Research Agency (Agence Nationale de la Recherche), whose financial support is gratefully acknowledged., and ANR-16-CE41-0005,ORDINEQ,La Mesure des Inégalités Ordinales et Multidimensionnelles(2016)
Subjects: Economics and Econometrics, education.field_of_study, Multi-attribute inequality, Inequality, Applied Mathematics, media_common.quotation_subject, 05 social sciences, Population, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Inframodular functions, Multidimensional Pigou–Dalton transfers, Order (business), 0502 economics and business, Econometrics, Inframodular order, 050207 economics, education, 050205 econometrics, media_common, Mathematics
Abstract: International audience; Motivated by the pertinence of Pigou–Dalton (PD) transfers for inequality measurement when only one attribute is involved, we show that inframodular functions are consistent with multidimensional PD transfers and that weakly inframodular functions fit more accurately with the traditional notion of PD transfers. We emphasize, for inequality rankings of allocations of multiple attributes in a population, the similarities of the inframodular order, defined using inframodular functions, with the concave order in the unidimensional framework.
Published: 2020

15. Online estimation of integrated squared density derivatives

Author: Abdelkader Mokkadem, Mariane Pelletier, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and We deeply thank the Referees for their thoughtful remarks, which led to a substantially improved version of our paper.
Subjects: Statistics and Probability, Recursive estimation, Mean squared error, 010102 general mathematics, Bandwidth (signal processing), Estimator, Probability density function, Density estimation, Online estimation, Rate of convergence, Stochastic algorithm, 01 natural sciences, 010104 statistics & probability, Kernel estimators of integrals, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Applied mathematics, 0101 mathematics, Statistics, Probability and Uncertainty, Mathematics, Parametric statistics
Abstract: Hall and Marron (1987) introduced kernel estimators of integrals of the squared m -order derivatives of a probability density. Mokkadem and Pelletier (2020) gave recursive versions of their estimators, but the main drawback of these estimators is that their update requires the use of all past data. The aim of this paper is the study of online versions of the estimators introduced by Hall and Marron (1987), that is of estimators which are not only recursive, but which also have the property that their update uses only the last available data. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987) and of Mokkadem and Pelletier (2020), our online estimators achieve the parametric rate n − 1 when m = 0 or when higher order kernels are used. For the case when the parametric rate is not obtained, we also study an online version of the estimator proposed by Jones and Sheather (1991). Finally, we provide recursive estimators of the optimal bandwidth in the framework of density estimation.
Published: 2020

16. Powers of conjugacy classes in a finite groups

Author: Carmen Melchor, Antonio Beltrán, Rachel Camina, María José Felipe, Apollo - University of Cambridge Repository, and Part of this paper was written during the stay of C. Melchor at the University of Cambridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castellón. C. Melchor would like to thank R. Camina and the Department of Mathematics for their warm hospitality. A. Beltrán, M.J. Felipe and C. Melchor are supported by Proyecto PGC2018-096872-B-100, Ministerio de Ciencia, Innovación y Universidades.
Subjects: Finite group, business.industry, Applied Mathematics, 010102 general mathematics, 4904 Pure Mathematics, Power of conjugacy classes, 01 natural sciences, Finite groups, Conjugacy classes, Mathematics::Group Theory, Conjugacy class, Hospitality, Solvability, 0103 physical sciences, 49 Mathematical Sciences, 010307 mathematical physics, Sociology, Characters, 0101 mathematics, business, MATEMATICA APLICADA, Humanities, Matemàtica
Abstract: [EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group., Part of this paper was written during the stay of C.Melchor at the University of Cambridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castellón. C. Melchor would like to thank R. Camina and the Department of Mathematics for their warm hospitality. A. Beltrán, M.J. Felipe and C. Melchor are supported by Proyecto PGC2018-096872-B-100, Ministerio de Ciencia, Innovación y Universidades.
Published: 2020

17. 'Small Data': Efficient Inference with Occasionally Observed States

Author: Andreas Lanz, Ole Wilms, Gregor Reich, Philipp Müller, Ecole des Hautes Etudes Commerciales (HEC Paris), and HEC Research Paper Series
Subjects: JEL: C - Mathematical and Quantitative Methods/C.C0 - General/C.C0.C01 - Econometrics, History, State variable, Small data, Polymers and Plastics, Computer science, 05 social sciences, Inference, Estimator, Method of simulated moments, Industrial and Manufacturing Engineering, Efficiency, 0502 economics and business, [SHS.GESTION]Humanities and Social Sciences/Business administration, Applied mathematics, Economic model, 050207 economics, Business and International Management, Likelihood function, 050205 econometrics
Abstract: We study the estimation of dynamic economic models for which some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from industrial organization to marketing to finance. If such occasional state observations are serially correlated, the likelihood function of the model becomes a potentially high-dimensional integral over a nonstandard domain. We propose a method that generalizes the recursive likelihood function integration procedure (RLI; Reich, 2018) to numerically approximate this integral, and demonstrate its statistical efficiency in several well-understood examples from finance and industrial organization. In extensive Monte Carlo studies, we compare the performance of our approach to a recently suggested method of simulated moments. In all our demonstrations, we consistently and efficiently identify all model parameters, and we find that the additional variance of our estimator when going from full to occasional state observations is small for the parameters of interest.
Published: 2020

18. Minimal NMR distance information for rigidity of protein graphs

Author: Leo Liberti, Benjamin Bardiaux, Michael Nilges, Thérèse E. Malliavin, Bradley Worley, Bruce R. Donald, Carlile Lavor, Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC), Universidade Estadual de Campinas (UNICAMP), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Duke University [Durham], Bioinformatique structurale, Institut Pasteur [Paris]-Centre National de la Recherche Scientifique (CNRS), C.L. would like to thank the Brazilian research agencies CNPq, FAPESP and B.D. would like to thank the NIH grants R01 GM-118543 and R01 GM-078031 for their financial support., We are also thankful to Angela Gronenborn and Michael Souza, for discussions that clarify some ideas in the paper, and to anonymous referees that made very important comments to this work., Bioinformatique structurale - Structural Bioinformatics, Universidade Estadual de Campinas = University of Campinas (UNICAMP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), and Institut Pasteur [Paris] (IP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Computational complexity theory, Nuclear Magnetic Resonance, 0211 other engineering and technologies, Structure (category theory), Rigidity (psychology), 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Topology, 01 natural sciences, Article, Cardinality, Protein structure, Distance Geometry, Discrete Mathematics and Combinatorics, Molecule, Combinatorial search, Mathematics, Quantitative Biology::Biomolecules, [SDV.BBM.BS]Life Sciences [q-bio]/Biochemistry, Molecular Biology/Structural Biology [q-bio.BM], Applied Mathematics, Solution set, 021107 urban & regional planning, [SDV.BBM.BP]Life Sciences [q-bio]/Biochemistry, Molecular Biology/Biophysics, [SDV.BBM.BS]Life Sciences [q-bio]/Biochemistry, Molecular Biology/Biomolecules [q-bio.BM], Vertex orders, 010201 computation theory & mathematics, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], Molecular structure
Abstract: International audience; Nuclear Magnetic Resonance (NMR) experiments provide distances between nearby atoms of a protein molecule. The corresponding structure determination problem is to determine the 3D protein structure by exploiting such distances. We present a new order on the atoms of the protein, based on information from the chemistry of proteins and NMR experiments, which allows us to formulate the problem as a combinatorial search. Additionally, this order tells us what kind of NMR distance information is crucial to understand the cardinality of the solution set of the problem and its computational complexity.
Published: 2019

19. Stochastic modeling reveals how motor protein and filament properties affect intermediate filament transport

Author: Sandrine Etienne-Manneville, Stéphanie Portet, Cécile Leduc, J. C. Dallon, Brigham Young University (BYU), Polarité cellulaire, Migration et Cancer - Cell Polarity, Migration and Cancer, Institut Pasteur [Paris]-Centre National de la Recherche Scientifique (CNRS), University of Manitoba [Winnipeg], This work was supported by: EPSRC grant numbers EP/K032208/1 and EP/R014604/1 and by La Ligue contre le cancer and the Institut Pasteur., The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme 'Coupling Geometric PDE’s with Physics for Cell Morphology, Motility and Pattern Formation' when the work on this paper was undertaken., Institut Pasteur [Paris] (IP)-Centre National de la Recherche Scientifique (CNRS), and ANR-16-CE13-0019,SiFi2Net,Filaments intermédiaires: du filament unique au réseau(2016)
Subjects: 0301 basic medicine, Statistics and Probability, Materials science, [SDV]Life Sciences [q-bio], Dynein, Biological Transport, Active, Kinesins, Catch bond, macromolecular substances, [SDV.BC]Life Sciences [q-bio]/Cellular Biology, Microtubules, Models, Biological, General Biochemistry, Genetics and Molecular Biology, Quantitative Biology::Cell Behavior, Protein filament, Motor protein, Quantitative Biology::Subcellular Processes, 03 medical and health sciences, 0302 clinical medicine, Molecular motor, Vimentin, Intermediate filaments, Intermediate filament, Cytoskeleton, Stochastic Processes, General Immunology and Microbiology, Applied Mathematics, Dyneins, Molecular motors, General Medicine, Kinesin, Stochastic, 030104 developmental biology, Modeling and Simulation, Biophysics, General Agricultural and Biological Sciences, 030217 neurology & neurosurgery
Abstract: International audience; Intermediate filaments are a key component of the cytoskeleton. Their transport along microtubules plays an essential role in the control of the shape and structural organization of cells. To identify the key parameters responsible for the control of intermediate filament transport, we generated a model of elastic filament transport by microtubule-associated dynein and kinesin. The model is also applicable to the transport of any elastically-coupled cargoes. We investigate the effect of filament properties such as number of motor binding sites, length, and elasticity on motion of filaments. Additionally, we consider the effect of motor properties, i.e. off rates, on filament transport. When one motor has a catch bond off rate it dictates the motion, whereas when motors have the same type of off rate filaments can alternate between retrograde and anterograde motions. The elasticity of filaments optimizes the filament transport and the coordination of motors along the length of the filament.
Published: 2019

20. Linear Search by a Pair of Distinct-Speed Robots

Author: Tomasz Kociumaka, Jurek Czyzowicz, David Ilcinkas, Leszek Gąsieniec, Ralf Klasing, Dominik Pająk, Evangelos Bampas, School of of Electrical and Computer Engineering [Athens] (School of E.C.E), National Technical University of Athens [Athens] (NTUA), Département d'Informatique et d'Ingénierie (DII), Université du Québec en Outaouais (UQO), Department of Computer Science [Liverpool], University of Liverpool, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), University of Warsaw (UW), Institute of informatics [Wrocław], See paper for details., ANR-11-BS02-0014,DISPLEXITY,Calculabilité et complexité en distribué(2011), ANR-13-JS02-0002,MACARON,Bouger et Calculer: Agents, Robots et Réseaux(2013), ANR-16-CE40-0023,DESCARTES,Abstraction modulaire pour le calcul distribué(2016), ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, Pajak, Dominik S, Laboratoire d'informatique Fondamentale de Marseille (LIF), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Institute of Informatics [Warsaw], Faculty of Mathematics, Informatics, and Mechanics [Warsaw] (MIMUW), University of Warsaw (UW)-University of Warsaw (UW), and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
Subjects: Engineering, General Computer Science, Computer science, different speeds, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0211 other engineering and technologies, 0102 computer and information sciences, 02 engineering and technology, Bang-bang robot, linear search, 01 natural sciences, Article, Computer Science::Robotics, Position (vector), mobile robots, 0202 electrical engineering, electronic engineering, information engineering, Cartesian coordinate robot, Point (geometry), Computer vision, [INFO]Computer Science [cs], Online algorithm, Simulation, Linear search, 021103 operations research, business.industry, Applied Mathematics, Mobile robot, Computer Science Applications, 010201 computation theory & mathematics, group search, Moment (physics), Line (geometry), Robot, 020201 artificial intelligence & image processing, Artificial intelligence, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business
Abstract: Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{17}+4\approx 8.123$$\end{document}17+4≈8.123 times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.
Published: 2019

21. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model

Author: Jérémy Rouot, Bernard Bonnard, Mathematics for Control, Transport and Applications (McTAO), 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 Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Vision et Analyse de Données (LABISEN-VISION-AD), Laboratoire ISEN (L@BISEN), Institut supérieur de l'électronique et du numérique (ISEN)-YNCREA OUEST (YO)-Institut supérieur de l'électronique et du numérique (ISEN)-YNCREA OUEST (YO), This research paper benefited from the support of the FMJH Program PGMO and from thesupport of EDF, Thales, Orange and the authors are partially supported by the Labex AMIES., ANR-10-LABX-0002,AMIES,Agency for mathematics in interaction with enterprise and society(2010), and ANR: 10-LABX-0002,AMIES,Agency for mathematics in interaction with enterprise and society(2010)
Subjects: 0209 industrial biotechnology, Control and Optimization, Computer science, 02 engineering and technology, 01 natural sciences, Biomechanics fo, 020901 industrial engineering & automation, Control theory, Sampled-data co, Pulse wave, Functional electrical stimulation, Hamiltonian dif, 0101 mathematics, Applied Mathematics, Frame (networking), Dynamics (mechanics), Pulse (physics), 010101 applied mathematics, Mechanics of Materials, Variational inequality, Trajectory, Geometric optim, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Geometry and Topology, Pontryagin type, Hamiltonian (control theory)
Abstract: International audience; A recent force-fatigue parameterized mathematical model, based on the seminal contributions of V. Hill to describe muscular activity, allows to predict the muscular force response to external electrical stimulation (FES) and it opens the road to optimize the FES-input to maximize the force response to a pulse train, to track a reference force while minimizing the fatigue for a sequence of pulse trains or to follow a reference joint angle trajectory to produce motion in the non-isometric case. In this article, we introduce the geometric frame to analyze the dynamics and we present Pontryagin types necessary optimality conditions adapted to digital controls, used in the experiments, vs permanent control and which fits in the optimal sampled-data control frame. This leads to Hamiltonian differential variational inequalities, which can be numerically implemented vs direct optimization schemes.
Published: 2021

22. Convergence regions for the Chebyshev–Halley family

Author: B. Campos, Jordi Canela, P. Vindel, and The authors would like to thank the anonymous referees for their suggestions and comments, which improved this paper. The first and third authors were supported by the Spanish project MTM2014-52016-C02-2-P, the Generalitat Valenciana Project PROMETEO/2016/089 and UJI project P1.1B20115-16. The second author was supported by RedIUM and MINECO (Spain) through the research network MTM2014-55580-REDT and by the mathematics institute IMAC (Castellon, Spain).
Subjects: roots, Numerical Analysis, Pure mathematics, Chebyshev–Halley family, Iterative method, polynomials, Applied Mathematics, Chebyshev systems, 010102 general mathematics, 010103 numerical & computational mathematics, dynamics, Parameter space, Fixed point, 01 natural sciences, Attraction, Chebyshev filter, Critical point (mathematics), Combinatorics, Quadratic equation, Modeling and Simulation, Polinomis, 0101 mathematics, Sistemes de Chebyshev, Mathematics
Abstract: In this paper we study the dynamical behavior of the Chebyshev–Halley methods on the family of degree n polynomials z n + c . We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having z = ∞ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of n grows. We also demonstrate that, although the convergence order of the Chebyshev–Halley family is 3, there is a member of order 4 for each value of n. In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots.
Published: 2018

23. Through the looking glass: Indirect inference via simple equilibria

Author: Veronika Czellar, Laurent E. Calvet, emlyon business school, Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), HEC Paris Research Paper Series, and business school, emlyon
Subjects: JEL: C - Mathematical and Quantitative Methods/C.C0 - General/C.C0.C01 - Econometrics, Large class, JEL: C - Mathematical and Quantitative Methods/C.C5 - Econometric Modeling/C.C5.C53 - Forecasting and Prediction Methods • Simulation Methods, Economics and Econometrics, Hidden Markov model, long-run risk, learning, value at risk, indirect inference, particle filters, Computer science, Monte Carlo method, jel:C01, Indirect Inference, 01 natural sciences, Value at risk, Indirect inference, 010104 statistics & probability, Simple (abstract algebra), 0502 economics and business, Econometrics, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C15 - Statistical Simulation Methods: General, Capital asset pricing model, Learning, Applied mathematics, JEL: C - Mathematical and Quantitative Methods/C.C5 - Econometric Modeling/C.C5.C58 - Financial Econometrics, 050207 economics, 0101 mathematics, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, Long-run risk, jel:C53, Applied Mathematics, 05 social sciences, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C13 - Estimation: General, Estimator, jel:C13, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, jel:C58, jel:C15, [SHS.GESTION]Humanities and Social Sciences/Business administration, Particle filters, [SHS.GESTION] Humanities and Social Sciences/Business administration, Particle filter
Abstract: International audience; This paper proposes an indirect inference (Gourieroux, Monfort and Renault, 1993; Smith, 1993) estimation method for a large class of dynamic equilibrium models. Our approach is based on the observation that the econometric structure of these systems naturally generates auxiliary equilibria that can serve as building blocks for estimation. We use this insight to develop an accurate estimator for the long-run risk model of Bansal and Yaron (2004). We demonstrate the accuracy of our method by Monte Carlo simulation and estimate the long-run risk model on U.S. data. We also illustrate the good performance of the methodology on an asset pricing model with investor learning.
Published: 2015

24. Natural Scales in Geographical Patterns

Author: Telmo Menezes, Camille Roth, Centre Marc Bloch (CMB), Ministère de l'Europe et des Affaires étrangères (MEAE)-Bundesministerium für Bildung und Forschung-Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.)-Centre National de la Recherche Scientifique (CNRS), Médialab (Sciences Po) (Médialab), Sciences Po (Sciences Po), Centre National de la Recherche Scientifique (CNRS), This paper has been partially supported by grants 'Phantomgrenzen' and 'Algodiv' (ANR-15-CE38-0001), funded respectively by the BMBF (German Federal Ministry for Education and Research) and by the ANR (French National Agency of Research)., and ANR-15-CE38-0001,ALGODIV,Algodiv: Recommandation algorithmique et diversité des informations du web(2015)
Subjects: FOS: Computer and information sciences, 0301 basic medicine, Physics - Physics and Society, FOS: Physical sciences, Distribution (economics), computer science, Network science, Physics and Society (physics.soc-ph), Space (commercial competition), human movement, Article, [INFO.INFO-SI]Computer Science [cs]/Social and Information Networks [cs.SI], Natural (archaeology), geographical networks, 03 medical and health sciences, network science, community detection, applied mathematics, 91D20, 91D30, Social and Information Networks (cs.SI), [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Multidisciplinary, business.industry, Orders of magnitude (acceleration), Computer Science - Social and Information Networks, [SHS.GEO]Humanities and Social Sciences/Geography, Partition (database), Discontinuity (linguistics), 030104 developmental biology, Geography, business, Scale (map), Cartography
Abstract: Human mobility is known to be distributed across several orders of magnitude of physical distances, which makes it generally difficult to endogenously find or define typical and meaningful scales. Relevant analyses, from movements to geographical partitions, seem to be relative to some ad-hoc scale, or no scale at all. Relying on geotagged data collected from photo-sharing social media, we apply community detection to movement networks constrained by increasing percentiles of the distance distribution. Using a simple parameter-free discontinuity detection algorithm, we discover clear phase transitions in the community partition space. The detection of these phases constitutes the first objective method of characterising endogenous, natural scales of human movement. Our study covers nine regions, ranging from cities to countries of various sizes and a transnational area. For all regions, the number of natural scales is remarkably low (2 or 3). Further, our results hint at scale-related behaviours rather than scale-related users. The partitions of the natural scales allow us to draw discrete multi-scale geographical boundaries, potentially capable of providing key insights in fields such as epidemiology or cultural contagion where the introduction of spatial boundaries is pivotal.
Published: 2017

25. Modeling carbon dioxide transport in PDMS-based microfluidic cell culture devices

Author: Antti-Juhana Mäki, Joose Kreutzer, Mikko Peltokangas, Pasi Kallio, S. Auvinen, Tampere University, Department of Automation Science and Engineering, Department of Materials Science, Research group: Paper Converting and Packaging, BioMediTech, and Integrated Technologies for Tissue Engineering Research (ITTE)
Subjects: Materials science, Computer simulation, Concentration Response, Applied Mathematics, General Chemical Engineering, Microfluidics, Nanotechnology, General Chemistry, 217 Medical engineering, Industrial and Manufacturing Engineering, Finite element method, chemistry.chemical_compound, Silicone, chemistry, Cell culture, Concentration gradient, Biological system, Carbon dioxide transport
Abstract: Maintaining a proper pH level is crucial for successful cell culturing. Mammalian cells are commonly cultured in incubators, where the cell culture medium is saturated with a mixture of air and 5% carbon dioxide (CO2). Therefore, to keep cell culture medium pH in an acceptable level outside these incubators, a suitable CO2 concentration must be dissolved in the medium. However, it can be very difficult to control and measure precisely local concentration levels. Furthermore, possible undesired concentration gradients generated during long-term cell culturing are almost impossible to detect. Therefore, we have developed a computational model to estimate CO2 transport in silicone-based microfluidic devices. An extensive set of experiments was used to validate the finite element model. The model parameters were obtained using suitable measurement set-ups and the model was validated using a fully functional cell cultivation device. The predictions obtained by the simulations show very good responses to experiments. It is shown in this paper how the model helps to understand the dynamics of CO2 transport in silicone-based cell culturing devices possessing different geometries, thus providing cost-effective means for studying different device designs under a variety of experimental conditions without the need of actual testing. Finally, based on the results from the computational model, an alternative strategy for feeding CO2 is proposed to accelerate the system performance such that a faster and more uniform CO2 concentration response is achieved in the area of interest. acceptedVersion
Published: 2015

26. Quality of Real-Time Streaming in Wireless Cellular Networks - Stochastic Modeling and Analysis

Author: Bartlomiej Blaszczyszyn, Miodrag Jovanovic, Mohamed Kadhem Karray, Dynamics of Geometric Networks (DYOGENE), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-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)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria), France Télécom Recherche & Développement (FT R&D), France Télécom, This paper reports the results of the research undertaken under CRE-CIFRE thesis co-advising agreement between Inria and Orange Labs., Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-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 National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Paris-Rocquencourt
Subjects: FOS: Computer and information sciences, Computer science, Throughput, Computer Science - Networking and Internet Architecture, Base station, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], outage, FOS: Mathematics, Wireless, Electrical and Electronic Engineering, Radio resource management, Dimensioning, deep outage, stochastic model, Networking and Internet Architecture (cs.NI), business.industry, Wireless network, Applied Mathematics, Quality of service, Probability (math.PR), Real-time streaming, capacity-sharing, Poisson process, Computer Science Applications, LTE, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], interruptions, Cellular network, quality of service, Resource allocation, business, Mathematics - Probability, mobile TV, Computer network
Abstract: We present a new stochastic service model with capacity sharing and interruptions, appropriate for the evaluation of the quality of real-time streaming (RTS), like e.g. mobile TV, in wireless cellular networks. The general model takes into account multi-class Markovian process of call arrivals, (to capture different radio channel conditions, requested streaming bit-rates and durations) and allows for a general resource allocation policy saying which users are temporarily denied the requested fixed streaming bit-rates (put in outage) due to resource constraints. We give expressions for several important performance characteristics of the model, including mean time spent in outage and mean number of outage incidents for a typical user of a given class. These expressions involve only stationary probabilities of the (free) traffic demand process, which is a vector of independent Poisson random variables describing the number of users of different classes. In order to analyze RTS in 3GPP Long Term Evolution (LTE) cellular networks, we specify our general model assuming orthogonal user channels with the peak bit-rates close to the theoretical Shannon's bound in the additive white Gaussian noise (AWGN) channel, which leads to the resource constraints in a multi-rate linear form. In this setting we consider a natural class of least-effort-served-first resource allocation policies, for which the characteristics of the model can be further evaluated using Fourier analysis of Poisson variables. Within this class we identify and evaluate an optimal and a fair policy, the latter being suggested by LTE implementations. We also propose some intermediate policies, which allow to solve the optimality/fairness tradeoff caused by unequal user radio-channel conditions. Our results can be used for the evaluation of the quality of RTS in LTE networks and dimensioning of these networks., Comment: (06/2012)
Published: 2014

27. Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pebbles

Author: Paola Flocchini, David Ilcinkas, Nicola Santoro, School of Electrical Engineering and Computer Science (EECS), University of Ottawa [Ottawa], Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), School of Computer Science [Ottawa], Carleton University, See paper for details, ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), and Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest
Subjects: Theoretical computer science, General Computer Science, FIFO (computing and electronics), [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Topology (electrical circuits), 0102 computer and information sciences, 02 engineering and technology, Dangerous graphs, Topology, 01 natural sciences, Graph exploration, Autonomous robots, 0202 electrical engineering, electronic engineering, information engineering, Search problem, Pebble, Mathematics, Applied Mathematics, Black hole search, Distributed computing, Computer Science Applications, 010201 computation theory & mathematics, Asynchronous communication, Theory of computation, 020201 artificial intelligence & image processing, Node (circuits), Mobile agents, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Abstract: International audience; We prove that, for the black hole search problem in networks of arbitrary but known topology, the pebble model of agent interaction is computationally as powerful as the whiteboard model; furthermore the complexity is exactly the same. More precisely, we prove that a team of two asynchronous agents, each endowed with a single identical pebble (that can be placed only on nodes, and with no more than one pebble per node), can locate the black hole in an arbitrary network of known topology; this can be done with Θ(nlog n) moves, where n is the number of nodes, even when the links are not FIFO. These results are obtained with a novel algorithmic technique, ping-pong, for agents using pebbles.
Published: 2012

28. A computational framework for gene regulatory network inference that combines multiple methods and datasets

Author: Philipp Antczak, Anna Stincone, Sarah Durant, Francesco Falciani, Andreas Bikfalvi, Rita Gupta, Roy Bicknell, School of Biosciences, University of Birmingham [Birmingham], Institute of Biomedical Research, Mecanismes Moleculaires de l'Angiogenese, Université Sciences et Technologies - Bordeaux 1-Institut National de la Santé et de la Recherche Médicale (INSERM), The work described in this paper was funded by the CRUK grant C8504/A9488 and partially funded by the BBSRC grant BBC5151041. AS is a recipient of a Darwin Trust PhD fellowship and PA is a recipient of a BBSRC PhD studentship., BMC, Ed., and Université Sciences et Technologies - Bordeaux 1 (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM)
Subjects: MESH: Hydrogen-Ion Concentration, Time Factors, Gene regulatory network, Inference, Multiple methods, computer.software_genre, 0302 clinical medicine, Structural Biology, Gene regulatory network inference, Neoplasms, MESH: Gene Silencing, MESH: Neoplasms, Gene Regulatory Networks, MESH: Stress, Physiological, lcsh:QH301-705.5, [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM], MESH: Gene Regulatory Networks, Genetics, 0303 health sciences, [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], MESH: Escherichia coli, Applied Mathematics, Systems Biology, Methodology Article, Hydrogen-Ion Concentration, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Computer Science Applications, Modeling and Simulation, MESH: Systems Biology, [SDV.BBM.GTP] Life Sciences [q-bio]/Biochemistry, Molecular Biology/Genomics [q-bio.GN], Reverse engineering, MESH: Cell Line, Tumor, Systems biology, Biology, Machine learning, Models, Biological, 03 medical and health sciences, Stress, Physiological, Modelling and Simulation, [SDV.BBM.GTP]Life Sciences [q-bio]/Biochemistry, Molecular Biology/Genomics [q-bio.GN], Cell Line, Tumor, Escherichia coli, Humans, Gene Silencing, Molecular Biology, 030304 developmental biology, MESH: Humans, business.industry, MESH: Time Factors, Ode, MESH: Models, Biological, lcsh:Biology (General), Time course, Artificial intelligence, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], business, computer, 030217 neurology & neurosurgery
Abstract: Background Reverse engineering in systems biology entails inference of gene regulatory networks from observational data. This data typically include gene expression measurements of wild type and mutant cells in response to a given stimulus. It has been shown that when more than one type of experiment is used in the network inference process the accuracy is higher. Therefore the development of generally applicable and effective methodologies that embed multiple sources of information in a single computational framework is a worthwhile objective. Results This paper presents a new method for network inference, which uses multi-objective optimisation (MOO) to integrate multiple inference methods and experiments. We illustrate the potential of the methodology by combining ODE and correlation-based network inference procedures as well as time course and gene inactivation experiments. Here we show that our methodology is effective for a wide spectrum of data sets and method integration strategies. Conclusions The approach we present in this paper is flexible and can be used in any scenario that benefits from integration of multiple sources of information and modelling procedures in the inference process. Moreover, the application of this method to two case studies representative of bacteria and vertebrate systems has shown potential in identifying key regulators of important biological processes.
Published: 2011

29. Communication algorithms with advice

Author: Pierre Fraigniaud, Andrzej Pelc, David Ilcinkas, Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Département d'Informatique et d'Ingénierie (DII), Université du Québec en Outaouais (UQO), See paper for details., ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), and Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest
Subjects: Computer Networks and Communications, Distributed computing, Message complexity, Network, 0102 computer and information sciences, 02 engineering and technology, Broadcasting, 01 natural sciences, Graph, Theoretical Computer Science, 0202 electrical engineering, electronic engineering, information engineering, Size of advice, Dissemination, Mathematics, Linear number, business.industry, Applied Mathematics, Telecommunications network, Algorithm, Computational Theory and Mathematics, 010201 computation theory & mathematics, Broadcast communication network, Graph (abstract data type), 020201 artificial intelligence & image processing, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business, Advice (complexity), Wakeup
Abstract: International audience; We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is {\em quantitative}: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, regardless of the type of information provided. We compare the size of advice needed to perform broadcast and wakeup (the latter is a broadcast in which nodes can transmit only after getting the source information), both using a linear number of messages (which is optimal). We show that the minimum size of advice permitting the {\em wakeup} with a linear number of messages in a $n$-node network, is $\Theta (n \log n)$, while the {\em broadcast} with a linear number of messages can be achieved with advice of size $O(n)$. We also show that the latter size of advice is almost optimal: no advice of size $o(n)$ can permit to broadcast with a linear number of messages. Thus an efficient wakeup requires strictly more information about the network than an efficient broadcast.
Published: 2010

30. On discretization schemes for stochastic evolution equations

Author: Annie Millet, Istvan Gyongy, School of Mathematics - University of Edinburgh, University of Edinburgh, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Statistique Appliquée et MOdélisation Stochastique (SAMOS), Université Paris 1 Panthéon-Sorbonne (UP1), Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques (MATISSE - UMR 8595), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), This paper was written while I. Gyongy was visiting the University of Paris X. The research of I. Gyongy is partially supported byEU Network HARP. The research of A. Millet is partially supported by the research project BMF2003-01345, and Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC)
Subjects: Discretization, 010102 general mathematics, Probability (math.PR), Banach space, MathematicsofComputing_NUMERICALANALYSIS, Stochastic evolution, 01 natural sciences, 010101 applied mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Monotone polygon, Convergence (routing), Monotone operators, FOS: Mathematics, Applied mathematics, finite elements, 60H15 65M60, coercivity, 0101 mathematics, Analysis, Stochastic evolution equations, Mathematics - Probability, Mathematics
Abstract: International audience; Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
Published: 2006

31. From left modules to algebras over an operad: application to combinatorial Hopf algebras

Author: Muriel Livernet, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), and this paper was written during the stay of the author at Institut Mittag-Leffler (djursholm, sweden).
Subjects: Pure mathematics, twisted bialgebra, 18D50 (Primary), 16W30, 16A06 (Secondary), Context (language use), 0102 computer and information sciences, Quasitriangular Hopf algebra, 01 natural sciences, Mathematics::Algebraic Topology, Mathematics::Category Theory, Mathematics::Quantum Algebra, FOS: Mathematics, S-module, 0101 mathematics, Mathematics, operad, Algebra and Number Theory, Functor, Quantum group, Applied Mathematics, 010102 general mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Mathematics::Rings and Algebras, Tensor algebra, combinatorial Hopf algebra, Mathematics - Rings and Algebras, Hopf algebra, MSC2000: Primary: 18D50, Secondary: 16W30, 16A06, Rings and Algebras (math.RA), 010201 computation theory & mathematics, free associative algebra, Geometry and Topology, Forgetful functor, Analysis, Vector space
Abstract: The purpose of this paper is two fold: we study the behaviour of the forgetful functor from S-modules to graded vector spaces in the context of algebras over an operad and derive from this theory the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for these Hopf algebras. Let O denote the forgetful functor from S-modules to graded vector spaces. Left modules over an operad P are treated as P-algebras in the category of S-modules. We generalize the results obtained by Patras and Reutenauer in the associative case to any operad P: the functor O sends P-algebras to P-algebras. If P is a Hopf operad then O sends Hopf P-algebras to Hopf P-algebras. If the operad P is regular one gets two different structures of Hopf P-algebras in the category of graded vector spaces. We develop the notion of unital infinitesimal P-bialgebra and prove freeness and cofreeness results for Hopf algebras built from Hopf operads. Finally, we prove that many combinatorial Hopf algebras arise from our theory, as Hopf algebras on the faces of the permutohedra and associahedra., Section 4.3 removed. To appear in Annales Math\'ematiques Blaise Pascal
Published: 2006

32. Labeling Schemes for Tree Representation

Author: David Ilcinkas, David Peleg, Pierre Fraigniaud, Amos Korman, Reuven Cohen, Department of Computer Science and Applied Mathematics [Rehovot], Weizmann Institute of Science [Rehovot, Israël], Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Pierre Fraigniaud and David Ilcinkas were supported by project ``PairAPair' of the ACI Masses de Données, project ``Fragile' of the ACI Sécurité et Informatique, and project ``Grand Large' of INRIA., Ajit Pal, Ajay D. Kshemkalyani, Rajeev Kumar, Arobinda Gupta, Department of Electrical and Computer Engineering [Boston University] (ECE), Boston University [Boston] (BU), Technion - Israel Institute of Technology [Haifa], See paper for details., and ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007)
Subjects: K-ary tree, General Computer Science, Symmetric graph, Edge-graceful labeling, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Combinatorics, symbols.namesake, 0202 electrical engineering, electronic engineering, information engineering, Connectivity, Mathematics, Minimum degree spanning tree, Discrete mathematics, spanning tree, Spanning tree, Applied Mathematics, Shortest-path tree, Complete graph, 020206 networking & telecommunications, 020207 software engineering, Numbering, Labeling scheme, Computer Science Applications, Planar graph, tree representation, Tree structure, 010201 computation theory & mathematics, symbols, Regular graph, Gomory–Hu tree
Abstract: International audience; This paper deals with compact label-based representations for trees. Consider an $n$-node undirected connected graph $G$ with a predefined numbering on the ports of each node. The {\em all-ports} tree labeling $\cL_{all}$ gives each node $v$ of $G$ a label containing the port numbers of all the {\em tree} edges incident to $v$. The {\em upward} tree labeling $\cL_{up}$ labels each node $v$ by the number of the port leading from $v$ to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted $M_{up}(T)$ and $S_{up}(T)$ for $\cL_{up}$ and $M_{all}(T)$ and $S_{all}(T)$ for $\cL_{all}$. The problem studied in this paper is the following: Given a graph $G$ and a predefined port labeling for it, with the ports of each node $v$ numbered by $0,\ldots,\deg(v)-1$, select a rooted spanning tree for $G$ minimizing (one of) these measures. We show that the problem is polynomial for $M_{up}(T)$, $S_{up}(T)$ and $S_{all}(T)$ but NP-hard for $M_{all}(T)$ (even for 3-regular planar graphs). We show that for every graph $G$ and port numbering there exists a spanning tree $T$ for which $S_{up}(T) = O(n\log\log n)$. We give a tight bound of $O(n)$ in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port assignments. We conclude by discussing some applications for our tree representation schemes.
Published: 2005

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30. On discretization schemes for stochastic evolution equations

31. From left modules to algebras over an operad: application to combinatorial Hopf algebras

32. Labeling Schemes for Tree Representation

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