Related papers: System size resonance in an attractor neural netwo…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the…
Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…
We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of…
It is held as a truism that deep neural networks require large datasets to train effective models. However, large datasets, especially with high-quality labels, can be expensive to obtain. This study sets out to investigate (i) how large a…
We carry out an analytical theory of generation-recombination noise for a two level resistor model which goes beyond those presently available by including the effects of both space charge fluctuations and diffusion current. Finite size…
We study the capacity with which a system of independent neuron-like units represents a given set of stimuli. We assume that each neuron provides a fixed amount of information, and that the information provided by different neurons has a…
We analyze the effects of lateral device size and magnetic material parameters on the ferromagnetic resonance (FMR) response. Results presented are directly relevant to widely used FMR experimental techniques for extracting magnetic…
We study finite-size fluctuations in a network of spiking deterministic neurons coupled with non-uniform synaptic coupling. We generalize a previously developed theory of finite size effects for uniform globally coupled neurons. In the…
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…
The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors…
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…
The implementation of artificial neural networks in hardware substrates is a major interdisciplinary enterprise. Well suited candidates for physical implementations must combine nonlinear neurons with dedicated and efficient hardware…
We focus on the long time behavior of complex networks of reaction-diffusion (RD) systems. We prove the existence of the global attractor and a $L^{\infty}$-bound for a network of $n$ RD systems with $d$ variables each. This allows us to…
A method allowing to distinguish interacting from non-interacting systems based on available time series is proposed and investigated. Some facts concerning generalized Renyi dimensions that form the basis of our method are proved. We show…
In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the…
In this lecture I will present some models of neural networks that have been developed in the recent years. The aim is to construct neural networks which work as associative memories. Different attractors of the network will be identified…
The capacity with which a system of independent neuron-like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses. Both discrete noiseless and continuous noisy…
We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular…
We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…