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1. The Two-Echelon Stochastic Multi-period Capacitated Location-Routing Problem

Author

Imen Ben Mohamed, Walid Klibi, Ruslan Sadykov, Halil Şen, François Vanderbeck, Kedge Business School (Kedge BS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Reformulations based algorithms for Combinatorial Optimization (Realopt), 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)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (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), Formulations étendues et méthodes de décomposition pour des problèmes génériques d'optimisation (EDGE), 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, Mapotempo, Atoptima, Experiments presented in this paper were carried out using the PlaFRIM (Federative Platform for Research in Computer Science and Mathematics), created under the Inria PlaFRIM development action with support from Bordeaux INP, LABRI and IMB and other entities: Conseil Régional d’Aquitaine, Université de Bordeaux, CNRS and ANR in accordance to the 'Programme d’Investissements d’Avenir' (see www.plafrim.fr/en/home).HS gratefully acknowledges the financial support of the FMJH ‘Program Gaspard Monge for optimization and operations research and their interactions with data science’, and EDF., 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 de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Institut de Mathématiques de Bordeaux (IMB), and 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-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
Information Systems and Management, General Computer Science, Modeling and Simulation, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], Management Science and Operations Research, Industrial and Manufacturing Engineering
Abstract

International audience; Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP). It considers a network partitioned into two capacitated distribution echelons: each echelon involves a specific location-assignment-transportation schema that must cope with the future demand. It aims to decide the number and location of warehousing/storage platforms (WPs) and distribution/fulfillment platforms (DPs), and on the capacity allocated from first echelon to second echelon platforms. In the second echelon, the goal is to construct vehicle routes that visit ship-to locations (SLs) from operating distribution platforms under a stochastic and time-varying demand and varying costs. This problem is modeled as a two-stage stochastic program with integer recourse, where the first-stage includes location and capacity decisions to be fixed at each period over the planning horizon, while routing decisions of the second echelon are determined in the recourse problem. We propose a logic-based Benders decomposition approach to solve this model. In the proposed approach, the location and capacity decisions are taken by solving the Benders master problem. After these first-stage decisions are fixed, the resulting sub-problem is a capacitated vehicle-routing problem with capacitated multiple depots (CVRP-CMD) that is solved by a branch-cut-and-price algorithm. Computational experiments show that instances of realistic size can be solved optimally within a reasonable time and provide relevant managerial insights on the impact of the stochastic and multi-period settings on the 2E-CLRP.

Published
2022

2. An iterative dynamic programming approach for the temporal knapsack problem

Author

Boris Detienne, Gaël Guillot, François Clautiaux, Reformulations based algorithms for Combinatorial Optimization (Realopt), 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)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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-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), This work was funded by Investments for the future Program IdEx Bordeaux, Cluster of ExcellenceSySNum.Experiments presented in this paper were carried out using the PLAFRIM experimental testbed,being developed under the Inria PlaFRIM development action with support from Bordeaux INP, LABRIand IMB and other entities: Conseil R ́egional d’Aquitaine, Universit ́e de Bordeaux, CNRS and ANR inaccordance to the programme d’investissements d’Avenir (see https://www.plafrim.fr/), Plafrim, RealOpt, Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Institut de Mathématiques de Bordeaux (IMB), and 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 de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
Mathematical optimization, Information Systems and Management, General Computer Science, Computer science, Generalization, Temporal knapsack, 0211 other engineering and technologies, 02 engineering and technology, Management Science and Operations Research, Industrial and Manufacturing Engineering, Set (abstract data type), symbols.namesake, Lagrangian Relaxation, 0502 economics and business, 050210 logistics & transportation, 021103 operations research, 05 social sciences, Exact algorithm, Successive Sublimation Dynamic Programming method, Exponential function, Dynamic programming, Lagrangian relaxation, Knapsack problem, Modeling and Simulation, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; In this paper, we address the temporal knapsack problem (TKP). In this generalization of the classical knapsack problem, selected items enter and leave the knapsack at fixed dates. We solve the TKP with a dynamic program of exponential size, which is solved using a method called Successive Sublimation Dynamic Programming (SSDP). This method starts by relaxing a set of constraints from the initial problem, and iteratively reintroduces them when needed. We show that a direct application of SSDP to the temporal knapsack problem does not lead to an effective method, and that several improvements are needed to compete with the best results from the literature.

Published
2021

3. 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

4. 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

5. 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

6. 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

7. Programming Strategies for Irregular Algorithms on the Emu Chick

Author

Jiajia Li, Ümit V. Çatalyürek, Rich Vuduc, Jeffrey Young, Bora Uçar, Eric R. Hein, Abdurrahman Yasar, Srinivas Eswar, Jason Riedy, Thomas M. Conte, Emu Technology, Georgia Institute of Technology [Atlanta], Pacific Northwest National Laboratory (PNNL), Optimisation des ressources : modèles, algorithmes et ordonnancement (ROMA), 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 de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de l'Informatique du Parallélisme (LIP), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), This work partially was supported by NSF Grant ACI-1339745 (XScala), an IARPA contract, and the Defense Advanced Research Projects Agency (DARPA) under agreement #HR0011-13-2-0001. Any opinions, findings, conclusions, or recommendations in this paper are solely those of the authors and do not necessarily reflect the position or the policy of the sponsors. Thanks also to the Emu Technology team for support and debugging assistance with the Emu Chick prototype, and to the reviewers for their thoughtful comments., École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL)

Subjects
FOS: Computer and information sciences, 0301 basic medicine, Computer science, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Memory bandwidth, 02 engineering and technology, Thread (computing), 020202 computer hardware & architecture, Computer Science Applications, 03 medical and health sciences, 030104 developmental biology, Computational Theory and Mathematics, Application-specific integrated circuit, Computer Science - Distributed, Parallel, and Cluster Computing, Hardware and Architecture, Modeling and Simulation, 0202 electrical engineering, electronic engineering, information engineering, Graph alignment, Bandwidth (computing), Distributed, Parallel, and Cluster Computing (cs.DC), [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Field-programmable gate array, Algorithm, Software, Analysis of algorithms
Abstract

The Emu Chick prototype implements migratory memory-side processing in a novel hardware system. Rather than transferring large amounts of data across the system interconnect, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each remote memory read. Previous work has characterized the performance of the Chick prototype in terms of memory bandwidth and programming differences from more typical, non-migratory platforms, but there has not yet been an analysis of algorithms on this system. This work evaluates irregular algorithms that could benefit from the lightweight, memory-side processing of the Chick and demonstrates techniques and optimization strategies for achieving performance in sparse matrix-vector multiply operation (SpMV), breadth-first search (BFS), and graph alignment across up to eight distributed nodes encompassing 64 nodelets in the Chick system. We also define and justify relative metrics to compare prototype FPGA-based hardware with established ASIC architectures. The Chick currently supports up to 68x scaling for graph alignment, 80 MTEPS for BFS on balanced graphs, and 50% of measured STREAM bandwidth for SpMV.

Published
2020

8. Bidirectional LSTM Autoencoder for Sequence Based Anomaly Detection in Cyber Security

Author

Ashima Chawla, Brian Lee, Paul Jacob, Sheila Fallon, and This project reported in this paper has received funding from the European Union Horizon 2020 research and innovation programme under grant agreement No. 700071 for the PROTECTIVE project.

Subjects
business.industry, Computer science, Pattern recognition, Autoencoders, Autoencoder, Embeddings, System call, Modeling and Simulation, Anomaly detection, Artificial intelligence, Host based intrusion, business, Software, CuDNNLSTM, Software Research Institute AIT, Sequence (medicine)
Abstract

Cyber-security is concerned with protecting information, a vital asset in today’s world. The volume of data that is generated can be usefully analyzed when cyber-security systems are effectively implemented with the aid of software support. Our approach is to determine normal behavior of a system based on sequences of system call traces made by the kernel processes in the system. This paper describes a robust and computationally efficient anomaly based host based intrusion detection system using an Encoder-Decoder mechanism. Using CuDNNLSTM networks, it is possible to obtain a set of comparable results with reduced training times. The Bidirectional Encoder and a unidirectional Decoder is trained on normal call sequences in the ADFA-LD dataset. Intrusion Detection is evaluated based on determining the probability of a sequence being reconstructed by the model yes

Published
2019

9. Quantifying model evidence for yellow fever transmission routes in Africa

Author

Katy A. M. Gaythorpe, Laurence Cibrelus, Tini Garske, Kévin Jean, Imperial College London, Laboratoire Modélisation, épidémiologie et surveillance des risques sanitaires (MESuRS), Conservatoire National des Arts et Métiers [CNAM] (CNAM), Pasteur-Cnam Risques infectieux et émergents (PACRI), Institut Pasteur [Paris]-Conservatoire National des Arts et Métiers [CNAM] (CNAM), World Health Organisation (WHO), Organisation Mondiale de la Santé / World Health Organization Office (OMS / WHO), Funding:This work was carried out as part of the Vaccine Impact Modelling Consortium (www.vaccineimpact.org),but the views expressed are those of the authors and not necessarily those of the Consortium or its funders.The funders were given the opportunity to review this paper prior to publication,but the final decision on the content of the publication was taken by the authors.We acknowledge joint Centre funding from the UK Medical Research Council and Department for International Development. The research leading to these results has received funding from the Bill & Melinda Gates foundation (OPP1117543,OPP1157270 http://www.gatesfoundation.org/)and from the Medical Research Council (MR/R015600/1https://mrc.ukri.org/)., HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), and Institut Pasteur [Paris] (IP)-Conservatoire National des Arts et Métiers [CNAM] (CNAM)

Subjects
0301 basic medicine, Viral Diseases, Epidemiology, Force of infection, Statics, Pathology and Laboratory Medicine, law.invention, Geographical Locations, Bayes' theorem, 0302 clinical medicine, law, [SDV.MHEP.MI]Life Sciences [q-bio]/Human health and pathology/Infectious diseases, Aedes, Statistics, Medicine and Health Sciences, Public and Occupational Health, Biology (General), Ecology, Physics, Yellow fever, Linear model, Classical Mechanics, Vaccination and Immunization, Geography, Transmission (mechanics), Infectious Diseases, Serology, Computational Theory and Mathematics, INFECTIONS, Modeling and Simulation, Physical Sciences, Yellow fever virus, Life Sciences & Biomedicine, Research Article, Generalized linear model, Biochemistry & Molecular Biology, Bioinformatics, QH301-705.5, Immunology, Bayesian inference, Models, Biological, Biochemical Research Methods, BAYESIAN MODEL, Infectious Disease Epidemiology, 03 medical and health sciences, Cellular and Molecular Neuroscience, Yellow Fever, Genetics, medicine, Animals, Humans, Molecular Biology, 01 Mathematical Sciences, Ecology, Evolution, Behavior and Systematics, Estimation, Science & Technology, Models, Statistical, Biology and Life Sciences, Computational Biology, Bayes Theorem, 06 Biological Sciences, medicine.disease, 030104 developmental biology, People and Places, Africa, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, Mathematical & Computational Biology, 08 Information and Computing Sciences, Preventive Medicine, 030217 neurology & neurosurgery
Abstract

Yellow fever is a vector-borne disease endemic in tropical regions of Africa, where 90% of the global burden occurs, and Latin America. It is notoriously under-reported with uncertainty arising from a complex transmission cycle including a sylvatic reservoir and non-specific symptom set. Resulting estimates of burden, particularly in Africa, are highly uncertain. We examine two established models of yellow fever transmission within a Bayesian model averaging framework in order to assess the relative evidence for each model’s assumptions and to highlight possible data gaps. Our models assume contrasting scenarios of the yellow fever transmission cycle in Africa. The first takes the force of infection in each province to be static across the observation period; this is synonymous with a constant infection pressure from the sylvatic reservoir. The second model assumes the majority of transmission results from the urban cycle; in this case, the force of infection is dynamic and defined through a fixed value of R0 in each province. Both models are coupled to a generalised linear model of yellow fever occurrence which uses environmental covariates to allow us to estimate transmission intensity in areas where data is sparse. We compare these contrasting descriptions of transmission through a Bayesian framework and trans-dimensional Markov chain Monte Carlo sampling in order to assess each model’s evidence given the range of uncertainty in parameter values. The resulting estimates allow us to produce Bayesian model averaged predictions of yellow fever burden across the African endemic region. We find strong support for the static force of infection model which suggests a higher proportion of yellow fever transmission occurs as a result of infection from an external source such as the sylvatic reservoir. However, the model comparison highlights key data gaps in serological surveys across the African endemic region. As such, conclusions concerning the most prevalent transmission routes for yellow fever will be limited by the sparsity of data which is particularly evident in the areas with highest predicted transmission intensity. Our model and estimation approach provides a robust framework for model comparison and predicting yellow fever burden in Africa. However, key data gaps increase uncertainty surrounding estimates of model parameters and evidence. As more mathematical models are developed to address new research questions, it is increasingly important to compare them with established modelling approaches to highlight uncertainty in structures and data., Author summary Yellow fever (YF) is notoriously under reported due to non-specific symptom spectrum and the true burden is highly uncertain as a result of a complex transmission cycle. As such, estimates surrounding YF burden are highly uncertain and the mechanisms behind transmission are often unclear. We assess these mechanisms and the resulting uncertainty by estimating two existing models of YF transmission within a product space framework. This allows us to produce updated estimates of transmission intensity and to compare the relative support for each model given the data. We find strong support for a model assuming a static force of infection, approximating the constant infection pressure from the sylvatic reservoir of YF. We also highlight areas where data is sparse, often the same areas estimated to have especially high transmission intensity. This is the first robust multi-model approach to applied YF modelling and provides a framework that could be extended to other disease models.

Published
2019

10. Multidimensional stability of V-shaped traveling fronts in time periodic bistable reaction–diffusion equations

Author

Wei-Jie Sheng, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and This paper was supported by NSF of China (11401134) and by China Scholarship Council for a one year visit of Aix Marseille Université.

Subjects
Current (mathematics), Bistability, 010102 general mathematics, Mathematical analysis, Time periodic V-shaped traveling fronts, 01 natural sciences, Stability (probability), 010101 applied mathematics, Bistable, Computational Mathematics, Computational Theory and Mathematics, Two-dimensional space, Reaction diffusion equations, Modeling and Simulation, Stability theory, Bounded function, Reaction–diffusion system, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Initial value problem, 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, Multidimensional stability, Mathematics
Abstract

International audience; This paper deals with the multidimensional stability of time periodic V-shaped traveling fronts in bistable reaction–diffusion equations. It is well known that time periodic V-shaped traveling fronts are asymptotically stable in two dimensional space. In the current study, we further show that such fronts are asymptotically stable under spatially decaying initial perturbations in Rn with n≥3. In particular, we show that the fronts are algebraically stable if the initial perturbations belong to L1 in a certain sense. Furthermore, we prove that there exists a solution oscillating permanently between two time periodic V-shaped traveling fronts, which implies that time periodic V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Finally we show that time periodic V-shaped traveling fronts are only time global solutions of the Cauchy problem if the initial perturbations lie between two time periodic V-shaped traveling fronts.

Published
2016

11. 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

12. 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

13. 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