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Transient and Attractor Dynamics in Models for Odor Discrimination
Ahn, Sungwoo

2010, Doctor of Philosophy, Ohio State University, Mathematics.

Understanding how sensory information is encoded and decoded in the brain is a fundamental challenge in neuroscience. The honeybee antennal lobe (AL) provides an ideal system to study the olfactory system because it is anatomically and genetically simpler than the olfactory bulb (OB) of mammals. While anatomical structures within the AL are relatively well known, their functional roles in sensory processing remain poorly understood. Processing in this network transforms the sensory input to give rise to dynamic spatiotemporal patterns that can be measured in the projection neurons (PNs) that provide output to other brain centers. Several studies showed that the dynamic processing in the AL may serve to decorrelate sensory representations through early transients rather than by reaching a stable attractor. Therefore, studying the transients and attractors in the given dynamical systems will be useful to better understand the olfactory system.

A primary goal of this thesis is to develop and analyze a
mathematical model for this olfactory system. This will help to better understand the mechanisms underlying spatiotemporal firing patterns in the AL. In the previous published papers, my co-authors and I analyzed biophysical excitatory-inhibitory neuronal network models. These models have been implicated in the generation of sleep rhythms, Parkinsonian tremor, sensory processing within the OB and
AL. While this type of network arises in many important regions throughout the central nervous systems, rigorous mathematical analysis is only in its beginning stage. We adapted various mathematical methods, such as geometric singular perturbation theory, combinatorics, iterated maps and graph theory, as well as computational methods. For a relatively simple but biophysical model, we rigorously reduced the continuous model to a discrete dynamical system and analyzed the discrete system. The analysis of
the discrete system was concerned with expected behavior under random connectivity. The first project of this thesis is characterizing all possible dynamics - transients and attractors - for certain important connectivities: directed cycles, strongly connected digraphs, Hamiltonian digraphs with one shortcut and (loop-free) complete digraph.

The second project of this thesis is improving our previous model to reproduce experimental results in the AL such as irregular firing patterns, a smooth transition and a smooth divergence of firing patterns in response to mixtures. I find that synaptic/non-synaptic plasticity helps to discriminate odorants and to reproduce realistic results mentioned above. With this new model, I numerically characterize the transients and attractors which may correspond to the odor identity.

David Terman (Advisor)
Winfried Just (Advisor)
Boris Pittel (Committee Member)
Ed Overman (Committee Member)
210 p.

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