Speaker
Josep Sardanyés (Centre de Recerca Matemàtica)

Description

   The inherent nonlinear behaviour of biological systems often involves the emergence of interesting dynamical phenomena. Also, different types of transitions (bifurcations) can cause important changes in the qualitative dynamics of these systems, sometimes involving clearance of pathogens or fading of tumor cells populations.

   In this seminar we will analyse a nonlinear differential equations model describing the dynamics of a heterogeneous population of tumor cells competing with healthy cells. By means of Eigen's quasispecies model, we will show the presence of an abrupt transition separating two phases given by tumor persistence and tumor extinction. The transition between these two phases is governed by a novel type of bifurcation that we have named as trans-heteroclinic bifurcation. Such a bifurcation involves the stability exchange between two distant fixed points that have an heteroclinic connection and that remain confined at the sides of an eight-dimensional simplex. This stability exchange, together with the no collision of the two equilibria, involves a discontinuous transition.

   We will comment on the possible novelty of this type of bifurcation in continuous flows. Finally, we will discuss the implications of our mathematical results within the framework of the so-called targeted cancer therapies and potential tumors' clearance.
 

Speaker
Annette Witt (Max Planck Institute for Dynamics and Self Organization, Gottingen, Germany)

Description

TBA

Speaker
Esther Ibañez Marcelo, ISI Foundation, Torino (Italy)

Description

Recently a number of techniques rooted in algebraic topology have beenproposed as novel tools for data analysis and pattern recognition. The fundamentally new character of these tools, collectively referred to as TDA or topological data analysis, stems from abandoning the standard measures between data points (or nodes, in the case of networks) as the fundamental building block, and focusing on extracting and understanding the “shape” of data at the mesoscopic scale. In doing so, this method allows for the extraction of relevant insights from complex and unstructured data without the need to rely on specific models or hypotheses.

Techniques like persistent homology have been recently used with success in biological and neurological contexts and play a key role in understanding ofcomplex systems in a wide range of fields by extracting useful information from big datasets.

In this talk it is given a TDA introduction and it is showed how taking advantage from persistent homology and summarizing it in the so called persistent scaffold we are able to detect differences between subjects before and after taking a drug, in this case LSD, from fMRI data.

Speaker
Raphael Poryles (Laboratoire de Physique, ENS Lyon)

Description

We study experimentally bubbles rising in different complex fluids confined in a vertical Hele-Shaw cell. The first experiment focuses on the morphology and dynamics of a single bubble rising in a polymer solution (Polyethylene Oxyde, PEO). This fluid is characterized as shear-thinning and viscoelastic. Different regimes are reported depending on the bubble volume. It can present a singularity (“cusp”) at its rear, and/or exhibit spontaneous instabilities. These instabilities can be either a deflection of the bubble trajectory or its fragmentation. The second experiment consists of gas injection at constant flow rate at the base of an immersed granular layer. It generates a fluidized zone consisting of a central air channel and two granular convection rolls on its sides. We investigate the size of the fluidized zone as well as the bubbles trapped in the granular bed.

Description

This is a week-long intensive school on the biology and mathematics of memory. Topics covered will be: synaptic plasticity, memory recall and consolidation, hippocampal and cortical models and more. This school is appropriate for graduate students, post-doctoral researchers and advanced researchers. 

Organizers
CRM