Related papers: Using of Phenomenological Piecewise Continuous Map…
We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs…
At the single-neuron level, precisely timed spikes can either constitute firing-rate codes or spike-pattern codes that utilize the relative timing between consecutive spikes. There has been little experimental support for the hypothesis…
A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…
Epilepsy is a disorder characterised by spontaneous, recurrent seizures. Both local and network abnormalities have been associated with epilepsy, and the exact processes generating seizures are thought to be heterogeneous and…
We propose a data-driven approach to represent neuronal network dynamics as a Probabilistic Graphical Model (PGM). Our approach learns the PGM structure by employing dimension reduction to network response dynamics evoked by stimuli applied…
We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
Spatial awareness in mammals is based on internalized representations of the environment---cognitive maps---encoded by networks of spiking neurons. Although behavioral studies suggest that these maps can remain stable for long periods, it…
Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy.…
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
Historically studies of behaviour on networks have focused on the behaviour of individuals (node-based) or on the aggregate behaviour of the entire network. We propose a new method to decompose a temporal network into macroscale components…
In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…
In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps…
Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…