Search

Your search keyword '"Fabien Campillo"' showing total 60 results
Start Over Author "Fabien Campillo"
60 results on '"Fabien Campillo"'

7. Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of bipolar disorder

Author

Efstathios Pavlidis, Fabien Campillo, Albert Goldbeter, Mathieu Desroches, Mathématiques pour les Neurosciences (MATHNEURO), 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), Neuromod Institute, Université Côte d'Azur (UCA), Unité de Chronobiologie Théorique [Brussels, Belgium], and Université libre de Bruxelles (ULB)

Subjects
[SCCO.NEUR]Cognitive science/Neuroscience, Cognitive Neuroscience, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Abstract

Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode of mania or depression. A four-dimensional model by A. Goldbeter [27, 28] rests upon the notion that manic and depressive symptoms are produced by two competing and auto-inhibited neural networks. Some of the rich dynamics that this model can produce, include complex rhythms formed by both small-amplitude (subthreshold) and large-amplitude (suprathreshold) oscillations and could correspond to mixed bipolar states. These rhythms are commonly referred to asmixed mode oscillations (MMOs)and they have already been studied in many different contexts [7, 50]. In order to accurately explain these dynamics one has to apply a mathematical apparatus that makes full use of the timescale separation between variables. Here we apply the framework of multiple-timescale dynamics to the model of BD in order to understand the mathematical mechanisms underpinning the observed dynamics of changing mood. We show that the observed complex oscillations can be understood as MMOs due to a so-calledfolded-node singularity. Moreover, we explore the bifurcation structure of the system and we provide possible biological interpretations of our findings. Finally, we show the robustness of the MMOs regime to stochastic noise and we propose a minimal three-dimensional model which, with the addition of noise, exhibits similar yet purely noise-driven dynamics. The broader significance of this work is to introduce mathematical tools that could be used to analyse and potentially control future, more biologically grounded models of BD.

Published
2022
Full Text
View/download PDF

16. Conductance-Based Refractory Density Approach for a Population of Bursting Neurons

Author

Serafim Rodrigues, Antoni Guillamon, Mathieu Desroches, Anton V. Chizhov, Fabien Campillo, A.F. Ioffe Physical-Technical Institute, Russian Academy of Sciences [Moscow] (RAS), Sechenov Institute of Evolutionary Physiology and Biochemistry, Basque Center for Applied Mathematics (BCAM), Basque Center for Applied Mathematics, Mathématiques pour les Neurosciences (MATHNEURO), 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), Universitat Politècnica de Catalunya [Barcelona] (UPC), Ikerbasque - Basque Foundation for Science, Basque Foundation for Science (IKERBASQUE), Basque Foundation for Science (Ikerbasque), Universitat Politècnica de Catalunya. Departament de Matemàtiques, and Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC

Subjects
0301 basic medicine, Computer science, General Mathematics, Immunology, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], General Biochemistry, Genetics and Molecular Biology, intrinsically bursting neuron, Piecewise linear function, Arquitectura i estalvi d'energia, 03 medical and health sciences, Bursting, 0302 clinical medicine, medicine, education, Edificació::Construcció sostenible [Àrees temàtiques de la UPC], neuronal population, ComputingMilieux_MISCELLANEOUS, General Environmental Science, Architecture and energy conservation, Pharmacology, Statistical ensemble, education.field_of_study, Quantitative Biology::Neurons and Cognition, General Neuroscience, [SCCO.NEUR]Cognitive science/Neuroscience, Conductance, conductance-based refractory density model, 030104 developmental biology, Brain state, medicine.anatomical_structure, nervous system, Computational Theory and Mathematics, Population model, 030220 oncology & carcinogenesis, Neuron, General Agricultural and Biological Sciences, Neuroscience
Abstract

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modeling interact- ing populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting popula- tion model makes use of slow-fast analysis, which leads to a novel method- ology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explo- rations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy). Russian Science Foundation grant (project 16-15- 10201) Spanish grant MINECO-FEDER-UE MTM-2015-71509-C2-2-R Catalan Grant number 2017SGR1049

Published
2019
Full Text
View/download PDF

17. Modélisation stochastique pour les biotechnologies : modèle anaérobie AM2b

Author

Fabien Campillo, Mohsen Chebbi, Salwa Toumi, Mathématiques pour les Neurosciences (MATHNEURO), 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), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM), and Institut National des Sciences Appliquées et de Technologie - Carthage (INSAT Carthage)

Subjects
pure jump process, modèle AM2b, [SDV]Life Sciences [q-bio], 010102 general mathematics, 05 social sciences, diffusion approximation, approximation diffusion, General Medicine, ordinary differential equation, stochastic differential equation, 01 natural sciences, AM2b model, processus de saut pur, Stochastic differential equation, équation différentielle stochastique, 0502 economics and business, Calculus, équation différentielle ordinaire, [CHIM]Chemical Sciences, 0101 mathematics, [MATH]Mathematics [math], Humanities, 050203 business & management, Mathematics
Abstract

Le modèle AM2b est classiquement représenté par un système d'équations différentielles. Toutefois ce modèle n'est valide qu'en grande population et notre objectif est d'établir plusieurs mo-dèles stochastiques à différentes échelles. À l'échelle microscopique, on propose un modèle sto-chastique de saut pur que l'on peut simuler de fa con exacte. Mais dans la plupart des situations ce genre de simulation n'est pas réaliste, et nous proposons des méthodes de simulation approchées de type poissonnien ou de type diffusif. La méthode de simulation de type diffusif peut être vue comme une discrétisation d'une équation différentielle stochastique. Nous présentons enfin de fa con infor-melle un résultat de type loi des grands nombres/théorème central limite fonctionnelle qui démontre la convergence de ses modèles stochastiques vers le modèles déterministe initial. The model AM2b is conventionally represented by a system of differential equations. However, this model is valid only in a large population context and our objective is to establish several stochastic models at different scales. At a microscopic scale, we propose a pure jump stochastic model that can be simulated exactly. But in most situations this exact simulation is not feasible, and we propose approximate simulation methods of Poisson type and of diffusive type. The diffusive type simulation method can be seen as a discretization of a stochastic differential equation. Finally, we formally present a result of law of large numbers and of functional central limit theorem which demonstrates the convergence of these stochastic models towards the initial deterministic models.

Published
2019
Full Text
View/download PDF

20. Conductance-Based Refractory Density Approach for a Population of Bursting Neurons

Author

Anton, Chizhov, Fabien, Campillo, Mathieu, Desroches, Antoni, Guillamon, and Serafim, Rodrigues

Subjects
Neurons, Epilepsy, Models, Neurological, Action Potentials, Brain, Cell Count, Mathematical Concepts, Biophysical Phenomena, Electrophysiological Phenomena, Spatio-Temporal Analysis, Linear Models, Potassium, Animals, Humans, Computer Simulation, Nerve Net
Abstract

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modelling interacting populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study, we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting population model makes use of slow-fast analysis, which leads to a novel methodology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explorations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).

Published
2018

21. Analysis and Approximation of a Stochastic Growth Model with Extinction

Author

Irène Larramendy-Valverde, Marc Joannides, Fabien Campillo, Littoral, Environnement : Méthodes et Outils Numériques (LEMON), 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), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratory of Excellence (Labex) NUMEV (Digital and Hardware Solutions, Modelling for the Environment and Life Sciences), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), and Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)

Subjects
Statistics and Probability, General Mathematics, Markov process, PDE, 01 natural sciences, 010305 fluids & plasmas, 010104 statistics & probability, symbols.namesake, 0103 physical sciences, Applied mathematics, Almost surely, 0101 mathematics, logistic model, Mathematics, extinction, Markov processes, Mathematical analysis, Ode, Probabilistic logic, Finite difference, Fokker-Planck equation, diffusion processes, Growth model, 16. Peace & justice, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Extinction (optical mineralogy), symbols, Fokker–Planck equation
Abstract

International audience; We consider a stochastic growth model for which extinction eventually occurs almost surely. The associated complete Fokker–Planck equation describing the law of the process is established and studied. This equation combines a PDE and an ODE, connected one to each other. We then design a finite differences numerical scheme under a probabilistic viewpoint. The model and its approximation are evaluated through numerical simulations.

Published
2015
Full Text
View/download PDF

22. Parameter identification for a stochastic logistic growth model with extinction

Author

Fabien Campillo, Irène Larramendy-Valverde, Marc Joannides, Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Mathématiques pour les Neurosciences (MATHNEURO), and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0301 basic medicine, Statistics and Probability, Extinction, Monte Carlo method, Inference, Logistic regression, 01 natural sciences, 010104 statistics & probability, 03 medical and health sciences, Stochastic differential equation, Identification (information), 030104 developmental biology, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Modeling and Simulation, Statistics, Fokker–Planck equation, 0101 mathematics, Logistic function, Computer Science::Databases, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

We consider a stochastic logistic growth model given by a stochastic differential equation, for which extinction can occur. We first propose appropriate adaptation of some standard inference method...

Published
2017
Full Text
View/download PDF

23. On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

Author

Fabien Campillo, Coralie Fritsch, Nicolas Champagnat, Mathématiques pour les Neurosciences (MATHNEURO), 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), TO Simulate and CAlibrate stochastic models (TOSCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Work (thermodynamics), integro-differential equation, Stochastic modelling, General Mathematics, infinite dimensional branching process, invasion fitness, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, Interpretation (model theory), Mathematics - Analysis of PDEs, piecewise-deterministic Markov process, Integro-differential equation, FOS: Mathematics, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Piecewise-deterministic Markov process, 0101 mathematics, Eigenvalues and eigenvectors, Mathematics, 021103 operations research, Applied Mathematics, Growth-fragmentation model, 010102 general mathematics, Probability (math.PR), Fragmentation (computing), Probabilistic logic, eigenproblem, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], bacterial population, individual-based model, Mathematics - Probability, Analysis of PDEs (math.AP)
Abstract

International audience; We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.

Published
2017
Full Text
View/download PDF

24. A numerical approach to determine mutant invasion fitness and evolutionary singular strategies

Author

Fabien Campillo, Otso Ovaskainen, Coralie Fritsch, Biosciences, Otso Ovaskainen / Principal Investigator, Centre of Excellence in Metapopulation Research, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), 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 Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Mathématiques pour les Neurosciences (MATHNEURO), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Biosciences [Helsinki], Faculty of Biological and Environmental Sciences [Helsinki], University of Helsinki-University of Helsinki, Centre for Biodiversity Dynamics, Norwegian University of Science and Technology [Trondheim] (NTNU), Norwegian University of Science and Technology (NTNU)-Norwegian University of Science and Technology (NTNU), and Helsingin yliopisto = Helsingfors universitet = University of Helsinki-Helsingin yliopisto = Helsingfors universitet = University of Helsinki

Subjects
DYNAMICS, 0106 biological sciences, Mathematical optimization, Individual-based model, Stochastic modelling, Computation, Population Dynamics, Population, Context (language use), Chemostat, Biology, 010603 evolutionary biology, 01 natural sciences, Quantitative Biology::Cell Behavior, Competitive exclusion principle, FOS: Mathematics, Evolutionary singular strategy, eigenvalue, Humans, Quantitative Biology::Populations and Evolution, 0101 mathematics, survival probability, education, Quantitative Biology - Populations and Evolution, Adaptive dynamics, POPULATION, Ecology, Evolution, Behavior and Systematics, Eigenvalues and eigenvectors, Stochastic Processes, education.field_of_study, Invasion fitness, Models, Genetic, [SDV.BID.EVO]Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE], Growth-fragmentation model, Numerical analysis, Probability (math.PR), Populations and Evolution (q-bio.PE), evolutionary singular, Biological Evolution, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], MODEL, 010101 applied mathematics, FOS: Biological sciences, 1181 Ecology, evolutionary biology, GROWTH, Genetic Fitness, strategy, Mathematics - Probability
Abstract

We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modeling of the small size mutant population by a stochastic model and the computation of its corresponding deterministic model. The use of the deterministic model greatly facilitates the numerical determination of the feasibility of invasion as well as the convergence-stability of the evolutionary singular strategy. Our approach combines standard adaptive dynamics with the link between the mutant survival criterion in the stochastic model and the sign of the eigenvalue in the corresponding deterministic model. We present our method in the context of a mass-structured individual-based chemostat model. We exploit a previously derived mathematical relationship between stochastic and deterministic representations of the mutant population in the chemostat model to derive a general numerical method for analyzing the invasion fitness in the stochastic models. Our method can be applied to the broad class of evolutionary models for which a link between the stochastic and deterministic invasion fitnesses can be established. (C) 2017 Elsevier Inc. All rights reserved.

Published
2016
Full Text
View/download PDF

25. Stochastic modeling of the chemostat

Author

Fabien Campillo, Marc Joannides, Irène Larramendy, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-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 national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)

Subjects
Continuous-time stochastic process, Mathematical optimization, [SDV.BIO]Life Sciences [q-bio]/Biotechnology, Scale (ratio), Differential equation, Stochastic modelling, 01 natural sciences, Microscopic scale, 010305 fluids & plasmas, symbols.namesake, Stochastic differential equation, Diffusion approximation, 0103 physical sciences, Runge–Kutta method, Applied mathematics, [INFO.INFO-BT]Computer Science [cs]/Biotechnology, 0101 mathematics, Pure jump process, Mathematics, Tau-leap method, Ecological Modeling, Gillespie algorithm, Monte Carlo method, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010101 applied mathematics, Stochastic partial differential equation, Chemostat, Stochastic differential equations, symbols
Abstract

International audience; The chemostat is classically represented, at large population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations. We expound the mechanism to switch from one model to another, together with the associated simulation procedures. We also describe the domain of validity of the different models.

Published
2011
Full Text
View/download PDF

26. Convolution Particle Filter for Parameter Estimation in General State-Space Models

Author

Fabien Campillo and Vivien Rossi

Subjects
Mathematical optimization, Dynamical systems theory, State-space representation, U10 - Informatique, mathématiques et statistiques, Estimation theory, Aerospace Engineering, State vector, 02 engineering and technology, Dynamical system, 01 natural sciences, Convolution, 010104 statistics & probability, Extended Kalman filter, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0101 mathematics, Electrical and Electronic Engineering, Particle filter, Algorithm, Mathematics
Abstract

The state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter (EKF) and the bootstrap particle filter (PF), fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. We propose a variant of the PF based on convolution kernel approximation techniques. This approach is tested on a simulated case study.

Published
2009
Full Text
View/download PDF

27. Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models

Author

Fabien Campillo, Coralie Fritsch, Nicolas Champagnat, Littoral, Environnement : Méthodes et Outils Numériques (LEMON), 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 Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), and Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0301 basic medicine, Mathematical optimization, Stochastic modelling, infinite dimensional branching process, Population, invasion fitness, integro- differential equation, Context (language use), Models, Biological, 01 natural sciences, piecewise- deterministic Markov process, Set (abstract data type), 010104 statistics & probability, 03 medical and health sciences, Mathematics - Analysis of PDEs, FOS: Mathematics, growth-fragmentation-death model, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Piecewise-deterministic Markov process, 0101 mathematics, education, Probability, Mathematics, Branching process, Stochastic Processes, education.field_of_study, Stochastic process, Applied Mathematics, Probability (math.PR), eigenproblem, Survival Analysis, Agricultural and Biological Sciences (miscellaneous), Death, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 030104 developmental biology, bacterial population, Modeling and Simulation, Piecewise, individual-based model, Mathematics - Probability, Analysis of PDEs (math.AP)
Abstract

International audience; We present two approaches to study invasion in growth-fragmentation-death mod- els. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the second one is based on an integro-differential model. The invasion of the population is described by the survival probability for the former model and by an eigenproblem for the latter one. We study these two notions of invasion fitness, giving different characterizations of the growth of the population, and we make links between these two complementary points of view. In particular we prove that the two approaches lead to the same crite- rion of possible invasion. Based on Krein-Rutman theory, we also give a proof of the existence of a solution to the eigenproblem, which satisfies the conditions needed for our study of the stochastic model, hence providing a set of assumptions under which both approaches can be carried out. Finally, we motivate our work in the context of adaptive dynamics in a chemostat model.

Published
2016
Full Text
View/download PDF

28. Weak Convergence of a Mass-Structured Individual-Based Model

Author

Fabien Campillo, Coralie Fritsch, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), French National Network of Complex Systems (RNSC), Meta-omics of Microbial Ecosystems (MEM) metaprogram of INRA, RNSC project MnMs (Numerical Models for Microbial ecosystems), INRA Metaprogram MEM (Metagenomics of Microbial Ecosystems), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)

Subjects
Control and Optimization, Monte Carlo method, Mathematics Subject Classification 60J80, 60J85, 37N25, 92D25, Chemostat, 01 natural sciences, Quantitative Biology::Cell Behavior, 010104 statistics & probability, 03 medical and health sciences, Integro-differential equation, Convergence (routing), Applied mathematics, 0101 mathematics, [MATH]Mathematics [math], Monte Carlo, 030304 developmental biology, Mathematics, 0303 health sciences, Weak convergence, Stochastic process, Applied Mathematics, Individually-based model, Mathematical analysis, Division (mathematics), Weak convergence of Markov processes, Mass-structured chemostat model, Ordinary differential equation
Abstract

International audience; We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and washout). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations

Published
2015
Full Text
View/download PDF

29. A modeling approach of the chemostat

Author

Fabien Campillo, Jérôme Harmand, Coralie Fritsch, Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Biotechnologie de l'Environnement [Narbonne] (LBE), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), 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), Meta-omics of Microbial Ecosystems (MEM) metaprogram of INRA, Project 'Modèles Numériques pour les écosystèmes Microbiens' of the French National Network of Complex Systems (RNSC call 2012), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), and Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Class (set theory), Mathematical optimization, Stochastic chemostat model, Differential equation, Population, Quantitative Biology - Quantitative Methods, Modeling and simulation, Law of large numbers, Applied mathematics, Quantitative Biology::Populations and Evolution, [MATH]Mathematics [math], Representation (mathematics), education, Quantitative Biology - Populations and Evolution, Monte Carlo, Quantitative Methods (q-bio.QM), Mathematics, Event (probability theory), education.field_of_study, Ecological Modeling, Population size, Mass structured chemostat model, Populations and Evolution (q-bio.PE), FOS: Biological sciences, Individually-based model (IBM), Chemostat model
Abstract

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links between these representations in terms of mathematical analysis but also in terms of modeling and numerical simulations. We illustrate this approach on the model of chemostat., Comment: arXiv admin note: substantial text overlap with arXiv:1308.2411

Published
2015
Full Text
View/download PDF

30. Erratum to: Weak convergence of a mass-structured individual-based mode

Author

Fabien Campillo, Coralie Fritsch, Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Littoral, Environment: MOdels and Numerics (LEMON), 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 Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)

Subjects
Individual based, Control and Optimization, weak convergence of Markov processes, Weak convergence, integro-differential equation, Applied Mathematics, Individually-based model, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], mass-structured chemostat model, Monte Carlo, Mathematics, Quantitative Biology::Cell Behavior
Abstract

Erratum, voir l'article original : http://prodinra.inra.fr/record/285362; International audience; We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and washout). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations.

Published
2015
Full Text
View/download PDF

31. Homogenised model linking microscopic and macroscopic dynamics of a biofilm: Application to growth in a plug flow reactor

Author

Chloé Deygout, Alain Rapaport, Annick Lesne, Fabien Campillo, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Institut des Hautes Études Scientifiques (IHES), IHES, French Agency of Research SYSCOMM [ANR AAP215-SYSCOMM-2009], Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
0106 biological sciences, Materials science, Scale (ratio), Computation, 010603 evolutionary biology, 01 natural sciences, biofilm, 03 medical and health sciences, partial differential equations, Macro, Plug flow reactor model, 030304 developmental biology, [SDV.EE]Life Sciences [q-bio]/Ecology, environment, 0303 health sciences, Mesoscopic physics, Partial differential equation, Plug flow, advection-diffusion, Ecological Modeling, Dynamics (mechanics), attachment-detachment, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 13. Climate action, Biological system, individual-based model, plug flow reactor
Abstract

We propose a new "hybrid" model for the simulation of biofilm growth in a plug flow bioreactor, that combines information from three scales: a microscopic one for the individual bacteria, a mesoscopic or "coarse-grained" one that homogenises at an intermediate scale the quantities relevant to the attachment/detachment process, and a macroscopic one in terms of substrate concentration. In contrast to existing partial differential equations models, this approach is based on a description of biological mechanisms at the individual scale, thus bringing in a biological justification of the attachment/detachment process responsible of the macroscopic behaviour. We found that compared to purely individual based or purely macroscopic models, * the approximate coarse-grained scale simplifies the change of scales from micro to macro, and speeds up the computation, * additional information about the stochasticity of the solution, especially at small populations, is revealed compared with the numerical simulations of partial differential equations models. Furthermore, the coarse-grained model can be much more easily adapted to various attachment/detachment hypotheses, that are at the core of the biofilm development.

Published
2013
Full Text
View/download PDF

32. Effect of population size in a predator-prey model

Author

Fabien Campillo, Claude Lobry, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-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 national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)

Subjects
Singular perturbation, Differential equation, 01 natural sciences, 010104 statistics & probability, 03 medical and health sciences, Stochastic differential equation, Birth and death processes, Applied mathematics, Quantitative Biology::Populations and Evolution, [INFO]Computer Science [cs], 0101 mathematics, [MATH]Mathematics [math], 030304 developmental biology, Variable (mathematics), Mathematics, Diffusion equations, 0303 health sciences, Extinction, Predator-prey model, Ecological Modeling, Gillespie algorithm, Ordinary differential equation, Jump, Mathematical economics, Ordinary differential equations
Abstract

International audience; We consider a hybrid version of the basic predator-prey differential equation model: a pure jump stochas- tic model for the prey variable x coupled with a differential equation model for the predator variable y. This hybrid model is derived from the classical birth and death process. The model contains a parameter ω which represents the number of individuals for one unit of prey: x = 1 corresponds to ω individual prey. It is shown by the mean of simulations and explained by a mathematical analysis based on a result from the singular perturbation theory - the so-called theory of Canards - that qualitative properties of the model like persistence or extinction are dramatically sensitive to ω. For instance, in our example, if ω = 107 we have extinction and if ω = 108 we have persistence. This means that we must be very cautious when we use continuous variables in place of discrete ones in dynamic population modeling even when we use stochastic differential equations in place of deterministic ones.

Published
2012
Full Text
View/download PDF

33. Particle filtering for the chemostat

Author

Jérôme Harmand, Brahim Cherki, Fabien Campillo, Boumediene Benyahia, Laboratoire d'Automatique de Tlemcen (LAT), Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen], Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Laboratoire de Biotechnologie de l'Environnement [Narbonne] (LBE), IEEE Control Systems Society. FRA., Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), and Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)

Subjects
Approximation theory, Stochastic process, Stochastic modelling, Context (language use), 02 engineering and technology, Chemostat, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, 020401 chemical engineering, Control theory, Nonlinear filter, Filtering problem, 0204 chemical engineering, 0101 mathematics, Biological system, Particle filter, Mathematics
Abstract

International audience; We develop a particle filter approximation of the optimal nonlinear filter in the context of the chemostat. We propose a stochastic model of the chemostat together with an observation model. One of the characteristics of applications in bioprocesses is that the time between two observations is relatively large. We account for this point in the development of the particle filter by refining the prediction step of the particle filter. We present numerical tests on simulated measurements.

Published
2012
Full Text
View/download PDF

34. Introduction to the special issue of Ecological Modelling: 'Modelling clonal plant growth: From ecological concepts to mathematics'

Author

J. M. Van Groenendael, Marc Garbey, Cendrine Mony, Fabien Campillo, Abdallah El Hamidi, Department of Aquatic Ecology & Environmental Biology, Radboud university [Nijmegen], Ecosystèmes, biodiversité, évolution [Rennes] (ECOBIO), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR)-Centre National de la Recherche Scientifique (CNRS), Department of computer Science [Houston], Rice University [Houston], Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Mathématiques, Image et Applications (MIA), Université de La Rochelle (ULR), Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR)-Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Mathématiques, Image et Applications - EA 3165 (MIA), Radboud University [Nijmegen], Université de Rennes (UR)-Institut Ecologie et Environnement (INEE), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and La Rochelle Université (ULR)

Subjects
0106 biological sciences, Plant growth, Management science, 010604 marine biology & hydrobiology, Ecological Modeling, Ecological modelling, Mathematics education, [SDE.BE]Environmental Sciences/Biodiversity and Ecology, 010603 evolutionary biology, 01 natural sciences, Mathematics
Abstract

Introduction à un n° spécial d'un journal; International audience

Published
2012
Full Text
View/download PDF

35. Simulation and analysis of an individual-based model for graph-structured plant dynamics

Author

Nicolas Champagnat, Fabien Campillo, Water Resource Modeling (MERE), 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 National de la Recherche Agronomique (INRA), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), TOSCA, INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), ANR: MODECOL,MODECOL, Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), ANR-08-SYSC-0012,MODECOL,Utilisation de la modélisation pour améliorer les services écologiques associés aux systèmes prairiaux(2008), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-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), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-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)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0106 biological sciences, Asymptotic analysis, Spacetime, Ecology, 010604 marine biology & hydrobiology, Ecological Modeling, Dynamics (mechanics), Structure (category theory), Markov process, clonal plant, 010603 evolutionary biology, 01 natural sciences, Field (geography), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, symbols.namesake, [SDV.EE.ECO]Life Sciences [q-bio]/Ecology, environment/Ecosystems, individual-based model (IBM), symbols, Graph (abstract data type), Applied mathematics, Quantitative Biology::Populations and Evolution, Mathematics
Abstract

International audience; We propose a stochastic individual-based model for clonal plant dynamics in continuous time and space, focusing on the effects of the network structure of the plants on the reproductive strategy of ramets. This model is coupled with an explicit advection-diffusion dynamics for resources. After giving a partially exact simulation scheme of the model, the capacity of the model to reproduce specific features of clonal plants, such as their efficiency to forage resources over the field, is numerically studied. Next, we propose a large population approximation of the model for phalanx-type populations, taking the form of an advection-diffusion PDE for population densities, where the influence of the local graph structure of the plant takes the form of a nonlinear dependence in the gradient of resources. Finally, extensions of the model and other possible large population scalings are discussed.

Published
2012
Full Text
View/download PDF

36. Approximation of the Fokker-Planck equation of the stochastic chemostat

Author

Irène Larramendy-Valverde, Fabien Campillo, Marc Joannides, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Institut National de Recherche en Informatique et en Automatique (Inria), and Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)

Subjects
General Computer Science, Stochastic modelling, Chemostat, stochastic differential equation, Theoretical Computer Science, Stochastic differential equation, FOS: Mathematics, Applied mathematics, Quantitative Biology::Populations and Evolution, Boundary value problem, Mathematics, Numerical Analysis, [STAT.AP]Statistics [stat]/Applications [stat.AP], chemostat, Applied Mathematics, Quantitative Biology::Molecular Networks, Mathematical analysis, Probability (math.PR), Fokker-Planck equation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Diffusion process, Modeling and Simulation, Finite difference scheme, Fokker–Planck equation, finite difference scheme, Mathematics - Probability
Abstract

In Mathematics and Computers in Simulation, 99 (SI, part. 1), 2014 Cf : https://prodinra.inra.fr/record/470553 (article séparé de la conférence à la demande de Nadine Hilgert)MAMERN IV--2011: The 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources- PART I; International audience; We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker-Planck associated with this diffusion process, in particular we describe the boundary conditions that modelize the washout. We propose an adapted finite difference scheme for the approximation of the solution of the Fokker-Planck equation.

Published
2011
Full Text
View/download PDF

37. Méthodes MCMC en interaction pour l'évaluation de ressources naturelles

Author

Philippe Cantet, Vivien Rossi, Rivo Rakotozafy, Fabien Campillo, Water Resource Modeling (MERE), 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 National de la Recherche Agronomique (INRA), Ouvrages hydrauliques et hydrologie (UR OHAX), Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF), Université de Fianarantsoa, Ecologie des forêts de Guyane (ECOFOG), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Université des Antilles et de la Guyane (UAG)-AgroParisTech-Centre National de la Recherche Scientifique (CNRS), and Université de Fianarantsoa [Fianarantsoa]

Subjects
Monte Carlo par chaîne de Markov, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, 0303 health sciences, 03 medical and health sciences, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Markov chain Monte Carlo, Bayesian inference, General Medicine, 0101 mathematics, 01 natural sciences, Inférence bayésienne, 030304 developmental biology
Abstract

Markov chain Monte Carlo (MCMC) methods together with hidden Markov models are extensively used in the Bayesian inference for many scientific fields like environment and ecology. Through simulated examples we show that the speed of convergence of these methods can be very low. In order to improve the convergence properties, we propose a method to make parallel chains interact. We apply this method to a biomass evolution model for fisheries., Les méthodes de Monte Carlo par chaînes de Markov (MCMC) couplées à des modèles de Markov cachés sont utilisées dans de nombreux domaines, notamment en environnement et en écologie. Sur des exemples simples, nous montrons que la vitesse de convergence de ces méthodes peut être très faible. Nous proposons de mettre en interaction plusieurs algorithmes MCMC pour accélérer cette convergence. Nous appliquons ces méthodes à un modèle d'évolution de la biomasse d'une pêcherie.

Published
2008
Full Text
View/download PDF

38. Optimal ergodic control of nonlinear stochastic systems

Author

Fabien Campillo

Subjects
Stochastic control, Nonlinear system, Mathematical optimization, Discretization, Finite difference, Ergodic theory, Invariant measure, Uniqueness, Infinitesimal generator, Mathematics
Abstract

We study a class of ergodic stochastic control problems for diffusion processes. We describe the basic ideas concerning the Hamilton-Jacobi-Bellman equation. For a given class of control problems we establish an existence and uniqueness property of the invariant measure. Then we present a numerical approximation to the optimal feedback control based on the discretization of the infinitesimal generator using finite difference schemes. Finally, we apply these techniques to the control of semi-active suspensions for road vehicle.

Published
2008
Full Text
View/download PDF

39. Recursive maximum likelihood estimation for structural health monitoring: tangent filter implementations

Author

L. Mevel, Fabien Campillo, Applications of interacting particle systems to statistics (ASPI), Université de Rennes (UR)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Statistical Inference for Structural Health Monitoring (I4S), Département Composants et Systèmes (IFSTTAR/COSYS), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon-PRES Université Nantes Angers Le Mans (UNAM)-PRES Université Lille Nord de France-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon-PRES Université Nantes Angers Le Mans (UNAM)-PRES Université Lille Nord de France-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Rennes – Bretagne Atlantique

Subjects
020301 aerospace & aeronautics, 010504 meteorology & atmospheric sciences, Covariance matrix, Condition monitoring, Tangent, 02 engineering and technology, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, 0203 mechanical engineering, Filter (video), Control theory, Flutter, Structural health monitoring, 0105 earth and related environmental sciences, Statistical hypothesis testing, Mathematics
Abstract

International audience; Flutter monitoring can be handled by tracking the real time variations of the modal parameters of a specified civil structure, be it a bridge or an aircraft. Previous algorithmic attempts encompass automated batch identification and damage detection through hypothesis testing. Both approaches appear impractical, the first one because of computational time consid- erations and the difficulty to select a windows length with the best trade off between bias and variance, the second because of the difficulty to obtain reference data set close to flutter regime. Here, we investigate the capabilities of a sample wise recursive linear Kalman filter coupled with a tangent filter. We also consider the nonlinear case.

Published
2006
Full Text
View/download PDF

40. Nonlinear system fault detection and isolation based on bootstrap particle filters

Author

F. Legland, Frédéric Cérou, Qinghua Zhang, Fabien Campillo, Applications and Tools of Automatic Control (SOSSO2), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Applications of interacting particle systems to statistics (ASPI), Université de Rennes (UR)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), IEEE--CSS, Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Rennes – Bretagne Atlantique

Subjects
0209 industrial biotechnology, Engineering, business.industry, 020206 networking & telecommunications, 02 engineering and technology, Fault detection and isolation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, 020901 industrial engineering & automation, Discrete time and continuous time, Control theory, Nonlinear dynamic systems, 0202 electrical engineering, electronic engineering, information engineering, Particle filter, business, Particle filtering algorithm
Abstract

International audience; A particle filter based method for nonlinear system fault detection and isolation is proposed in this paper. It is applicable to quite general stochastic nonlinear dynamic systems in discrete time. The main result consists of a new particle filter algorithm, derived from the basic bootstrap particle filter, and capable of rejecting a subset of the faults possibly affecting the considered system. Fault isolation is then achieved by the evaluation of the estimated likelihoods related to the designed filters.

Published
2005
Full Text
View/download PDF

41. Ergodic control applied to car suspension design

Author

E. Pardoux, Frédéric Cérou, and Fabien Campillo

Subjects
Engineering, Class (set theory), Shock absorber, business.industry, Stochastic process, Control theory, Feedback control, Ergodic control, Hamilton–Jacobi–Bellman equation, Vibration control, business, Optimal control
Abstract

Stochastic ergodic control is used to compute feedback laws for semiactive vehicle suspensions. The authors present an overview of a study supported by Renault and conducted by J. Alanoly and S. Sankar (1988). For the practical implementation, the Hamilton-Jacobi-Bellman equation can be numerically solved, which gives an approximation of the optimal law. Another possibility is to seek for the best feedback in a given class of parametrized feedbacks via a stochastic gradient algorithm. >

Published
2005
Full Text
View/download PDF

42. Optimal ergodic control for a class of nonlinear stochastic systems: application to semi-active vehicle suspensions

Author

Fabien Campillo

Subjects
Stochastic control, Nonlinear system, Discretization, Control theory, Control system, MathematicsofComputing_NUMERICALANALYSIS, Finite difference, Ergodic theory, Infinitesimal generator, Optimal control, Mathematics
Abstract

A class of ergodic stochastic control problems for diffusion processes is studied. A numerical approximation to the optimal feedback control, which is based on the discretization of the infinitesimal generator using finite difference schemes, is presented. These techniques are applied to the control of semi-active suspensions for a road vehicle. >

Published
2003
Full Text
View/download PDF

43. Effective diffusion in vanishing viscosity

Author

Andrey Piatnitski and Fabien Campillo

Subjects
Random potential, Logarithm, 010102 general mathematics, Mathematical analysis, Perturbation (astronomy), 01 natural sciences, Homogenization (chemistry), 010101 applied mathematics, Periodic function, Elliptic operator, Percolation theory, 0101 mathematics, Exponential decay, Mathematics
Abstract

We study the asymptotic behavior of effective diffusion for singular perturbed elliptic operators with potential first order terms. Assuming that the potential is a random perturbation of a fixed periodic function and that this perturbation does not affect essentially the structure of the potential, we prove the exponential decay of the effective diffusion. Moreover, we establish its logarithmic asymptotics in terms of proper percolation level for the random potential.

Published
2002
Full Text
View/download PDF

44. Homogenization of random parabolic operator with large potential

Author

Andrey Piatnitski, Fabien Campillo, Marina Kleptsyna, Stochastic Dynamical Systems (SYSDYS), 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), Dobrushin laboratory of Mathematics (IITP), Institute for Information Transmission Problems, Narvik Institute of Technology (Department of Mathematics), and University of Tromsø (UiT)

Subjects
Cauchy problem, Statistics and Probability, Spacetime, Stochastic process, Applied Mathematics, Mathematical analysis, Homogenization (chemistry), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Operator (computer programming), Maximum principle, Stochastic dynamics, Modeling and Simulation, Modelling and Simulation, Martingale (probability theory), Mathematics
Abstract

International audience; We study the averaging problem for a divergence form random parabolic operators with a large potential and with coefficients rapidly oscillating both in space and time variables. We assume that the medium possesses the periodic microscopic structure while the dynamics of the system is random and, moreover, diffusive. A parameter α will represent the ratio between space and time microscopic length scales. A parameter β will represent the effect of the potential term. The relation between α and β is of great importance. In a trivial case the presence of the potential term will be "neglectable". If not, the problem will have a meaning if a balance between these two parameters is achieved, then the averaging results hold while the structure of the limit problem depends crucially on α (with three limit cases: one classical and two given under martingale problems form). These results show that the presence of stochastic dynamics might change essentially the limit behavior of solutions.

Published
2001
Full Text
View/download PDF

45. A Monte Carlo Method to Compute the exchange coefficient in the double porosity model

Author

Fabien Campillo, Antoine Lejay, Applications of interacting particle systems to statistics (ASPI), Université de Rennes (UR)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Probabilistic numerical methods (OMEGA), 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)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), VSP, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Rennes – Bretagne Atlantique, Stochastic Dynamical Systems (SYSDYS), and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Statistics and Probability, Monte Carlo method, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], 01 natural sciences, 010305 fluids & plasmas, Physics::Geophysics, Hybrid Monte Carlo, 010104 statistics & probability, 0103 physical sciences, Statistics, Kinetic Monte Carlo, Statistical physics, 0101 mathematics, Mathematics, double porosity model, Applied Mathematics, Monte Carlo methods, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], random walk on squares, Macroscopic scale, AMS 76S05, 65C05, 76M35, Dynamic Monte Carlo method, Monte Carlo method in statistical physics, Porous medium, fissured media, Monte Carlo molecular modeling
Abstract

This article was written while the authors were members of the SYSDYS team (INRIA Sophia-Antipolis & LATP, Universite de Provence, Marseille).; The double porosity model allows to compute the pressure at a macroscopic scale in a fractured porous media, but requires the computation of some exchange coefficient characterizing the passage of the fluid from and to the porous media (the matrix) and the fractures. We propose a new Monte Carlo method to estimate this coefficient. Here we give an overview of some article from F. Campillo and A. Lejay

Published
2000

46. Small noise asymptotics of the GLR test for off-line change detection in misspecified diffusion processes

Author

Fabien Campillo, François Le Gland, Yury A. Kutoyants, Stochastic Dynamical Systems (SYSDYS), 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), Laboratoire Manceau de Mathématiques (LMM), Le Mans Université (UM), Applications of interacting particle systems to statistics (ASPI), Université de Rennes (UR)-Inria Rennes – Bretagne Atlantique, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Score test, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Stochastic differential equation, Robustness (computer science), Likelihood-ratio test, Statistics, Applied mathematics, False alarm, Noise (electronics), Change detection, Mathematics, Exponential function
Abstract

International audience; We consider the problem of the non-sequential detection of a change in the drift coefficient of a stochastic differential equation, when a misspecified model is used. We formulate the generalized likelihood ratio (GLR) test for this problem, and we study the behaviour of the associated error probabilities (false alarm and nodetection) in the small noise asymptotics. We obtain the following robustness result: even though a wrong model is used, the error probabilities go to zero with exponential rate, and the maximum likelihood estimator (MLE) of the change time is consistent, provided the change to be detected is larger (in some sense) than the misspecification error. We give also computable bounds for selecting the threshold of the test so as to achieve these exponential rates.

Published
2000
Full Text
View/download PDF

47. Numerical methods in ergodic optimal stochastic control application to semi-active vehicle suspensions

Author

J. Nekkachi, Fabien Campillo, and E. Pardoux

Subjects
Stochastic control, Mathematical optimization, Semi active, Engineering, Control theory, Stochastic process, business.industry, Numerical analysis, Ergodic control, MathematicsofComputing_NUMERICALANALYSIS, Ergodic theory, business, Optimal control
Abstract

It is shown how to compute the gradient for the implementation of a stochastic gradient algorithm for the purpose of solving an optimal stochastic ergodic control problem. The techniques are applied to the control of semi-active suspensions for road vehicles. >

Published
1990
Full Text
View/download PDF

48. La méthode d'approximation de Gauss-Galerkin en filtrage non linéaire

Author

Fabien Campillo, Université de Provence - UER de Mathématiques, Université de Provence - Aix-Marseille 1, and Campillo, Fabien

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Numerical Analysis, Computational Mathematics, Partial differential equation, Applied Mathematics, Modeling and Simulation, Numerical analysis, Applied mathematics, Fokker–Planck equation, Galerkin method, Analysis, Mathematics
Abstract

International audience; On étudie une méthode d'approximation de l'équation du filtrage non linéaire unidimensionnel avec observation en temps discret et en temps continu. On présente la méthode appliquée à l'équation de Fokker-Planck. On démontre la convergence de l'approximation et on traite un exemple numérique

Published
1986
Full Text
View/download PDF

49. {MLE} for partially observed diffusions: direct maximization vs. the {EM} algorithm

Author

Fabien Campillo, François Le Gland, MEFISTO, Inria Sophia Antipolis - Méditerranée (CRISAM), and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Statistics and Probability, Mathematical optimization, nonlinear smoothing, Discretization, Estimation theory, Applied Mathematics, diffusion processes, Maximization, Markov model, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Discrete time and continuous time, nonlinear filtering, Modelling and Simulation, Modeling and Simulation, Expectation–maximization algorithm, Skorokhod integral, Applied mathematics, maximum likelihood, parameter estimation, EM algorithm, Likelihood function, Smoothing, time discretization, Mathematics
Abstract

Two algorithms are compared for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes: • • the EM algorithm, investigated by Dembo and Zeitouni (1986), an iterative algorithm where, at each iteration, an auxiliary function is computed and maximized; • • the direct approach where the likelihood function itself is computed and maximized. This yields to a comparison of nonlinear smoothing and nonlinear filtering for computing a class of conditional expectations related to the problem of estimation. In particular, it is shown that smoothing is indeed necessary for the EM algorithm approach to be efficient. Time discretization schemes for the stochastic PDE's involved in the algorithms are given, and the link with the discrete time case (hidden Markov model) is explored. Numerical results are presented with the conclusion that direct maximization should be preferred whenever some noise covariances associated with the parameters to be estimated are small.

Published
1989

50. A Monte Carlo method without grid for a fractured porous domain model

Author

Fabien Campillo, Antoine Lejay, Stochastic Dynamical Systems (SYSDYS), 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), Laboratoire d'Analyse, Topologie, Probabilités (LATP), and Université Paul Cézanne - Aix-Marseille 3-Université de Provence - Aix-Marseille 1-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, ACM: G.: Mathematics of Computing/G.3: PROBABILITY AND STATISTICS/G.3.7: Probabilistic algorithms (including Monte Carlo), Discretization, Stochastic process, double porosity model, Applied Mathematics, Monte Carlo method, Mechanics, Random walk, Monte-Carlo method, Physics::Geophysics, simulation of Brownian motion exit time, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], Matrix (mathematics), ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.8: Partial Differential Equations, AMS 76S05, 65C05, 76M35, Calculus, Dynamic Monte Carlo method, Porous medium, Brownian motion, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics, fractured porous media
Abstract

International audience; The double porosity model allows one to compute the pressure at a macroscopic scale in a fractured porous media, but requires the computation of some exchange coefficient characterizing the passage of the fluid from and to the porous media (the matrix) and the fractures. This coefficient may be numerically computed by some Monte Carlo method, by evaluating the time a Brownian particle spends in the matrix and the fissures. Although we simulate some stochastic processes, the approach presented here does not use approximation by random walks, and then does not require any discretization. We are interested only in the particles in the matrix. A first approximation of the exchange coefficient may then be computed. In a forthcoming paper, we will present the simulation of the particles in the fissures.

Catalog

Books, media, physical & digital resources
See catalog results