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Mathematical, Computational and Experimental Neuroscience

The focus of my research lies at the interface between Mathematical, Computational and Experimental Neuroscience and the aim is three-fold. First, to mathematically explain neurophysiological mechanisms that underlie the activity observed in experimental and clinical studies. These observables, depend on the measurement modality (e.g. chemical, light, electrical etc), which display complex spatio-temporal dynamics (both in normal and pathological brain states). The grand challenge is not only to mathematically explain these observations but also to unify these explanations across modalities. Second, to provide new mathematical and computational tools that enable the implementation of novel technologies, in order to push the boundaries of experimental design and clinical therapies. To this end, we are developing novel tools based on mathematical control theory to track stability boundaries and unstable states directly from noisy data measured in closed-loop experiments. This will lead for example to intelligent machine-brain interfaces (including deep-brain stimulators) to treat neurological disorders. The hope is that some of these technologies will be commercially exploited by targeting specific industries.


Figure 1: Multi-scale nature of brain processes. Different modalities and a multi-disciplinary approach is required to understand brain processes.

Goal
Explain how the brain processes and stores information, how these are disrupted under pathological conditions and develop novel technologies to treat neurodegenerative diseases.
Method
Biophysics, Statistical Physics, Theory of Multi-timescale Dynamical system, Bifurcation theory, Mathematical control theory and Closed-loop controlled experiments.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)