Related papers: Transition to chaos in random networks with cell-t…
Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of…
In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic…
What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we…
Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences for how such networks encode streams of temporal stimuli? On the one…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
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…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
We set up a signal-driven scheme of the chaotic neural network with the coupling constants corresponding to certain information, and investigate the stochastic resonance-like effects under its deterministic dynamics, comparing with the…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs…