OPEN MAMBA SEMINAR

Presentation:

The Open MAMBA Seminar is an internal seminar open to all which takes place once every month at INRIA Paris. The talks are given by PhD/post-docs with the following goals:

  •  Reinforce the team spirit by centering the talks on MAMBA (extended) students works
  •  Bring more math-bio at the INRIA center (in complement with the INRIA-LJLL meetings)
  • Favor scientific exchanges on current projects, each talk being followed by an (informal) discussion between researchers.

The seminar takes place once every month on mondays from 1:30 to 3 pm. It is composed of two talks of 30mn, each followed by 15mn discussions.

Location:

INRIA Paris, 2 rue Simone Iff (see How to reach), Room ‹‹ Jacques-Louis Lions ››, bâtiment C

NB: An ID card is necessary to enter the building

Organizers:

Diane Peurichard: diane.a.peurichard@inria.fr

Dirk Drasdo: dirk.drasdo@inria.fr

Talks:

  • Monday, march 19:

    1.Hugo Martin

Title: Measure solution for the classical size-equation with linear growth rate

Abstract: In a recent paper, E. Bernard, M. Doumic and P. Gabriel showed the existence of a cyclic asymptotic bahaviour of the solution of the size-equation with linear growth rate in a weighted L^2 space which consists in a Fourier serie built on the eigenfunctions of the model. On another hand, P. Gabriel recently solved the age Equation and showed a relation with the related principal eigenfunction. We are now wondering how this behaviour appear for measure solutions in the case of the size Equation. After defining what a measure solution to a PDE is, I will explain the semigroups methods we attempt to use to obtain the desired result and the difficulties we are already facing.

2. Camille Pouchol

Title: Dirichlet control towards steady states for the 1D monostable and bistable equations

Abstract: I will talk about the problem of controlling parabolic semilinear equations arising in population dynamics, namely the 1D monostable and bistable equations on (0,L) for a density of individuals between 0 (extinction) and 1 (invasion), by means of Dirichlet controls between 0 and 1. I will explain why driving the system towards 0 or 1 asymptotically is always possible for the state 1, and for 0 as well if L is below some threshold value, computable by phase plane analysis. In the bistable case, I will prove that the other homogeneous steady state 0 < θ < 1, though unstable for the corresponding ODE, can be reached in finite time. The central tools are the phase portrait for the stationary problem, the parabolic maximum principle, and the staircase method in control theory.

  • Monday, february 12:

    1. Mathieu Mezache:

Title:An oscillatory kinetic model for the Prion aggregation process.
Abstract: We investigate the oscillatory behaviour of the PrP protein during the polymerization/depolymerization process. In order to modelize this oscillatory process, we study a simplified Belousov Zhabotinsky reaction from a kinetic point of view. This simplified oscillatory system of chemical reactions allows us to introduce a modified Becker-Döring system where the trajectories oscillate. A key to have a closed oscillatory polymerization/depolymerization system is to consider different specices of polymers and monomers. The main goal is to investigate the size distribution in the polymerisation /depolymerisation process of the PrP protein.”

      2. Martin Strugarek

Title: Mosquito population replacement: an optimal control viewpoint
(in collaboration with Luis Almeida, Yannick Privat (LJLL) and Nicolas Vauchelet (LAGA))


Abstract: Transinfection of Wolbachia bacteria is currently used in wild Aedes populations to suppress these mosquitoes’ ability to transmit some viruses (vector competence), in particular dengue viruses. This recently developed technique relies on the mass rearing and release of lab-infected individuals of both sexes. The introduced phenotype can replace the wild one thanks to an asymmetric sterile crossing known as cytoplasmic incompatibility (CI). It is expected to practically stop disease circulation and be very cost-efficient as the Wolbachia infection will maintain 
once established over many generations, thanks to almost perfect vertical transmission from mother to offspring. Our work aims at improving these so-called “Wolbachia population replacement strategies”, using mathematical modeling to design the release sizes and timings (and, in future, locations). Here, we formulate this as an optimal control problem for an ODE system and prove qualitative properties of the optimal strategies under resource constraints. Numerical simulations illustrate these results. We also recover a bistable scalar equation on the proportion of infected individuals by a proper scaling of the parameters, and rigorously prove the convergence of the optimization problems to a limit problem for which uniqueness and explicit solution are established.

  • Monday, january 22:

1. Yi Yin:

2. Jieling Zhao:

Title: A dynamic activator-inhibitor system to model liver fibrosis at early stage
 
Abstract: Liver fibrosis is a characteristic of most types of liver disease due to chronic liver damage. During the process of fibrosis, excessive accumulation of extracellular matrix (ECM) proteins, such as type I and III collagen are produced by activated fibroblast-type cells in the liver, which leads to cirrhosis and eventually the failure of the liver. Due to the complexity of the whole process, the mechanism behind is still elusive. Computational modeling aspects of the liver fibrosis may provide some insights towards the understanding of the mechanism and developing novel treatment strategies. In this study, we develop a dynamic activator-inhibitor system to study the liver fibrosis at early stage. Our modeled pattern of the activator which promotes the ECM deposition can roughly capture the observed ECM pattern upon chronic liver injury. This result can be used as preliminary pattern as guidance for the further exploration of the formation of ECM pattern observed in vivo.