Context:
The primary visual cortex V1 is an area of the brain responsible for a first treatment of images arriving from the retina. High level geometric models of V1 proved to be remarkable in their predictive capability. Wilson-Cowan equations, based on averaging the discrete structure of the cortex, have been succesfully used to identify recurring visual hallucinatory patterns. These nonlinear integro-differential equations are used to model neuronal activity in cortical areas, where an integral kernel encodes mutual activity inhibition and excitation between neurons based on their relative positions. In the visual cortex, activity is generated by an exterior input in the form of a visual stimulation. In the right circumstances, this can lead to the emergence of new self induced activity in the visual cortex, that we understand as geometric visual hallucinations. We are interested in detecting the occurence of such phenomena in the context of in vivo measuring of the visual cortex activity, and we rely on tools from estimation of dynamical systems to achieve this goal.
Objectives of the internship:
The goal of this work is to study the evolution of activity in V1 from an input-output perspective. The student will first familiarize themself with the properties of the Wilson-Cowan dynamical model for cortical activity, and their applications to the determination of hallucinatory patterns in the visual cortex. Relying on different scenarios regarding measurement of the visual cortex activity, the student will then be asked to study observability properties of Wilson-Cowan equations. Using this analysis, it is possible to assess the emergence of hallucinatory patterns in the visual cortex, manifesting in the form of stable periodic solutions to the equation, using tools from observation theory. Depending on the inclinations of the intern, some importance will be given to the numerical aspect of the work, and simulations of estimation algorithms. This line of inquiry can also be expanded into a PhD project if the intern shows good potential.
Work environment:
For Master 2 students. The internship will take place in 2022 and it will last 4 to 6 months.
Advisors: Ludovic Sacchelli, Dario Prandi
Please contact us for any information.
