Olfactory System
Dissecting Components of Network Spiking Activity
I have long been interested in neural attributes that explain whole network spiking activity (a key observable thanks to tremendous advances in micro-electrode array recording technologies). The range of complexities are staggering, with issues arising from differences in "spontaneous" to sensory-evoked time periods, the specifics of sensory stimulation, prescribed time windows, etc. The dynamics of spike statistics is strongly implicated in function, i.e., scale-free `criticality' <=> info transmission/storage. Along with some olfactory papers, see a b c (where we use linear response theory on recurrent heterogeneous networks).
Visual Cortex
With Krusienki's and Atulasimha's labs, we are working on a biophysical model of the visual cortex, specifically focussing on the temporal stimuli modulation, in hopes of capturing the measured EEG response to visual stimuli.
Dynamics of Heterogeneity
The probability density of phase differences of 2 cells in the same coupled heterogeneous network, captured by an asymptotic calculation with weak noise, coupling, and correlation (see Ly SIAM J Appl Dyn Syst 2014).
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Theory from Ly JCNS 2015 and application here. Some ideas were motivated by electric fish data by the Marsat Lab; see Kyle's work too.
Cardiovascular Modeling
The sinus node (SAN) pacemakers are heterogeneous and entrains the rest of the heart. Realistic models with >30 variables for each cell present mathematical challenges to characterize dynamics that we have tackled (Ly & Weinberg J Theor Biol 2018). We hope to extend models and analyses to other regions; pinpointing dynamics of detailed models allows theoretical explorations of specific mutations (e.g., ion channels) that can ultimately help cure cardiac diseases.
