Participation is only available for CRM membres and affiliated researchers

CRM- Maria de Maeztu Interdisciplinary Workshop: Mathematical Biology and Neuroscience

Sign in
Workshop
From June 08, 2022
to June 09, 2022
Registration deadline 26 / 05 / 2022

INFORMATION

Morning sessions: CRM A1 Room

Afternoon sessions: CRM Polivalent Rooms 1 & 2

OBJECTIVES

One of the goals of the Maria de Maeztu programme at the CRM is to promote multidisciplinary and applied mathematical research to relevant problems in different areas such as Biology or Neuroscience. In this sense, the use or combination of different mathematical approaches can provide novel knowledge to problems related to health, ecology, phylogenetics, development, brain dynamics, cognition, or memory, among others. These interdisciplinary studies allow us to develop solid theories and to deepen our understanding of such complex systems which are highly non-linear and tipically display novel emergent, collective phenomena.

The first CRM-Maria de Maeztu Interdisciplinary Workshop seeks to boost collaborations between the researchers at CRM working in the areas of Mathematical Biology and Neuroscience with the rest of the researchers at the center working in other mathematical disciplines such as Dynamical Systems, Analysis and PDEs, Algebra, Geometry, Number theory, Topology, Combinatorics, Logics, and Algorithmics. This workshop will be organised in morning lectures, followed by thematic working sessions in the afternoon.

REGISTRATION

Registration is free but mandatory. If you wish to participate in the Workshop, please note that it will be necessary to register by clicking on SIGN IN (at the top of the page) and to fill in the following questionnaire for participants.

This workshop is only offered to CRM members and affiliated researchers and includes coffee breaks.

SCHEDULE

8 June 2022: Mathematical Biology Session

9:50

10:00

Workshop Welcome

10:00

10:45

Josep Sardanyés (CRM)

10:45

11:30

Àngel Calsina (UAB-CRM)

11:30

12:00

COFFEE BREAK

12:00

12:45

Kevin Martínez (CRM)

12:45

13:30

Jesús Fernández (UPC-CRM)

13:30

15:30

LUNCH

15:30

18:00

Working Groups Activities

9 June 2022: Neuroscience Session

10:00

10:45

Antoni Guillamon (UPC-CRM)

10:45

11:30

Alex Roxin (CRM)

11:30

12:00

COFFEE BREAK

12:00

12:45

Gemma Huguet (UPC-CRM)

12:45

13:30

Alexandre Hyafil (CRM)

13:30

15:30

LUNCH

15:30

18:00

Working Groups Activities

SPEAKERS 

Àngel Calsina  |  Universitat Autònoma de Barcelona / Centre de Recerca Matemàtica | Abstract

Jesús Fernández  Universitat Politècnica de Catalunya / Centre de Recerca Matemàtica | Abstract

Antoni Guillamon  | Universitat Politècnica de Catalunya / Centre de Recerca Matemàtica | Abstract

Gemma Huguet | Universitat Politècnica de Catalunya / Centre de Recerca Matemàtica | Abstract

Alexandre Hyafil | Centre de Recerca Matemàtica | Abstract

Kevin Martínez |  Centre de Recerca Matemàtica | Abstract

Alex Roxin  | Centre de Recerca Matemàtica | Abstract

Josep Sardanyés | Centre de Recerca Matemàtica | Abstract

 

WORK GROUPS

    Mathematical Biology Work Groups (June, 8th)

WG-BioMat1. Population dynamics, complexification, and game theory in Ecology and Virology

Organizers: Àngel Calsina,  Sílvia Cuadrado, Josep Sardanyés, Blai Vidiella, Tomás Lázaro, Ernest Fontich

Topic: Population dynamics: qualitative theory for PDEs, global manifolds and bifurcations, complexification, and Game Theory applied to Ecology and Virology

Description: Differential equations (ODEs or PDEs) are used to investigate population dynamics with respect to their state/s (spatial position, age, abundances, phenotype, etc.). However, in the infinite-dimensional (PDE) case there are no theorems allowing a qualitative theory based on linearization. The delay formulation, where the state variables are birth rates and, in the nonlinear case, interacting variables, based on Volterra integral equations, allows a semilinear formulation even when the corresponding PDEs are only quasilinear and consequently a consistent and rigorous qualitative theory. One of the goals of the WG-Biomat1 will consist in studying the limits of the delay formulation through several study cases and the possible version for discretely structured populations. In the WG-Biomat1 we will also introduce a system of ODEs models for prey-predator dynamics with habitat loss. Our interest is to extend a published work by adding functional responses (saturation in predation) to the dynamics and provide local, and, especially, global information into the dynamics. These include how a described heteroclinic bifurcation changes with such functional responses. We will also address how chaotic intermittency can be studied using complexification techniques and holomorphic dynamics. Finally, we will address novel approaches to investigate virus dynamics using game theory.

WG-BioMat2. Phylogenetics and likelihood functions

Organizers: Marta Casanellas, Jesús Fernández

Topic: Computing the exact number of real and positive maxima for likelihood functions

Description: For small phylogenetic trees evolving on simple evolutionary models, there are conjectures stating that there is a unique real and positive local maximum of the likelihood function for generic data. In order to address these conjectures, tools from computational algebra and real algebraic geometry are needed.

WG-BioMat3. Phylogenetics and transition matrices

Organizers: Marta Casanellas, Jesús Fernández

Topic: Evaluating the embeddability of transition matrices on real data

Description: The assumption that molecular substitution processes are time homogeneous is very restrictive mathematically speaking, as less than 1% of transition matrices are embeddable. However, this is usually assumed in phylogenetics. We want to analyze real data and test whether the estimated transition matrices can be assumed to be embeddable or not. This requires a good knowledge of statistics methods that can address this type of problem.

WG-BioMat4. Wavelet theory applied to reaction-diffusion Systems

Organizers: Isaac Salazar Ciudad, Kevin Martínez

Topic: Harmonic analysis and wavelet theory applied to pattern formation

Description: Our results suggest that the classical Fourier approach to pattern formation in reaction-diffusion systems is not enough to account for some local features of the highly irregular patterns produced by some non-Turing networks and we wonder whether a different approach using different tools from Harmonic analysis or wavelet theory can be a fruitful attempt.

    Neuroscience Work Groups (June, 9th)

WG-Neuro1. Neuroscience and machine learning

Organizers: Àlex Roxin, Alex Hyafil, Klaus Wimmer

Topic: The relationship between biologically plausible plasticity rules and machine-learning rules

Description: In neuroscience we have models of several types of rules governing how synaptic weights change in response to pre- and post-synaptic activity, inferred from experimental work. These rules are local and unsupervised, while it seems most rules used to train neural networks to perform some task are highly supervised. Is there some role for biologically realistic plasticity rules in machine learning? Another hot topic in neuroscience is whether perception relies on probabilistic codes and if so: What type of approximate inference algorithm (e.g. mean-field, expectation-propagation, MCMC, etc.) does the brain deploy to compute probabilities over the presence of feature in the environment. We would need a partner with expertise in machine learning for these to make sense.

WG-Neuro2. Oscillations and topological data analysis

Organizers: Antoni Guillamon and Gemma Huguet

Topic: Mathematical Neuroscience, what are the challenges for mathematics?

Description: Many mathematical and quantitative tools have been applied successfully to Neuroscience in order to provide answers to the comprehension of the mechanisms underlying brain function. After a general overview in the morning session, in this WG we will discuss specific challenging problems that the field of Neuroscience is currently posing to mathematicians. In particular, we will focus on problems related with the study of brain oscillations with dynamical systems tools and classification of activity regimes in neuronal populations using topological data analysis.

LIST OF PARTICIPANTS

Name Institution
Sudhir Singh National Institute of Technology Trichy India
Núria Fagella Universitat de Barcelona
Xavier Jarque Universitat de Barcelona
Sílvia Cuadrado Universitat Autònoma de Barcelona
Pan Ye Universitat Autònoma de Barcelona
MICHAEL ORIEUX Universitat Politècnica de Catalunya
David Reyner Parra Universitat Politècnica de Catalunya
Marta Casanellas Rius Universitat Politècnica de Catalunya
J. Tomás Lázaro Universitat Politècnica de Catalunya
Gemma Huguet Universitat Politècnica de Catalunya
José-Angel Oteo Universitat de València
Jordi Canela Universitat Jaume I de Castelló
Stefano Pedarra Centre de Recerca Matemàtica
Josep Sardanyés Centre de Recerca Matemàtica
Klaus Wimmer Centre de Recerca Matemàtica
Jordi Baró Urbea Centre de Recerca Matemàtica
Santiago Elena CSIC
Juan Carlos Muñoz Sánchez CSIC

 

For inquiries about this event please contact the research programs coordinator Ms. Núria Hernández at nhernandez@crm.cat​​