Latching dynamics in Potts neural networks

One purpose of Computational Neuroscience is to try to understand by using models how at least some parts in the brain work or how cognitive phenomena occur and are organized in terms of neuronal activity. The Hopfield model of a neural network, rooted in Statistical Physics, put forward by J. Hopfield in the 1980s, was one of the first attempts to explain how associative memory could work. It was successful in guiding experiments, e.g., in the hippocampus and primate inferotemporal cortex. However, some higher level cognitive functions that the brain accomplishes require, to be approached quantitaively, by more advanced models beyond simple cued retrieval..

Effective Action for Cosmological Scalar Fields at Finite Temperature

Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this environment is crucial to understand the implications for cosmology. We calculate the finite temperature effective action for the field expectation value in two particularly important cases, for damped oscillations near the ground state and for scalar fields with a flat potential. We find that the behavior in both cases can in good approximation be described by a complex valued effective potential that yields Markovian equations of motion. Near the potential minimum, we recover the solution to the well-known Langevin equation. For large field values we find a very different behavior, and our result for the damping coefficient differs from the expressions frequently used in the literature. We illustrate our results in a simple scalar model, for which we give analytic approximations for the effective potential and damping coefficient. We also provide various expressions for loop integrals at finite temperature that are useful for future calculations in other models.Comment: 34 pages plus appendix, 17 figures: minor corrections, modifications of discussions, added references, version published in JHE

Reducing a cortical network to a Potts model yields storage capacity estimates

An autoassociative network of Potts units, coupled via tensor connections, has been proposed and analysed as an effective model of an extensive cortical network with distinct short- and long-range synaptic connections, but it has not been clarified in what sense it can be regarded as an effective model. We draw here the correspondence between the two, which indicates the need to introduce a local feedback term in the reduced model, i.e., in the Potts network. An effective model allows the study of phase transitions. As an example, we study the storage capacity of the Potts network with this additional term, the local feedback w, which contributes to drive the activity of the network towards one of the stored patterns. The storage capacity calculation, performed using replica tools, is limited to fully connected networks, for which a Hamiltonian can be defined. To extend the results to the case of intermediate partial connectivity, we also derive the self-consistent signal-to-noise analysis for the Potts network; and finally we discuss implications for semantic memory in humans

Two Cases of Hypertensive Encephalopathy Involving the Brainstem

Hypertensive encephalopathy is a medical emergency whose clinical manifestations are usually associated with bilateral parieto-occipital lesions. Predominant brainstem edema without accompanying occipital lesions is rare in hypertensive encephalopathy and usually occurs in patients with secondary hypertension. We describe the clinical and radiological features of two patients with reversible hypertensive brainstem encephalopathy. Both patients had chronic renal failure, but the extensive neuroimaging abnormalities revealed few clinical features of brainstem involvement. The clinical findings and neuroimaging abnormalities resolved once the hypertension was treated