Ermentrout-Kopell canonical model

Commentary on Structured chaos shapes spike-response noise entropy in balanced neural networks, by Lajoie, Thivierge, and Shea-Brown

Animals with nervous systems generate complex adaptive behaviors in part through the computational capabilities arising from large networks of interconnected neurons in their brains (Churchland and Sejnowski, 1992). Although a full description of the nervous system would take into account the interactions of central circuits with sensory and motor systems (Chiel and Beer, 1997) it is more commo...

Foundations of Mathematical Neuroscience Bard Ermentrout

A Model for Shell Patterns Based on Neural Activity by BARD ERMENTROUT

The patterns of pigment on the shells of mollusks provide one of the most beautiful and complex examples of animal decoration. Recent evidence suggests that these patterns may arise from the stimulation of secretory cells in the mantle by the activity of the animal's central nervous system. We present here a mathematical model based on this notion. A rather simple scheme of nervous activation a...

The grand canonical ABC model

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean-field interactions. The three types of particles are designated as A, B and C. The system is described by a grand canonical ensemble with temperature T and chemical potentials T λA, T λB and T...

Model Tuning with Canonical Correlation

4 Knowledge of the relationship between model parameters and forecast quantities is 5 useful because it can aid in setting the values of the former for the purpose of having 6 a desired effect on the latter. Here, it is proposed that a well-established multivariate 7 statistical method known as Canonical Correlation Analysis can be formulated to gauge 8 the strength of that relationship. The me...