Mathematical and Computational Neuroscience

Our research develops in the field of dynamical systems with applications to biology, mostly to neuroscience. We focus on a genuine immersion in neuroscience problems with the help of experimental experts, and a posterior choice of appropriate mathematical tools to model and study specific problems. We implement computational methods, use and analyze a variety of mathematical tools. Our main research topics are:

• Adapted computation of invariant manifolds to study phases of oscillators, with application to the synchronization of neurons in a network.
• Estimation of synaptic conductances: designing nonlinear estimation methods to infer, from the membrane potential of a neuron, the input conductances. From a mathematical point of view, it is an inverse problem tackled both with tools from dynamical systems and statistical inference.
• Multistable perception: models of multiestable phenomena in order to elucidate the brain mechanisms that allow perception to change without altering the sensory stimuli.
• Short-term synaptic depression (neuronal plasticity): using computational methods to study the effects on a network of neurons of the probability of neurotransmitter release.

Contact: Antoni Guillamon, Gemma Huguet, Tere M. Seara, Amadeu Delshams, Alberto Pérez-Cervera