Sheaves are an incredible interesting concept in mathematics and there is a lot of potential applications
for them in science. Unfortunately, the mathematical details are extremely dense and it is hard to gain an intuition
for what's actually going on. So I wrote a paper
doing my best to explain them in a very elementary way with lots of
concrete examples and anaologies instead of the one-sentence definitions only intelligible by people who already know
what a sheaf is.
The retina does an immense amount of processing of visual information before it even sends signals to the rest of the brain. There
are many types of retinal ganglion cells (the cells that then project to other areas in the brain) and they all are specialized to
extract different features from a visual scene as quickly and efficiently as possible.
Here, we study a few different types of RGCs
and learn how the spiking patterns that are specific to them help optimize the type of information they extract. Bursty suppressed-by-contrast
cells (bSbCs) will burst at a baseline rate and actually decrease their activity when presented with a stimulus. This requires the downstream
neurons to detect when a gap in spikes occurs and how to detect that gap quickly and reliably. It turns out that the particular way bSbCs
organize their spikes allows gaps in their activity to be detect with the highest fidelity.
check out the paper
Coming eventually! But maybe not! Idk if what I'm trying is going to work.