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We study the stability and information encoding capacity of synchronized states in a neuronal network model that represents part of thalamic circuitry. Our model neurons have a Hodgkin-Huxley-type low threshold Calcium channel, display post inhibitory rebound, and are connected via GABAergic inhibitory synapses. We find that there is a threshold in synaptic strength, $tau_c$, below which there are no stable spiking network states. Above threshold the stable spiking state is a cluster state, where different groups of neurons fire consecutively, and each neuron fires with the same cluster each time. Weak noise destabilizes this state, but stronger noise drives the system into a different, self-organized, stochastically synchronized state. Neuronal firing is still organized in clusters, but individual neurons can hop from cluster to cluster. Noise can actually induce and sustain such a state below the threshold of synaptic strength. We do find a qualitative difference in the firing patterns between small ($sim 10$ neurons) and large ($sim 1000$ neurons) networks. We determine the information content of the spike trains in terms of two separate contributions: the spike time jitter around cluster firing times, and the hopping from cluster to cluster. We quantify the information loss due to temporally correlated interspike intervals. Recent experiments on the locust olfactory system and striatal neurons suggest that the nervous system may actually use these two channels to encode separate and unique information.
We use a neural network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We obtain the scaled cumulant-generating function for the dynamical activity of the Fredrick
The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases. It is show
Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory spiking network
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reacti
We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation conc