Related papers: Homoclinical structure of SICNNs with rectangular …
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…
Numerical investigations have been made of responses of a Hodgkin-Huxley (HH) neuron to spike-train inputs whose interspike interval (ISI) is modulated by deterministic, semi-deterministic (chaotic) and stochastic signals. As deterministic…
Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video…
We investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous…
We numerically study dynamical behaviors of the quasiperiodically forced Hodgkin-Huxley neuron and compare the dynamical responses with those for the case of periodic stimulus. In the periodically forced case, a transition from a periodic…
The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four body problem. The problem can be viewed as a two parameter family of conservative autonomous vector fields. The main tools are…
In this paper we address the importance and the impact of employing structure preserving neural networks as surrogate of the analytical physics-based models typically employed to describe the rheology of non-Newtonian fluids in Stokes…
Hexagonal CNN models have shown superior performance in applications such as IACT data analysis and aerial scene classification due to their better rotation symmetry and reduced anisotropy. In order to realize hexagonal processing, existing…
Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification…
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…
We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. We show that the system can have a robust attractor that responds to a specific detuning between certain pairs of the oscillators…
Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…
We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…
Over the past decade Spiking Neural Networks (SNN) have emerged as one of the popular architectures to emulate the brain. In SNN, information is temporally encoded and communication between neurons is accomplished by means of spikes. In…
Spiking Neural Networks are powerful computational modelling tools that have attracted much interest because of the bioinspired modelling of synaptic interactions between neurons. Most of the research employing spiking neurons has been…
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…
We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…