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We are interested in finding different mathematical approaches to learning from data inspired by modern Mathematics, Neuroscience and collective behavior


[See also GitLab webpage]


We are a group of Physicists, Mathematicians, and Biologists at Champalimaud Foundation in beautiful Lisbon.

On the theoretical side, we develop new frameworks to take advantage of different mathematical properties.  We are using Model Theory/Abstract Algebra to be able to simultaneously learn from data and formal knowledge in a transparent way, see algebraic.ai.

We also push the state-of-the-art in data analysis and modelling, and we test them in specific biological problems. We have chosen to mostly concentrate on collective behaviour for its relevance and beauty. To test our models, we also perform experiments in zebrafish collectives. We extract the data from these experiments using tracking systems based on identifying each individual in large groups of up to 100 animals, see idTracker and idtracker.aiand developed tools for behaviour classification and analysis.

We are using deep modular networks to obtain predictive models and gain insight into the form of interactions by analyzing the lower-dimensional functions implemented by the modules. We have also derived formal expressions for the decisions in collectives from first-principles using Bayesian estimation (generalized here) and control theory. We have checked that some of the predictions can be obtained largely independent of any model, see here. We also took advantage of how the interaction changes during development to study its simplest form here.  Using zebrafish and other laboratory fish species opens a window into the neuroscience of social behaviour and individuality. We have used some of these results to explain human behaviour in collectives.

Before this work, we enjoyed thinking about neuronal coding, deviations from optimality in biologywiring economy in brains and quantum mechanics.

You can also find more of our work present and past at google scholar.

If you are interested, please contact us at mathematics4ai@gmail.com or gonzalo.polavieja@neuro.fchampalimaud.org.



Champalimaud Foundation

Champalimaud Centre for the Unknown

Avenida Brasília, 1400-038 Lisbon, Portugal

T (+351) 210 480 200