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What is the context of this research?

How reliable are responses of neural networks to a given stimulus signal? That is, if one presents an electrical signal to a network on repeated trials, where the internal state (electrical potential of each neuron in the network) is different at the onset of each trial, how similar are the responses? Will each cell spike at the same time on each trial or will there be variability in the evoked activity? Our research project aims at investigating this question in a theoretical setting, where we use mathematical models to represent neural networks. By doing so, a neural network is treated as a Dynamical System (DS). DS theory is comprised of mathematical tools which enables us to analyze the stability of solutions (neural responses). In this context, a reliable network is stable while an unreliable one is chaotic. Therefore, another way to pose our question is to ask: How chaotic are neural networks? We use a blend of analytical (pencil and paper) mathematical techniques as well as large scale computer simulations to approach this problem.

What is the significance of this project?

Although this project asks a fundamental question, it is motivated by more down-to-earth problems. A better understanding of neural dynamics reliability could lead to novel medical treatment of neuropathologies, such as Parkinson's disease or Epilepsy. A better understanding of the neural code can also streamline the design of neural prosthetics - known as brain machine interfaces - which can help subjects control external systems such as prosthetic limbs.

What are the goals of the project?

My general interests concern driven neural networks. More precisely, mathematical models of neurons coupled together, in various degrees of biological realism and then driven by an external signal meant to mimic sensory or artificial stimuli. The idea is to start from experimental knowledge about biophysical properties of neurons and extract the fundamental mechanisms that govern neural activity. We then formulate simplified mathematical models that capture these mechanisms and analyze them to obtain general dynamical properties of the brain.