This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This research consists of three projects that will develop new theoretical approaches and experimental predictions about recurrent networks in the mammalian brain. The first two projects are primarily concerned with stimulus representation via recurrent networks, while the third project focuses on spontaneous activity. Project 1 formalizes and develops an algebra-geometric framework previously introduced in joint work with Vladimir Itskov. The main idea is to associate geometry and topology to population spike train data -- primarily from electrophysiological recordings in cortex and hippocampus. Project 2 explores the relationship between stimulus space topology and recurrent network connectivity. The goal of this project is to find experimental predictions about the connectivity of recurrent networks in cases where either the stimulus space structure or the topographic structure of the underlying network is known. Project 3 investigates the interaction between the activity of single neurons and the population activity of the local network.
Building accurate representations of the world is one of the basic functions of the brain. When a stimulus is paired with pleasure or pain, an animal quickly learns the association. However, we also learn the (neutral) relationships between stimuli of the same type. For example, a bar held at a 45-degree angle seems closer to one held at 50 degrees than to a perfectly vertical one. Upon hearing a pair of distinct pure tones, one seems higher than the other. We do not perceive the world as a stream of unrelated stimuli; rather, our brains organize different types of stimuli into structured stimulus spaces. Regardless of immediate relevance to survival, it appears to be beneficial for the brain to reflect as much structure as possible of the outside world. The main goal of this research is to improve our understanding of how stimulus spaces are represented via recurrent networks in the brain. To this end, we develop ideas and techniques coming from geometry and topology to extract novel insights from neuroscience experiments. How the brain represents the world is a fundamental and age-old question. Progress in understanding how the structure of neural circuits underlies representational functions may also provide clues in the study of neurological disease.
