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We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
Several guiding principles for thought processes are proposed and a neural-network-type model implementing these principles is presented and studied. We suggest to consider thinking within an associative network built-up of overlapping…
The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…
Inhibitory neurons play a crucial role in maintaining persistent neuronal activity. Although connected extensively through electrical synapses (gap-junctions), these neurons also exhibit interactions through chemical synapses in certain…
We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is…
Transient or partial synchronization can be used to do computations, although a fully synchronized network is frequently related to epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
Synthetic reverberating activity patterns are experimentally generated by stimulation of a subset of neurons embedded in a spontaneously active network of cortical cells in-vitro. The neurons are artificially connected by means of…
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…
We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…
Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…
The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Neural activity exhibits a vast range of timescales that can be several fold larger than the membrane time constant of individual neurons. Two types of mechanisms have been proposed to explain this conundrum. One possibility is that large…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…