Salle Chaire UNESCO, ENIT, Tunis

2024-2025 Seminars

LAMSIN Weekly SeminAR SERIES

LAMSIN Weekly Seminar Series

Wednesday 3:00 – 4:00pm

Time zone: Africa/Tunis

Google Meet joining info

Video call link: https://meet.google.com/fnk-bphd-mtj

Wednesday November 6, 2024 at 3PM (GMT+1)

Prof. Baba C. Vemuri, CISE, University of Florida

ManifoldNet: A Deep Neural Network for Manifold-valued Data with Applications

Joint work with R. Chakraborty, J. Bouza and J. Manton

Abstract: Developing deep neural networks (DNNs) for manifold-valued data sets has gained significant interest of late in the deep learning research community. Manifold-valued data abound many fields of Engineering and Sciences including but not limited to, Medical Imaging, Computer Vision, Robotics, etc., for example, diffusion tensor images (DTI), shape (landmarks) data, directional data, covariance matrices, GPS data and others. In this talk, a new theory and supporting architecture for DNNs tailored for manifold-valued data inputs dubbed, ManifoldNet, will be presented. Analogous to vector spaces where convolutions are equivalent to computing weighted means, manifold-valued data convolutions will be defined using the weighted Frechet Mean (wFM). To this end, a provably convergent recursive  algorithm for computation of the wFM of the given data is presented, where the weights are to be learned.

Further, the proposed wFM operator is provably equivariant to the natural group actions admitted by the data manifold and achieves a contraction mapping. A novel network architecture to realize the ManifoldNet will be detailed during the talk. Experiments showcasing the performance of the ManifoldNet on regression and classification problems in Neuroimaging will be presented. Finally, if time permits, a generalization of the ManifoldNet to accommodate higher order manifold-valued convolutions will be briefly discussed.

Biosketch: Baba Vemuri received his PhD in Electrical and Computer Engineering from the University of Texas at Austin. He is currently a Distinguished University Professor and holds the Wilson and Marie Collins Professorship in Engineering at the University of Florida, Gainesville, Florida. His research interests include Geometric Deep Learning, Geometric Statistics, Medical Image Computing, Computer Vision, Machine Learning and Information Geometry. He has published over 200 refereed journal and conference articles in the aforementioned areas and received several best paper awards. He has served as a program chair and area chair of several IEEE sponsored conferences. He was an associate editor for several area journals and is currently an associate editor for the journal of Information Geometry. Professor Vemuri is a recipient of the IEEE Computer Society’s Technical Achievement Award (2017) and is a fellow of the IEEE (2001) and the ACM (2009).

Wednesday November 13, 2024 at 3PM (GMT+1)

Prof. Radhouane Fekih Salem, ENIT, University of Tunis El Manar & LAMSIN

Modélisation et analyse mathématique des bioprocédés dans des bioréacteurs

Abstract: Dans une première partie, nous proposons un modèle général de floculation et de compétition des espèces microbiennes dans un chémostat. En utilisant des taux de croissance généraux, nous fournissons une analyse mathématique approfondie du comportement asymptotique du système dynamique.En considérant que les espèces les plus compétitives floculant avec les mêmes taux de dilution, nous avons mis en évidence les effets communs du phénomène de floculation et de l'inhibition du substrat sur l'émergence de cycles limites par bifurcations de Hopf. Cependant, sous l'effet conjoint de la floculation et de la mortalité, le modèle peut présenter des bifurcations de Hopf et homocliniques correspondant à l'apparition ou à la disparition d'orbites périodiques stables. L'étude théorique du diagramme opératoire détermine les diverses courbes de bifurcations dans le plan opératoire ainsi que le comportement asymptotique du processus dans les diverses régions. Les diagrammes de bifurcation à un et deux paramètres sont également obtenus par la méthode de continuation numérique en utilisant le logiciel MATCONT, qui nous a permis de détecter d'autres types de bifurcations à deux paramètres telles que les bifurcations de Bogdanov-Takens et Cusp. 

Dans une deuxième partie,  en utilisant la méthode d'Analyse de Composantes Principales du Maximum de Vraisemblance "MLPCA", nous déterminons le nombre approprié de réactions et la stœchiométrie correspondante à partir de données expérimentales réelles d'un bioprocédé de production des anticorps monoclonaux à partir des cellules d'hybridome. En choisissant des produits de facteurs de Monod pour décrire les cinétiques de réactions, les paramètres du modèle sont estimés à l'aide d'une méthode des moindres carrés pondérés. Le modèle mécaniste fournit des prédictions satisfaisantes en validation directe et croisée.  

Wednesday November 20, 2024 at 3PM (GMT+1)

Prof. Saloua Toumi, INSAT, University of Carthage & LAMSIN

Propagation of chaos: a review of  the theory and linked applications for neurosciences

Abstract: Chaos propagation consists in studying mean field limits for N particles in interactions where each particle is submitted to the influence of all other particles and when N tends to infinity. Interactions are observed in the drift (tendency) term of an ordinary differential equation (ODE) or in the drift of a stochastic differential equation (SDE) corresponding to the different N particles when independent Brownian motions Bi introduce randomness for the dynamic of each particle i. The first question to ask when dealing with mean field limits, given an initial position (distribution) of the particles, is to know the position of these particles at a time t ≥ 0. Obviously, this is not possible.

Instead, we can wonder what is the law distribution of particles for any time when the initial distribution is random and/or the dynamic itself includes a random aspect. The scaling parameter N allows to define and to analyze mean behavior of state variables over all interacting particles, particularly when all particles are symmetric and exchangeable and when N tends to infinity and this asymptotic behaviour is an aspect of a generalized (LLN).

In fact, when the number of particles N is large, all particles continue to interact but interactions between any couple of particles are sufficiently weak such that forces/influences applied on a given particle remain finite at the limit. Moreover, particles are expected to be asymptotically independent. In addition, due to the symmetric/exchangeable property of particles, they are expected to be identically distributed and therefore, asymptotically, we expect to have i.i.d particles, at any time t.

With an initial independence hypothesis between particles at time t=0, we prove asymptotic independence between particles, the fundamental condition for (LLN). This asymptotic independence is called spread of chaos property and it is important in two ways:

First, it provides statistical information on microscopic dynamics. Second, it ensures that the empirical random measure for the state variables, which informs us/measures the positioning of all particles, is asymptotically deterministic, which suggests the possibility of a deterministic macroscopic equation governing the evolution of this empirical measure (Mack-Kean Vlasov PDE), which has a unique (at least weak solution) under suitable conditions. When dealing with mean field limit, in practice and technically, we show first the convergence of law of the trajectory of each particle to the guessed mean field limit process.

The fundamental theorems dealing with mean field limit, using the following notes :

• Villani, C. Limite de champ moyen. Cours de DEA, 2001.

• Alain-Sol Sznitman. Topics in propagation of chaos. Springer, 1991.

As for our two papers linked to chaos propagation, it consisted respectively in studying models for a group of neurons dealing with uniform propagation of chaos and with existence of a solution for the asymptotic SDE equation for the dynamics of particles (neurons) SDE’s.

• Salhi, J., MacLaurin, J., & Toumi, S. On uniform propagation of chaos. Stochastics, 2018, vol. 90, no 1.

• MacLaurin, J., Salhi, J., & Toumi, S. (2018). Mean field dynamics of a wilson–cowan neuronal network with nonlinear coupling term. Stochastics and Dynamics, 18(06).

Wednesday November 27, 2024 at 3PM (GMT+1)

Prof. Emmanuel Chevalier, Aix-Marseille Université

Equivariant log-extrinsic means on symmetric cones

Abstract: In this talk, I will introduce a notion of mean on irreducible symmetric cones developed with Frank Nielsen. It is based on the product decomposition between the determinant one hypersurface and the determinant. Irreducible symmetric cones and their determinant on surfaces form an important class of spaces for statistics and data science, since they encompass positive definite self-adjoint operators as well as Lorentz cones and hyperbolic spaces. By construction, log-extrinsic means have similar equivariance properties as those of the Fréchet means. Moreover, the two means coincide under some symmetry assumption on the distribution. However, the log-extrinsic mean admits an explicit expression and is much simpler to compute. Numerical experiments show that the log-extrinsic means are a relevant alternative to log-Euclidean means. Furthermore, along with the log-extrinsic mean, we introduce a corresponding notion of Gaussian distributions, called log-extrinsic Gaussians. 

Wednesday December 11, 2024 at 3PM (GMT+1)

Prof. Cyril Bénézet, ENSIIE Paris 

Switching problems with controlled randomization and associated obliquely reflected BSDEs

Abstract: We introduce and study a new class of optimal switching problems, namely switching problems with controlled randomization, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value of the switching problem is related to a new class of multidimensional obliquely reflected BSDEs. These BSDEs allow as well to construct an optimal strategy and thus to completely solve the initial problem. The other main contribution of our work is to prove new existence and uniqueness results for these obliquely reflected BSDEs. This is achieved by a careful study of the domain of reflection and the construction of an appropriate oblique reflection operator in order to invoke results from Jean-François Chassagneux and Adrien Richou (2020).

Wednesday December 18, 2024 at 3PM (GMT+1)

Prof. Karim Yadi, Université de Tlemcen 

Sur des modèles épidémiologiques singulièrement perturbés

Abstract: Le point de départ de cette étude en cours  est un travail dans la littérature sur un modèle structuré en âge consistant à combiner un modèle SIS à une équation démographique, donnant lieu à un système lent-rapide. On examine quelques généralisations.

Wednesday January 15, 2025 at 3PM (GMT+1)

Prof. Moncef Mahjoub, LAMSIN-ENIT, Univ. of Tunis El Manar

Mathematical modelling and inverse problems in cardiac electrophysiology 

Abstract: The electric wave in the heart is gouverned by a system of reaction-diffusion partial differential equations called the bidomain model. This system is coupled nonlinearly to an ordinary differential equations (ODEs) modeling the cellular membrane dynamics. The bidomain model is widely used in cardiac electrophysiology simulation. This mathematical model takes into account the electrical properties of the cardiac muscle. Different numerical methods have been used for solving the bidomain model. Finite element method, finite difference method and finite volume method.

In the first part of my talk, we consider the inverse problem of space-dependent multiple ionic parameters identification in cardiac electrophysiology modelling from a set of observations. We use the monodomain system known as a state-of-theart model in cardiac electrophysiology, and we consider a general Hodgkin–Huxley formalism to describe the ionic exchanges at the microscopic level. This formalism covers many physiological transmembrane potential models, including those in cardiac electrophysiology. Our main result is the proof of the uniqueness and a Lipschitz stability estimate of ion channels conductance parameters based on some observations on an arbitrary subdomain. The key idea is a Carleman estimate for a parabolic operator with multiple coefficients and an ordinary differential equation system.

In the second part, we consider an inverse problem of determining multiple ionic parameters of a 2 x 2 strongly coupled parabolic-elliptic reaction-diffusion system arising in cardiac electrophysiology modeling. We use the bidomain model coupled to an ordinary differential equation (ODE) system and we consider a general formalism of physiologically detailed cellular membrane models to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate of the ion channels conductance parameters of the model using subboundary observations over an interval of time. The key ingredients are a global Carleman-type estimate with a suitable observations acting on a part of the boundary.

Finally, we present an optimal control formulation for the bidomain model in order to estimate maximal conductances parameters in the physiological ionic model. We consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microcopic level. We consider the parameters as control variables to minimize the mismatch between the measured and the computed potentials under the constraint of the bidomain system. The solution of the optimization problem is based on a gradient descent method, where the gradient is obtained by solving an adjoint problem. We show through some numerical examples the capability of this approach to estimate the values of sodium, calcium and potassium ion channels conductances in the Luo Rudy phase I model.

Wednesday February 5, 2025 at 3PM (GMT+1)

Prof. Mathieu Desroches, INRIA & Université de Montpellier

Classifying bursting oscillations using slow-fast dynamics 

Abstract: In this talk, I will present recent work on multiple-timescale dynamical systems displaying complex oscillations with both slow and fast components. I will first review bursting oscillations and how to classify them using the bifurcation structure of the so-called fast subsystem. Then, I will show how to extend the previous classification by using both fast and slow subsystems, in the case of four-dimensional bursting models with two slow and two fast variables. 

This is joint work with Serafim Rodrigues (BCAM, Bilbao, Spain) and John Rinzel (NYU and Courant Institute, New York, USA).

Wednesday February 12, 2025 at 2:30PM (GMT+1)

Prof. Monia Rekik, Université Laval

Carriers selection for TL transportation services using combinatorial auctions

Abstract: Combinatorial auctions have already proven their economic efficiency as a trading mechanism for the strategic procurement of truckload (TL) services. Much of this success has been attributed to their ability to capture the economy of scope that characterizes TL operations. In a combinatorial auction, a carrier can express its preferences for a package of contracts in a single bid. In this case, if the bid is won, all the contracts it covers, are assigned to the carrier, otherwise, none of these contracts are won. The design of combinatorial auctions implies solving several decisional problems, mainly: the winner determination problem (WDP), the bid construction or bid generation problem (BCP). In this talk, I will provide an overview of the different variants of WDPs and BCPs addressed in the literature for TL services procurement auctions. I will detail recent approaches that we have proposed to solve several challenging issues related to BCP and WDP in uncertain environments. I will conclude my presentation with the challenges that remain to be raised and the future promising research avenues.

 Wednesday February 19, 2025 at 3PM (GMT+1)

Prof. Wissal Sabbagh, Le Mans Université

Cyber risk management with impulse control 

Abstract: Cyber risk is a major concern for public entities and private companies, and constitutes a systemic threat to the resilience of the financial and economic world. In fact, 1 % of the world’s GDP, or 1, 000 billion, goes up every year because of cyber-crime. Cyberattacks are now the biggest threat to the financial system, says Jerome Powell, Chairman of the Federal Reserve global. In this talk, we develop a first study in which a cluster owner aims to protect a computer network by regularly updating or by purchasing security software against cyber-attacks. On the one hand, not protecting the computer network induces non-negligible financial losses for the owner of the cluster. On the other hand, cyber attacks can infect the network and lead to significant cyber incidents for the cluster owner and the customers of the service provided. First, we characterize the optimal protection policy for a network against effective hacking taken as a worst-case scenario. Based on an epidemiological model, we determine the optimal (dynamic) protection strategy, as a function of the evolution of attack strategies and the network’s level of infection. Then, we solve optimization problems by using deep learning methods to approximate a system of fully coupled equations. 

Joint work with C. Hillairet and T. Mastrolia

Wednesday March 5, 2025 at 2PM (GMT+1)

Prof. Térence Bayen,Université D'Avignon

Stability and optimal control of the chemostat system including a mutation term 

Abstract: In this presentation, I will consider the chemostat system with a perturbation term representing any type of exchange between species (and a constant dilution rate). The conversion term depends on species and substrate concentrations but also on a positive perturbation parameter. The objective is to prove a global stability result toward some equilibrium point as the perturbation parameter goes to zero. To do so, I will first enunciate a version of the Malkin-Gorshin Theorem and I will recall a Theorem by Smith and Waltman about perturbations of a globally stable steady state. After having written the invariant manifold as a union of a family of compact subsets, I will present the main result which states that for each subset in this family, there is a positive threshold for the perturbation parameter below which, the system is globally asymptotically stable in the corresponding subset. I will also discuss properties of the steady-state when the exchange term is linear with  respect to the species. Finally, I will also show numerical simulations concerning the optimization of biodiversity versus production of species among solutions to the previous dynamical system in which the dilution rate is now a control variable. 

Wednesday March 12, 2025 at 2PM (GMT+1)

Prof. Frédéric Jean, Institut Polytechnique de Paris

Modélisation de la planification des mouvements humains par le contrôle optimal  

Abstract: Il a été mis en évidence expérimentalement que dans la plupart des mouvements humains (par exemple les mouvements de pointage du doigt, les saccades oculaires), il y a une phase préliminaire de planification (contrôle en boucle ouverte) avant que le retour sensoriel ne soit pris en compte (contrôle en boucle fermée). Dans cet exposé, nous montrerons le rôle que le contrôle optimal peut jouer dans cette phase, soit dans un cadre déterministe (en utilisant des problèmes de contrôle optimal inverse) pour modéliser la prise en compte du temps, soit dans un cadre stochastique pour expliquer les phénomènes de co-contraction musculaire. 

2023-2024 Seminars

Wednesday October 18, 2023 at 3PM (GMT+1)

Prof. Skander HACHICHA, ENIT, University of Tunis El Manar & King Faisal University, Saudi Arabia

On irreducibility and positivity improvement of norm continuous quantum Markov semigroups

Abstract: We show that for a norm continuous quantum Markov semigroup irreducibility and positivity improvement for any time t>0 are equivalent under some general conditions that hold, in particular, in the finite-dimensional case. This result is applied to quantum Markov semigroups of weak coupling limit type. We also discuss the discrete-time case.

Wednesday October 25, 2023 at 3PM (GMT+1)

Prof. Anna DOUBOVA, Universidad de Sevilla

Inverse problems related to Burgers equation and related systems

Abstract: We consider inverse problems concerning viscous one-dimensional Burgers equation and some related nonlinear systems (involving heat effects and variable density). We are dealing with inverse problems in which the goal is to find the size of the spatial interval from some appropriate boundary observations. Depending on the properties of the initial and boundary data, we prove uniqueness and non-uniqueness results. Moreover, we also solve these inverse problems numerically and computing approximations of the interval sizes.

This is a joint work with Jone Apraiz (University of Basque Country), Enrique Fernandez-Cara (University of Sevilla) and Masahiro Yamamoto (University of Tokyo).

Wednesday November 1st, 2023 at 3PM (GMT+1)     (Postponed)

Prof. Marwa KHALIL, ENIT, University of Tunis El Manar

Quelques contributions à l'étude de la solution de l’équation différentielle des ondes perturbée par un bruit additif fractionnaire

Résumé : L’exposé se focalise sur l’étude de la solution de l’équation des ondes perturbée par un bruit additif fractionnaire en vue d’applications statistiques.  L’idée est l’analyse de la structure de la covariance de cette solution spatio-temporelle en appliquant les techniques classiques du calcul de Malliavin, afin de construire un estimateur consistant et asymptotiquement normal pour le paramètre de Hurst H relatif au bruit stochastique.

Wednesday November 15, 2023 at 3PM (GMT+1)

Prof. Badreddine RJAIBI, ENIT, University of Tunis El Manar

First  and second order topological gradient for x-ray tomographic reconstruction

Abstract: A new method for x-ray tomography reconstruction is proposed. This method is based on the first and second order topological gradient approach. The use of the topological asymptotic analysis for detecting the important  geometric information  of the data allows us to filter the noise while inverting the Radon transform. Experimental results obtained on noisy data illustrate the efficiency of this promising approach in the case of Magnetic Resonance Imaging. We also study the sensitivity of the algorithm with respect to several regularization and weight parameters.

Wednesday November 22, 2023 at 3PM (GMT+1)

Prof. Alexander TOWNSEND, Cornell University

Recovering Green's functions associated with elliptic PDEs

Abstract: Can one learn a solution operator associated with a differential operator from pairs of solutions and righthand sides? If so, how many pairs are required? These two questions have received significant research attention in operator learning. More precisely, given input-output pairs from an unknown elliptic PDE, we will derive a theoretically rigorous scheme for learning the associated Green's function. By exploiting the hierarchical low-rank structure of Green’s functions and randomized linear algebra, we will have a provable learning rate. Along the way, we will develop a more general theory for the randomized singular value decomposition and show how these techniques extend to parabolic and hyperbolic PDEs. This talk partially explains the success of operator networks like DeepONet in data-sparse settings.

Wednesday December 6, 2023 at 3PM (GMT+1)

Dr. Yassine TAHRAOUI, Center for Mathematics and its Application, Universidade NOVA de Lisboa,Portugal

On large deviations and invariant measures of solutions to stochastic obstacle problems

Abstract: Obstacle problems are well known in the literature of applied mathematics and lead to numerous applications. My objective is to present some results on the qualitative properties of the solution of a stochastic T-monotone obstacle problem studied in [1]. First, the small noise large deviation principle (LDP) where the difficulty lies in dealing with the singularities caused by the obstacle. The idea is to use Lewy-Stampacchia’s inequalities estimates to manage the singularities caused by the obstacle. Then, using some recent results in the literature to establish LDP for the corresponding stochastic dynamics. Next, I will discuss also the existence of invariant measures and it’s ergodicity associated with this type of dynamics. This talk will be based on [1, 2] and another submitted work.

References:

[1] Tahraoui, Y. and Vallet, G., Lewy-Stampacchia’s inequality for a stochastic T-monotone obstacle problem, StochPDE: Anal Comp 10, 90-125 (2022). https://doi.org/10.1007/s40072-021-00194-x

[2] Y. Tahraoui. Large deviations for obstacle problems with non linear T-monotone operators and multiplicative noise. https://arxiv.org/abs/2308.02206

Wednesday January 17, 2024 at 3PM (GMT+1)

Prof. Olfa Draouil, FST, Université de Tunis El Manar

White Noise calculus for time changed Brownian motion

Abstract: In this work, we investigate the time change process Λ=(Λt)t≥0 in the framework of infinite dimensional analysis and especially within White Noise calculus. We prove that the time changed Brownian motion is a martingale with respect to an associated enlarged filtration as well as its natural one. Also depending on Λ, it is not in general a process with independent increments. We define the Hida-Malliavin derivative with respect to the time changed Brownian motion. Finally, we obtain the  Clark Ocone formula with respect to the time changed Brownian motion BΛ.

Wednesday January 24, 2024 at 3PM (GMT+1)

Prof. Faouzi Triki, Université de Grenoble

An improved spectral inequality for sums of eigenfunctions

Abstract: In the talk we revisit the problem of  unique continuation of a finite sum of eigenfunctions of an elliptic operator in a divergence form from an open set to the whole domain.

Wednesday February 21, 2024 at 3PM (GMT+1)

Mohamed Atouani, CDF, Paris

Une brève histoire des nombres : la racine carrée entre arithmétique, analyse et géométrie

Abstract: La découverte de l'irrationalité de la racine carrée de 2 par Hippase de Métaponte a marqué un tournant majeur dans l'histoire des mathématiques. Dans cette présentation, nous nous proposons d'explorer quelques-unes des conséquences de cette découverte et de souligner l'importance d'intégrer des éléments clés de l'histoire des mathématiques dans l'enseignement. Nous mettrons ainsi en évidence l'impact significatif de ces avancées sur la pensée mathématique et sur ses développements ultérieurs.

Wednesday March 6, 2024  at 3PM (GMT+1)

Dr. Ahmed Elyes, SINTEF Digital, Oslo, Norway

Efficient Adaptive Solvers for Doubly Degenerate Elliptic

Equations using a Posteriori Error Estimates

Abstract: In this work, we derive a posteriori error estimates for a class of doubly nonlinear and degenerate elliptic equations, including the Stefan problem and fast and slow diffusion in porous media. Our approach employs equilibrated flux reconstructions, providing guaranteed and fully computable upper bounds on an energy-type norm and local efficiency. These bounds remain independent of the strength of nonlinearity and degeneracy rates. These estimators drive an adaptive solver, dynamically switching between nonlinear solvers to achieve optimal iterations. The adaptive algorithm accounts for discretization, regularization, quadrature, and linearization error components. When Newton’s method encounters challenges in achieving convergence, the adaptive algorithm transitions to the L-scheme solver. This solver optimally precomputes the stabilization (or tuning) parameter L > 0 during an offline phase, mirroring the behavior of the Jacobian. The adaptive algorithm is exemplified through four prototypical examples, showcasing its effective error control and notable computational savings.

Wednesday March 13, 2024  at 3PM (GMT+1)

Dr. Mohamed Aziz Boukraa, ENSTA

Seismic imaging of Dam-Rock interface using shape optimization method

Abstract: Understanding the concrete-rock interface of hydroelectric dams is crucial for assessing their stability. The goal of this study is to acquire a non-destructive 2D image of the interface using seismic waves. While traditional processing techniques often fail due to the complexity of data acquisition conditions, in this work, we propose exploring geophysical measurement techniques for processing seismic data. Our approach relies on Full-Waveform Inversion (FWI) coupled with shape optimization, where the gradient of the cost functional is computed using an adjoint state and shape derivatives. Numerical results from realistic experiments demonstrate the method's ability to accurately recover the interface with limited measurement points and in noisy conditions.

Wednesday April 24, 2024  at 3PM (GMT+1)

Prof. Mohameden Ahmedou, Giessen University

An abstract framework for the critical point theory at infinity

Abstract: In this talk we report on some new progress in setting up  an abstract framework, under which Morse theoretical methods can be applied to some non compact variational problem by computing the difference of topology induced by the so called  "critical points at infinity". As application we show how to apply such a method to the Nirenberg problem on spheres, recovering all existence results available in the literature.

This is a joint work with Thomas Bartsch (Giessen University).

Tuesday April 30, 2024  at 2PM (GMT+1)

Prof. Konstantinos Nikolantonakis Kostas, Université de Macédoine-Occidentale, Grèce

Analyse et synthèse algorithmique dans les Métriques de Héron d'Alexandrie 

et la Collection Mathématique de Pappos d'Alexandrie

Abstract: Nous décrirons d'abord l'analyse géométrique et la synthèse algorithmique dans les Métriques de Héron d'Alexandrie et soulignerons l'originalité de l'utilisation de la méthode d'analyse et de synthèse.

Nous examinerons ensuite comment elle est définie et appliquée dans les livres 4 et 7 de la Collection Mathématique de Pappos d'Alexandrie. Le but principal de cette présentation est de donner une image de l'état des questions sur l'analyse ancienne.

Wednesday May 8, 2024  at 2PM (GMT+1)

Prof. Sayed Sayari, ISTEUB

Formulation discontinue de Galerkin pour les équations de Maxwell en régime harmonique

Abstract: Dans cet exposé on va proposer une méthode DG pour la résolution des équations de Maxwell  en régime stationnaire. On dérive la formulation faible d'un problème mixte pour aboutir à un problème de type point selle.

Dans un premier temps, on montre l'équivalence entre le problème fort et la formulation faible, puis on approche le problème dans un espace discret et on étudie les propriétés des formes bilinéaires pour montrer l'existence et l'unicité de la solution discrète. Ensuite on établit une estimation d'erreur a priori d'ordre k+1 en u et k en p. Enfin, on présente des tests numériques basés sur l'algorithme d'Uzawa pour confirmer  les résultats théoriques obtenus.

Wednesday May 29, 2024  at 3PM (GMT+1)

Prof. Nawres Khlifa, ISTMT, University of Tunis El Manar

Intelligence Artificielle: théories et applications

Abstract: L'objectif de cette présentation est de créer un moment d'échanges autour du concept de l'intelligence artificielle et plus particulièrement l'apprentissage automatique (machine learning). Nous allons introduire quelques notions de base et présenter des exemples de leurs applications dans notre vie courante.

Wednesday June 19, 2024  at 2PM (GMT+1)

Dr. Marcella Bonazzoli, INRIA &  Institut Polytechnique de Paris

One-shot inversion methods with domain decomposition

Abstract: When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively, for instance by domain decomposition methods. In this framework, one-shot inversion methods iterate at the same time on the inverse problem unknown and on the forward and adjoint problem solutions. We are especially interested in the case where the inner iterations for the direct and adjoint problems are incomplete, that is, stopped before achieving a high accuracy on their solutions. If two or more inner iterations are performed on the state and adjoint state before updating the parameter, by starting from the previous iterates as initial guess for the state and adjoint state, we speak of multi-step one-shot methods.

For general linear inverse problems and fixed-point iterations for the associated forward/adjoint problems, we analyze several variants of multi-step one-shot methods, in particular semi-implicit schemes with a regularization parameter. We establish sufficient conditions on the descent step for convergence which are explicit in the number of inner iterations. We provide numerical experiments to illustrate the convergence of these methods in comparison with the classical gradient descent, where the forward and adjoint problems are solved exactly by a direct solver instead.

This is joint work with Tuan Anh Vu and Houssem Haddar.

Wednesday July 3, 2024  at 2PM (GMT+1)

Pr. Mohamed Sadok Guellouz,  ENIB, Université de Carthage

Structures cohérentes à grande échelle dans les canaux complexes

Abstract: La connaissance de l'écoulement turbulent, du transfert de chaleur et du transport de scalaire dans des canaux complexes est au cœur d'une grande variété d'applications d'intérêt technologique. La thermohydraulique des réacteurs nucléaires, l'hydraulique et la dispersion des polluants dans les rivières, la conception de systèmes de climatisation et le refroidissement des composants électroniques n'en sont que quelques exemples. Les canaux complexes incluent comprennent tous les conduits composés contenant des régions d'écoulement étroites, par exemple les canaux rectangulaires équipés de fentes ou d'ailettes axiales, les canaux ouverts à profondeur variable (plaines inondables des rivières) et les faisceaux de tiges. Le regain d'intérêt pour l'étude des écoulements dans les canaux complexes vient non seulement de leur importance pratique, mais également de la découverte de la formation de structures cohérentes à grande échelle au voisinage des régions d'écoulement étroites de telles configurations. Ces structures d'écoulement peuvent être définies comme des tourbillons quasi-périodiques convectés le long de l'écoulement. Il s'agit de phénomènes d'écoulement importants car ils transportent le fluide, sa quantité de mouvement et la chaleur beaucoup plus efficacement et sur des distances beaucoup plus grandes que la diffusion turbulente, réduisant ainsi les différences de vitesse et de température et améliorant le transfert de chaleur et de masse dans les régions étroites.

La conférence présentera un programme de recherche en cours visant à étudier l'écoulement dans les canaux complexes. Les objectifs généraux à long terme du programme sont d'améliorer la compréhension de la structure de ce type d'écoulement et de caractériser les structures cohérentes qui se forment au voisinage des régions étroites des canaux, en les reliant aux caractéristiques géométriques et dynamiques de l’écoulement. 

Plusieurs géométries appartenant à la famille des canaux complexes sont étudiées expérimentalement et numériquement. Les résultats des mesures, des visualisations d'écoulement, des simulations numériques et des analyses de stabilité seront présentés. Le but est d’exposer la problématique et surtout de discuter les derniers résultats de simulations numériques et de solliciter vos inputs sur le traitement de certaines conditions aux limites et leurs effets sur les résultats.