Questions for lecture 1 & 2

[indigorose1]

Lecture 1: –The graphs we've been shown so far in lecture represent aspects of a brain like neuron interconnectivity, but can they be modified to show other aspects of a neuron, like length of axon (distinct distance between nodes on a graph?), or conductivity constants like λ and τ1/τ2 (rate of signals interacting with each other in the graph)? Is this what multi-graphs/weighted-graphs can be extended to include? –So far, it seems the position of the nodes in a graph aren't treated as important, but in the real brain neurons have a position which contributes to their connectivity. Should we assign position values to the nodes of a graph and keep track of them or would this just cause a whole jumble of unimportant information?

Lecture 2: –In the real brain, the neurons span the distance between each other and the synapses act as (relatively) discrete connection points. Because of this, wouldn't it make more sense to treat the synapses as the nodes and the neurons as the edges? –What would self-loops do if they were included in a graph? Self-modulation by proteins is important in the nervous system, would having weighted self-loops in graphs be a valid way the represent this or would it do something else entirely? Has anyone tried comparing models of self-looping graphs with similar ones that don't have self-loops and seeing what happens?

[SandyaS72]

Addressing your second point from the first lecture, for most clinical applications like diagnostics or therapeutics, you actually do want to know something about the locations of the "nodes", for example if you wanted to localize abnormal activity to a particular area of the brain or predict its spread or target therapy to a specific region of the brain. So it's actually pretty valuable to have some way of keeping track of the exact locations of nodes- the more exact, the better. A few of us in the class have worked on a seizure localization project for patients with epilepsy, and if we didn't have electrode labels for where the "nodes" are, everything we do would be kind of useless in the end because we couldn't actually tie it back to a specific part of the brain after all the computation.

[DSP137]

Lecture 2, question 1: As far as I can tell (granted, my knowledge of the subject is limited), we tend to use neurons as nodes because we are interested in which neurons send to information to other neurons, and where are those neurons located. Since we tend to be more interested in which neurons send information to which other neurons, it would make sense to make the edges the means of communication between neurons (namely the synapses would make sense as edges, even though they are smaller in size).

How would changing the model so that synapses were the vertices change the information that you obtain from the graph? What information would you then be gathering?