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Register a new userStorage capacity of phase-coded patterns in sparse neural networks
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We study the storage of multiple phase-coded patterns as stable dynamical attractors in recurrent neural networks with sparse connectivity. To determine the synaptic strength of existent connections and store the phase-coded patterns, we introduce a learning rule inspired to the spike-timing dependent plasticity (STDP). We find that, after learning, the spontaneous dynamics of the network replay one of the stored dynamical patterns, depending on the network initialization. We study the network capacity as a function of topology, and find that a small- world-like topology may be optimal, as a compromise between the high wiring cost of long range connections and the capacity increase.
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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 reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons rebirth). Thus the number of firing neurons reveals a minimum at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by the neurons with higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving an analytic mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, the system passes from a perfectly regular evolution to an irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.
We analyse the storage and retrieval capacity in a recurrent neural network of spiking integrate and fire neurons. In the model we distinguish between a learning mode, during which the synaptic connections change according to a Spike-Timing Dependent Plasticity (STDP) rule, and a recall mode, in which connections strengths are no more plastic. Our findings show the ability of the network to store and recall periodic phase coded patterns a small number of neurons has been stimulated. The self sustained dynamics selectively gives an oscillating spiking activity that matches one of the stored patterns, depending on the initialization of the network.
We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using an STDP-based learning process, we store in the connectivity several phase-coded spike patterns, and we find that, depending on the excitability of the network, different working regimes are possible, with transient or persistent replay activity induced by a brief signal. We introduce an order parameter to evaluate the similarity between stored and recalled phase-coded pattern, and measure the storage capacity. Modulation of spiking thresholds during replay changes the frequency of the collective oscillation or the number of spikes per cycle, keeping preserved the phases relationship. This allows a coding scheme in which phase, rate and frequency are dissociable. Robustness with respect to noise and heterogeneity of neurons parameters is studied, showing that, since dynamics is a retrieval process, neurons preserve stablecprecise phase relationship among units, keeping a unique frequency of oscillation, even in noisy conditions and with heterogeneity of internal parameters of the units.
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors, including periodic and irregular global spiking signals, as well as coherent oscillations, an unexpected form of synchronization. Our numerical results also show that the properties of the population firing rate depend on the size of the system, particularly its structure and average value over time. However, a few straightforward dynamical and topological strategies can be introduced to enhance or hinder these global behaviors, rendering a scenario where signal control is attainable, which incorporates a basic mechanism to turn off the dynamics permanently. As our main result, here we present a framework to estimate, in the stationary state, the mean firing rate over a long time window and to decompose the global dynamics into average values of the inter-spike-interval of each connectivity group. Our approach provides accurate predictions of these average quantities when the network exhibits high heterogeneity, a remarkable finding that is not restricted exclusively to the scale-free topology.
We consider a sparse random network of excitatory leaky integrate-and-fire neurons with short-term synaptic depression. Furthermore to mimic the dynamics of a brain circuit in its first stages of development we introduce for each neuron correlations among in-degree and out-degree as well as among excitability and the corresponding total degree, We analyze the influence of single neuron stimulation and deletion on the collective dynamics of the network. We show the existence of a small group of neurons capable of controlling and even silencing the bursting activity of the network. These neurons form a functional clique since only their activation in a precise order and within specific time windows is capable to ignite population bursts.
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