The aim of the present project is to provide the numerical modeling of neural processes, which can help to interpret the experimental data coming from EEG imaging. With this purpose we will use the Neural Field Equations (NFE), a widely used class of equations to model connected areas of neurons in the brain, in one to three dimensions. We emphasize on employing stochastic variants of NFEs to describe neural activity. We intend to develop new numerical methods and use them to carry out numerical simulations of the processes under investigation. We will test the results of our simulations by comparing them with the ones obtained by other methods in neuroscience, in particular data driven methods. The project includes in its final phase a collaboration with a research team working with medical data. The applicant, Pedro Lima (www.math.ist.utl.pt/~plima), is a member of the CEMAT (Center of Mathematics and Applications- www.cemat.ist.utl.pt), a research unit of the Instituto Superior Técnico (www.ist.utl.pt ), which is part of the Technical University of Lisbon (www.utl.pt). He will visit for one year the Johannes Kepler Univesity (JKU- www.jku.at ) at Linz, where he will work at the Institute of Stochastics ( www.jku.at/stochastik) , under the direction of Prof. Evelyn Buckwar (the leader of the Institute).The main training objective of the applicant is the development of expertise in Stochastic Numerical Analysis, Modelling with NFEs and Mathematical Neuroscience. He will benefit from the excellent experience of the research team of the Institute of Stochastics of the JKU, which is renowned for its interdisciplinary strengths and track record on applied mathematical modeling. This project will have a very significant impact in the career of the applicant, giving him skills that will enable him to participate in multidisciplinary projects in the field of neuroscience. In this way he will reinforce a position of professional maturity.
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