Speaker
Prof.
John Hertz
(NORDITA)
Description
We can learn something about how large neuronal networks
function from models of the spike pattern distributions
constructed from data. In our work, we do this for data
generated from simulated models of local cortical networks,
using the approach introduced by Schneidman et al, modeling
this distribution by an Ising model: P[S] =
Z^{-1}exp(½Σ_{ij}J_{ij}S_iS_j+Σ_i h_i S_i). To estimate the
parameters J_{ij} and h_i we use a technique based on
inversion of the TAP equations. We perform the estimation
procedure for subsets of the neurons of sizes N ranging from
6 up to 800 (all the excitatory neurons in the simulated
network) and study the statistics of the inferred
parameters. The N-dependences of both the means and the
variances are well-fit, at large N, by functions of the form
a/(b +N). This dependence can be accounted for in a simple
way by assuming that the system is an SK spin glass in its
normal phase. We verify a posteriori the assumption that it
is in the normal, rather than the spin glass phase; thus,
this description is self-consistent.
