Related papers: Comparison principles and asymptotic behavior of d…
We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of…
Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the…
In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…
Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables.…
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the…
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a…
Paced finger tapping is one of the simplest tasks to study sensorimotor synchronization. The subject is instructed to tap in synchrony with a periodic sequence of brief tones, and the time difference (called asynchrony) between each…
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…
Synapses change on multiple timescales, ranging from milliseconds to minutes, due to a combination of both short- and long-term plasticity. Here we develop an extension of the common Generalized Linear Model to infer both short- and…
Spiking Neural P systems, SNP systems for short, are biologically inspired computing devices based on how neurons perform computations. SNP systems use only one type of symbol, the spike, in the computations. Information is encoded in the…
Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with…
Neural networks rely on learning synaptic weights. However, this overlooks other neural parameters that can also be learned and may be utilized by the brain. One such parameter is the delay: the brain exhibits complex temporal dynamics with…
Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochastic Volterra equations as a physics-inspired architecture,…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
Spiking neural networks (SNN) distinguish themselves from artificial neural networks (ANN) because of their inherent temporal processing and spike-based computations, enabling a power-efficient implementation in neuromorphic hardware. In…
This paper attempts to review our studies on the propagation of signals in nerves over the past decade. The need for interdisciplinary studies is stressed that helps to understand the physical mechanisms of coupling the electrical,…
We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems…