Related papers: Self-consistent moment dynamics for networks of sp…
Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
We propose a novel backpropagation algorithm for training spiking neural networks (SNNs) that encodes information in the relative multiple spike timing of individual neurons without single-spike restrictions. The proposed algorithm inherits…
Neural decoding may be formulated as dynamic state estimation (filtering) based on point process observations, a generally intractable problem. Numerical sampling techniques are often practically useful for the decoding of real neural data.…
Self-consistency improves reasoning by aggregating diverse stochastic samples, yet the dynamics behind its efficacy remain underexplored. We reframe self-consistency as a dynamic distributional alignment problem, revealing that decoding…
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…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and…
Based upon the moment closure approach, a Gaussian random field is constructed to quantitatively and analytically characterize the dynamics of a random point field. The approach provides us with a theoretical tool to investigate…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
This work is part of an effort to understand the neural basis for our visual system's ability, or failure, to accurately track moving visual signals. We consider here a ring model of spiking neurons, intended as a simplified computational…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter $\gamma$, corresponding…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…