  Simultaneously recorded neurons exhibit correlations whose underlying causes
are not known. Here, we use a population of threshold neurons receiving
correlated inputs to model neural population recordings. We show analytically
that small changes in second-order correlations can lead to large changes in
higher correlations, and that these higher-order correlations have a strong
impact on the entropy, sparsity and statistical heat capacity of the
population. Remarkably, our findings for this simple model may explain a couple
of surprising effects recently observed in neural population recordings.
