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open-connectome-classes / StatConn-Spring-2015-Info

introductory material
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Stochastic Block Models First Steps Question #65

Open imichaelnorris opened 9 years ago

imichaelnorris commented 9 years ago

I have a question about the paper by Holland et al.

On page 113, it states that "definition 3 formalizes the concept of "internal homogeneity."

Can someone explain the second paragraph of this page better, possibly using neuroscience instead of graphs, and how is internal homogeneity important for a stochastic block model?

akim1 commented 9 years ago

I think this is just a fancy way of saying that all neurons in a given block have to be connected in the same way. For instance, a neuroscience example would be that all the neurons in a given block are in an all-to-all network. There should be an inherent symmetry in the graphs that doesn't allow you to single out a neuron with connection pattern that is different from the rest

Internal homogeneity is important because you take a particular region of the brain and just assume that all its constituents behave in the same way. Any given input to that block regardless of which neuron is actually excited should yield the same output. The only way this can be accomplished is if the condition described in the previous paragraph is met.