Statistical analysis of Potts neural networks and latching dynamics

This thesis focuses on the Potts model of long-range cortical interactions. The model is simple enough to allow a quantitative analysis, e.g., mean-field treatment, on the global cortical level. At the same time, it is so rich in its dynamic repertoire that we can simulate diverse aspects of associative memory processing in the cortex. We have pushed the Potts model one step closer to biological plausibility by differentiating the frontal subnetwork from the posterior one. Though this binary distinction is still far away from reality, it gives us an unexpected observation as well as a potentiality to address interesting questions related to cognitive processes. Firstly, we study the glassy nature of a discrete Potts model, within mean-field theory, to find a previously unreported effect of {\em speed inversion}, which might be relevant for learning dynamics of cortical networks (Chapter 3). Secondly, we discuss the storage capacity of a discrete Potts neural network when stored memories have a compositional structure, in connection with recalling spatial scenes (Chapter 4). Thirdly, by using {\em latching dynamics} of a continuous Potts model, we propose a network model for short-term memory that can explain experimental data on free recall as well as serial recall (Chapter 5). Lastly, we offer a preliminary attempt to model prefrontal schemata by means of latching dynamics, in connection with an empirical observation from brain-lesioned patients (Chapter 6).