Fabien Campillo

• PhD
• Research Director at National Institute for Research in Computer Science and Control

Dravet syndrome is a developmental and epileptic encephalopathy, characterized by the early onset of drug-resistant seizures and various comorbidities. Most cases of this severe and complex pathology are due to mutations of NaV1.1, a sodium channel mainly expressed in fast-spiking inhibitory neurons. Layer et al. (Front. Cell. Neurosci. 15, 2021) s...

We present lateral habenula (LHb) neural data that display a variety of bursting patterns, with two dominant types and a third one that appears as a mix of the other two. We analyse these patterns using elementary statistical tools and characterise them from the perspective of average frequency during the burst and burst duration, which yields two...

Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the particles: t...

We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the approximation is established. We finally present a numerical example.

Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the particles: t...

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 Goldbeter (Progr Biophys Mol Biol 105:119–127, 2011; Pharmacopsychiatry 46:S44–S52, 2013) rests upon the notion that manic and depressive...

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 o...

In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system, and a finite volume method (based on an upwind implicit scheme) for the mean-field model. The finite volume m...

International audience 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 simul...

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 methods when the process is observed at discrete time. Secondly, we show that the individual birth and death can be identified separately to some extent.

We study the variations of the principal eigenvalue associated to a growth-fragmen- tation-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 b...

We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds. We illustrate this method with a mass-structured individual-based chemostat model. We assume that the mutations are rare and that...

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 modelling of the small size mutant population by a stochastic model an...

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 p...

The AM28 model is conventionally represented, in large population, as a system of ordinary differential equations. Our goal is to build several models at different scales. At the microscopic scale (the scale of the individual), we propose a pure jump stochastic model. This model can be exactly simulated. However, when the size of the population is...

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter. 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...

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...

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 view...

We propose land use dynamics models corresponding to parcels located on the edge of the forest corridor, Madagascar. We use semi-Markov chain to infer the land-use dynamics. In addition to the empirical and maximum likelihood methods, we estimate the semi-Markov kernel by a Bayesian approach. In the latter case, we use Jeffreys' non-informative pri...

International audience We present a Markov model of a land-use dynamic along a forest corridor of Madagascar. A first approach by the maximum likelihood approach leads to a model with an absorbing state. We study the quasi-stationary distribution law of the model and the law of the hitting time of the absorbing state. According to experts, a transi...

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 betwe...

Textes et Documents pour la Classe (TDC) No 1062: Les mathématiques de la Terre

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...

We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the law of the process is established and studied. We then use its solution to build a likelihood function for the...

Brève de Mathématiques de la Planète Terre

Dans le classique modèle de ''Rosenzweig-MacArthur d'une relation ressource-consommateur, pour certaines valeurs des paramètres le système possède un cycle limite tel que la plus petite valeur atteinte par la ressource sur ce cycle est si petite que le modèle n'a plus de sens : c'est "l'atto-fox problem". On considère deux iles telles que sur chacu...

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...

Nous présentons un modèle de Markov d’une dynamique d’utilisation des sols le long d’uncorridor forestier de Madagascar. Une première approche par maximum de vraisemblance conduit àun modèle avec un état absorbant. Nous étudions la loi de probabilité quasi-stationnaire du modèle etla loi du temps d’atteinte de l’état absorbant. Selon les experts, u...

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 deve...

Introduction à un n° spécial d'un journal

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...

Animal growth curves may be well described by di erential equations which can be used in a mixte model approach, see Strathe (2009), et al. (2010). As growth is a stochastic process, Donnet et al. (2010) suggested a bayesian hierarchial model where the regression term arised from a stochastic di erentiel equation. These corresponding stochastic gro...

il s'agit d'un type de produit dont les métadonnées ne correspondent pas aux métadonnées attendues dans les autres types de produit : SOFTWARE

We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in the differential equation model x = 1 means that there are \omega individuals in the discontinuous one -- is der...

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 descri...

a b s t r a c t 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 microsc...

The application of the Markov chain to modeling agricultural succession is well known. In most cases, the main problem is the inference of the model, i.e. the estimation of the transition matrix. In this work we present methods to estimate the transition matrix from historical observations. In addition to the estimator of maximum likelihood (MLE),...

We propose a new "hybrid" model for the simulation of biofilm growth in a plug flow bioreactor. Our approach consists in combining three scales: a mi-croscopic one for the individual bacteria, a mesoscopic or "coarse-grained" one that homogenises at an intermediate scale the quantities relevant to the at-tachment/detachment process, and a macroscop...

We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure...

The logistic model is usually expressed as an ordinary differential equation (ODE). This model is in fact a macroscopic and deterministic representation of a microscopic and stochastic model. We recall the stochastic formulation of this phenomenon in the the form of a birth and death process. We propose also a formulation at an intermediate scale a...

On analyse un modèle Idividu Centré (Individually Based Model : IBM) de croissance d'une population de bactéries dans un chémostat. Les individus-bactéries sont caractérisés par leur taille qui croît de 1 à 2 ; une bactérie de taille 2 se divise en 2 bactéries de taille 1. Chaque bactérie croît en consommant du substrat et peut disparaitre aléatoir...

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov chains (MCMC) interact in order to get an approximation of an independent N-sample of a given target law. In this method each individual chain proposes candidates for all oth...

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...

We propose an individual-based models (IBM) of a terrestrial plant sys- tems. Each individual plant is explicitly represented as well as the basic mechanisms acting on each individual: natural birth and death, dispersion, death due to compe- tition. The resulting model is a Markovian model of branching particles with diffu- sion. We describe the mo...

An individual-based model (IBM) of a spatiotemporal terrestrial ecological population is proposed. This model is spatially explicit and features the position of each individual together with another characteristic, such as the size of the individual, which evolves according to a given stochastic model. The population is locally regulated through an...

il s'agit d'un type de produit dont les métadonnées ne correspondent pas aux métadonnées attendues dans les autres types de produit : SOFTWARE

International audience 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, w...

International audience Computational probabilistic modeling and Bayesian inference has met a great success over the past fifteen years through the development of Monte Carlo methods and the ever increasing performance of computers. Through methods such as Monte Carlo Markov chain and sequential Monte Carlo Bayesian inference effectively combines wi...

We present a Markov model for agricultural successions with 4 states. The application of Markov models to agricultural succession problems is not new, but relatively new tools of numerical Bayesian inference allow us to test general prior laws. I addition to the maximum likelihood estimate, we consider the Jeffreys prior (non-informative), and calc...

Finely tuned process-based tree-growth models are of considerable help in understanding the variations of biomass increments measured in the dendrochronological series. Using site and species parameters, as well as daily climate variables, the MAIDEN model computes the water balance at ecosystem level and the daily increment of carbon storage in th...

Lettre de l'INRIA Sophia Antipolis Méditerranée (LISA)

LISA (Lettre de l'INRIA Sophia Antipolis)

Bayesian modelling is fluently employed to assess natural ressources. It is associated with Monte Carlo Markov Chains (MCMC) to get an approximation of the distribution law of interest. Hence in such situations it is important to be able to propose N independent realiza- tions of this distribution law. We propose a strategy for making N parallel Mo...

This paper deals with the problem of real time identification of the linear characteristics of the linear system associated with a mechanical structure. More than the parameter itself, the algorithm presented here is interested in estimating the confidence intervals for the parameter of interest. The algorithm is based on the particular filtering t...

In many situations it is important to be able to propose N independent real- izations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an indepen- dent N-sample of a given target law. In this method each individual chain proposes can- didates for a...

The state-space modeling of partially observed dynamic systems generally requires estimates of unknown parameters. From a practical point of view, it is relevant in such filtering contexts to simultaneously estimate the unknown states and parameters. Efficient simulation-based methods using convolution particle filters are proposed. The regularizat...

One applies Monte Carlo methods to state sapce models with unknown parameters. The first one is a Monte Carlo Markov Chain algorithm. The second one is the particle filtering. We compare these methods applied to a biomass evolution model for fisheries.

In many situations it is important to be able to propose $N$ independent realizations of a given distribution law. We propose a strategy for making $N$ parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an independent $N$-sample of a given target law. In this method each individual chain proposes candidates for a...

We present the problem of controlling the shock-absorber of a road-vehicle. We consider here a simplified one-dimensional model (which would be realistic as a model of the seat of a truck driver). The shock-absorber is controllable in the sense that one of its caracteristics can be modified as time evolves. We look for an optimal feedback based on...

We study a degenerate non linear optimal stochastic control problem of ergodic type. We first prove that for each feedback control law, there exists a unique invariant measure which is equivalent to Lebesgue measure. This is proved using an accessibility property of the stochastic differential equation, after the discontinuous part of the drift has...

In Campillo [4] we presented a numerical algorithm for the computation of the optimal feedback law in an ergodic stochastic optimal control problem. This method, based on the discretization of the associated Hamilton-Jacobi-Bellman equation, can be used only in low dimensions (2,4, or 6 in a parallel computer). For higher dimensional problems, we p...

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...

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 computation...

Ce cours est une introduction aux modèles de Markov cachés à espace discret et à espace continu. Il s'adresse à des élèves ingénieurs. Il contient la théorie classique des modèles de Markov cachés à espace fini ainsi que les méthodes d'approximation particulaire (filtrage particulaire, filtre bootstrap, Monte Carlo séquentiel...). Il est illustré d...

Ce document se décompose en trois axes: – Le premier s'attache à différents problèmes de filtrage et de statistique pour des processus de diffusion partiellement observés. – Le deuxième traite d'un problème de contrôle stochastique de type ergodique. il s'agit de calculer des lois de commande pour des amortisseurs semi–actifs (contrat avec Renault)...

We consider a Monte Carlo Markov chain (MCMC) algorithm for fisheries stock assess-ment. The biomass of this stock at a given year could be modeled as a nonlinear function of the biomass and catch for the two previous years, of different parameters (recruitment, growth rate, nat-ural mortality rate). Given a time series of annual catch and effort d...

We study nonstationary linearized reaction-diusion problem in a medium with locally periodic microstructure. Under the assumption that the characteristics of the medium are random stationary rapidly oscillating functions of time, we construct and justify a homogenized problem.

This paper is concerned with change detection in a partially observed diffusion model, i.e. detection of a change, occuring at some unknown change time, in the drift coefficient or the observation function. The problem is to decide, based on observations fY t ; 0 t Tg in a finite time interval, between : ffl The null hypothesis (H 0 ) dX t = b(X t...

Introduction The stability properties of linear deterministic systems X t = AX t , X 0 = x is well known. We can now suppose that the matrix A is subject to a Gaussian white noise perturbation j, i.e. the previous systems reads X t = [A 0 + l=1 A l j t ] X t , X 0 = x 6= 0, or as a Stratonovich stochastic differential equation (sde) dX t = A 0 X t...

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 ev...

Nous proposons un modèle probabiliste pour décrire l'évolution de protéines. Les paramètres de ce modèle sont identifiés par maximum de vraisemblance. Pour un exemple numérique nous étudions l'hétérogénéité du taux d'évolution le long de la séquence protéique et son rapport avec la structure secondaire.

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...

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 coeOEcient characterizing the passage of the AEuid from and to the porous media (the matrix) and the fractures. This coeOEcient may be numerically computed by some Monte Carlo method, by evaluati...

In [4] we presented a numerical algorithm for the computation of the optimal feedback law in an ergodic stochastic optimal control problem. This method, based on the discretization of the associated Hamilton-Jacobi-Bellman equation, can be used only in low dimension (2, 4, or 6 in a parallel computer). For higher dimensional problems, we propose he...

This paper is concerned with detection of a change in the drift coefficient or in the observation function at some unknown change time, in partially observed diffusion processes. The problem is to decide, based on observations Y T = fY t ; 0 t Tg in a finite time interval, between the null hypothesis (H 0 )

We study a degenerate non linear optimal stochastic control problem of ergodic type. We first prove that for each feedback control law, there exists a unique invariant measure which is equivalent to Lebesgue measure. This is proved using an accessibility property of the stochastic differential equation, after the discontinuous part of the drift has...

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...

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. This coefficient may be numerically computed by some Monte Carlo method, by evalua...

We study the asymptotic behavior of eoeective dioeusion for singular perturbed elliptic operators with potential rst order terms. Assuming that the potential is a random perturbation of a xed periodic function and that this perturbation does not aoeect essentially the structure of the potential, we prove the exponential decay of the eoeective dioeu...

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 th...

We consider the nonlinear #ltering problem for systems with noise#free state equation. First, we study a particle approximation of the a posteriori probability distribution, and we give an estimate of the approximation error. Then we show, and we illustrate with numerical examples, that this approximation can produce a non consistent estimation of...

We consider a stochastic differential equation with linear feedback control~: \begindisplaymath dX_t = (A+B\,K)\,X_t\, dt + \sum_k=1^r(A_k+B_k\,K)\,X_t\,\circ\! dW_k(t) \enddisplaymath where $K$ is the feedback gain matrix. For each value of $K$, let $\lambda_K$ be the Lyapunov exponent associated with the solution of the SDE. The set of $\lambda_K...