## Séminaire Mathématiques pour la biologie

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 Organisateurs Fanny Delebecque, Sabine Mercier Horaire habituel Jeudi 13h30 Lieu habituel Salle de conférence MIP, (bâtiment 1R3, 1er étage)

• ### Jeudi 24 octobre 13:30-14:30 - Matthias Zytnicki - INRA Castanet MIAT

Finding differentially expressed sRNA-Seq regions with srnadiff, plus some stories about genome assembly.

Résumé : In a first part, I will present my work on small RNA (sRNA) differential expression. sRNAs encompass a great variety of different molecules of different kinds, such as micro RNAs, small interfering RNAs, Piwi-associated RNA, among other. Small RNA sequencing is thus routinely used to assess the expression of the diversity of sRNAs, usually in the context of differentially expression, where two conditions are compared. Many tools have been presented to detect differentially expressed micro RNAs, because they are well documented, and the associated genes are well defined. However, tools are lacking to detect other types of sRNAs, which are less studied, and have an imprecise gene’’ structure. We present here a new method, called srnadiff, to find all kinds of differentially expressed sRNAs.
In a second part, I will present you my current (preliminary) work on genome assembly, and more specifically on scaffolding using linked reads (10X technology).
I will try to show how it can be related to a 1D-segmentation problem.
I am looking forward to your advice on this type of data.

Lieu : Salle MIP, 1er étage 1R3 IMT

• ### Jeudi 14 novembre 13:30-14:30 - Daniele Avitabile - University of Nottingham

slow passage through bifurcations in infinite-dimensional dynamical systems

Résumé : Ordinary Differential Equations (ODEs) in which state variables evolve according to disparate time scales are known to support solutions exhibiting slow passages through bifurcations and canard segments. These solutions are indeed considered to be footprints of time-scale separation, and they have been studied extensively in the past decades to explain a vast repertoire of temporal patterns including mixed-mode oscillations, bursting, and excitable dynamics.
The literature on the topic deals primarily with finite- (and usually low-) dimensional dynamical systems. In the mathematical neuroscience community, for instance, there exists a well-defined methodology for single-cell models with time-scale separation, but not for spatially-extended or network models.
I will present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a large class of infinite-dimensional dynamical systems with time-scale separation. The framework, which relies on a centre-manifold reduction proposed by Iooss and coworkers, is applicable to models where an infinite-dimensional dynamical system for fast variables is coupled to a finite-dimensional dynamical system for slow variables. I will discuss examples where the fast variables evolve according to systems of local and nonlocal reaction-diffusion PDEs, integro-differential equations, or delay-differential equations. This approach opens up the possibility of studying spatio-temporal canards and slow passages through bifurcations in spatially-extended systems, and it provides an analytical foundation for several numerical observations recently reported in literature.
This is joint work with Mathieu Desroches, Romain Veltz, and Martin Wechselberger.

Lieu : salle MIP, 1er étage bat 1R3

• ### Jeudi 21 novembre 13:30-14:30 - Sarah Penington - University of Bath

The motion of hybrid zones and genealogies in pushed waves

Résumé : Suppose two populations with different genetic types live close to each other and can interbreed, but hybrid offspring have a lower evolutionary fitness. The interface between such populations is known as a hybrid zone. We can model this situation using a stochastic process. I will discuss a result on the motion of the interface, which is related to a well-known PDE result connecting the Allen-Cahn equation and mean curvature flow.
If we take a simplified model in only one spatial dimension, we can trace the ancestral lineages of individuals backwards in time and (in some cases) determine the asymptotic behaviour of the genealogy of a sample of individuals. Several interesting questions about the genealogies remain open.
Partly based on joint work with Alison Etheridge and Nic Freeman.

Lieu : Attention ! Salle 106 bat 1R1

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