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Sheaves —
Recently, I've been fascinated by the mathematical structures called sheaves. Originating in algebraic geometry, sheaves are incredibly powerful tools that can connect seemingly distant ideas in beautiful ways. Their ability to fit into so many mathematical concepts comes at the cost of being very abstract and hard to pin down. Just look at the mathematical definition of a sheaf. It makes like no sense unless you already know what a sheaf is. In short, a sheaf is a tool that allows us to look at something at a very small resolution and stitch together our "local" observations to construct a "global" understanding of the object in question.

Stimulus Coding in Retinal Ganglion Cells —
Currently, I'm working on modeling two different types of cells in the mouse retina and trying to understand why they exhibit the behavior they do. Suppressed-by-contrast cells are ganglion cells that burst fairly regularly and then turn off when the eye detects a change in luminance (contrast). The other type, off-sustained-alpha cells, tonically spike and then turn off when presented with contrast, these cells are also particularly sensitive so they are good at detecting small changes in luminance. My project is trying to determine why the retina has two different types of cells that respond to the same stimulus, contrast, and why they exhibit different behavior, bursting versus spiking.

We think that these cells encode different features of the same stimulus. Suppressed-by-contrast cells we think encode when the stimulus appears (timing) and the off-sustained-alpha cells encode how much contrast there is (magnitude). So we are working on creating a model that simulates the different behaviors of these two neurons and testing whether different spiking patterns better encode different features of contrast.

Functional Connectivity in Motor Cortex —
The brain has many different areas that all fulfill different purposes and are populated by a variety of distinct cell types. Ongoing work with the Miri Lab is investigating how various regions of the mouse motor cortex communicate to generate complex movement. One technique we are using is called transfer entropy, which measures information-theoretic relationships, in this case, between neurons. Transfer entropy is a very assumption-free metric to determine when a neuron has any causal influence over another. It does not tell us if two neurons are synaptically connected, so if there is a significant amount transfer entropy observed between two cells then they might be one, two, three, or more synapses apart or maybe just have a common input. This gives us one way to measure how different brain areas interact and we are using this technique in conjuction with other metrics to get a more holistic view of motor-cortical regions to understand both the high-level information flow as well as anatomical synaptic organization of the motor cortex.