Ph.D., University of Minnesota, 1998
Theoretical neurobiology; quantitative principles of cortical design; computer science; applied mathematics
The brain contains an astronomical number of neurons. Neurons must be connected in a precise fashion to make the brain’s function possible. These connections are made inside a crowded, limited volume, where about 60 percent of space is occupied by neurons and their processes. Signals must propagate through the network in fractions of a second, to ensure the organism’s survival, and have to be represented with confidence despite enormous amounts of noise. The network is allotted only 20 watts of power to operate, about four times less than a Pentium processor. How does the brain accommodate these limitations and yet emerge as a powerful, functioning entity? Of course, the nervous system differs from Laplace’s Demon; it is not designed to perform all possible calculations. Instead, it concentrates on specific tasks needed by the organism, which must be performed under constraints of energy, space, and time.
We study how neural circuits deal with these constraints. One of many tasks we are interested in is short-term memory. How long can one remember a specific fact or event and how is this time related to properties of neural nets, such as synaptic channel properties or firing rates? How and why do short-term memories decay?
If we consider the image of the visual world which is projected to the retina and then represented in many brain areas, most of these representations are topographically correct, meaning that inside our heads we have a resemblance of TV screens on which one could watch the image of the outside in multiple simultaneous copies. Topographic maps efficiently minimize the length of connections between neurons, thereby satisfying volumetric constraints. Thus, exploring constraints and their solutions in the nervous system can yield clues to the function of a given circuit.
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Koulakov, A.A., Raghavachari, S., Kepecs, A., and Lisman, J.E. 2002. Model for a robust neural integrator. Nat. Neurosci. 5: 775–782.
Koulakov, A.A., and Chklovskii, D.B. 2002. Direction of motion maps in the visual cortex: a wire length minimization approach. Neurocomputing 44–46: 489–494.
Koulakov, A.A. and Chklovskii, D.B. 2001. Orientation preference patterns in mammalian visual cortex: a wire length minimization approach. Neuron 29: 519–527.
Koulakov, A.A. 2001. Properties of synaptic transmission and the global stability of delayed activity states. Network 12: 47–74.