Dynamics of Noisy Oscillators. The probalility density of the phase difference for 2 pairs 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).

Cardiac 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.

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Statistics of Spiking Activity. Spike count (Pearson's) correlation ρ in different time windows can captured by linear response calculations, even in recurrent heterogeneous network models (see Barreiro & Ly PLoS CB 2017 and JMNS 2018) . Also see Ly, Middelton, Doiron 2010 .

Firing rate heterogeneity of weakly electric fish modulates with blockade of feedforward inputs in different ways (recordings from the Marsat Lab).

Olfactory system modeling. Simultaneous dual-array recordings by collaborators (Shew Lab) have resulted in many fascinating research questions. Are there cells in either olfactory bulb (OB) or piriform cortex (CX) that are selective for modes of respiration? If so, what is the dependence on odor type? velocity of stimuli? etc. Dual array recordings also help narrow down parameter space with new relationships for how spiking activity in different regions are inter-related in different states (see Barreiro, Hari Gautam, Shew, Ly PLoS CB 2017) .

Theory from Ly JCNS 2015

Modulation of Heterogeneity. Neural response heterogeneity has implications for how sensory signals are coded. We mathematically characterize the dynamics of heterogeneity from neural attributes in mechanistic cortical network models; our work has led to predictions of network connectivity (stimulus dependent) structure in the electrosensory system of weakly electric fish. See Ly JCNS 2015, Ly & Marsat JCNS 2018, and Kyle's (PhD student) paper: WL MBE 2019.

There's always more to do, so if any of this interests you, please contact me!

".... do not underestimate how much genius, inspiration, creaetivity, success, etc. comes from hard work ..."

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