Related papers: The attractors in sequence processing neural netwo…
Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…
Continuous attractor neural networks generate a set of smoothly connected attractor states. In memory systems of the brain, these attractor states may represent continuous pieces of information such as spatial locations and head directions…
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…
The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…
We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…
In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…
The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience. In this work, we investigate how the structure of recurrent connectivity influences…
We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…
A wide range of networks, including small-world topology, can be modelled by the connectivity $\gamma$, and randomness $\omega$ of the links. Both learning and attractor abilities of a neural network can be measured by the mutual…
Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the…
The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path…
We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree $k$ is proportional to $k^{\alpha}$, where $\alpha$ is a tuning parameter. We study both numerically and analytically three…
Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…