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We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. We calculate the number of stored environments. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the cross-talk between the maps, and memory of environments is lost. Analytical predictions are corroborated by numerical simulations.
A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped
The spontaneous transitions between D-dimensional spatial maps in an attractor neural network are studied. Two scenarios for the transition from on map to another are found, depending on the level of noise: (1) through a mixed state, partly localized
Artificial neural networks have diverged far from their early inspiration in neurology. In spite of their technological and commercial success, they have several shortcomings, most notably the need for a large number of training examples and the resu
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the configuration space
Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy. In this p