Chemosensory information has been demonstrated as encoded in complex and spatially distributed spatio-temporal neuron firing patterns in the olfactory bulb of both insects and mammals. Such coding patterns are global time-space modal structures—or so-called principal components—in the olfactory bulb that are activated via different characteristic odors. The olfactory bulb is comprised of a large number of excitatory and inhibitory neurons connected both globally and locally. The data-driven method we have pursued extracts the minimal set of dynamical variables necessary for describing the fundamental behavior of the olfactory system. This renders the system low-dimensional in the natural, and experimentally determined, codes of the olfaction system. Success in this first model reduction has led us to consider a broader class of neuronal systems, including 1) low-dimensional control models for insect flight and locomotion, 2) retinal wave propagation in pre-birth mice, and 3) collective behavior (dynamics) of groups of neurons in general network configurations.
Broadly, I am interested in complex and highly nonlinear systems that exhibit readily identifiable coherent structures. These structures indicate that the observed dynamics are essentially restricted to a lower dimensional manifold. The purpose of dimensionality reduction is to generate a dynamical system, with fewer degrees of freedom, that still accurately reproduces a subset of the dynamics, or low-dimensional manifold, of the full system. The reduced system is desirable because the smaller dimension of the state space decreases the computational cost of simulation and makes problems involving control, optimization, or parameter space exploration more computationally tractable.
I am interested in a research partner who, besides having an interest and curiosity in this subject matter, has some background in science and mathematics (or other equivalent background and experience).