Related papers: Synchronization of Boundary Coupled Hindmarsh-Rose…
We study the effect that the heterogeneity present among the elements of an ensemble of coupled excitable neurons have on the collective response of the system to an external signal. We have considered two different interaction scenarios,…
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…
Through the last years, different strategies to enhance synchronization in complex networks have been proposed. In this Letter, we show that the synchronization in a small-world network of attractively coupled non-identical neurons is…
We present an adaptive algorithm that guarantees synchronization in diffusively coupled systems. We first consider compartmental systems of ODEs, where each compartment represents a spatial domain of components interconnected through…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
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.…
We investigate the phase response properties of the Hindmarsh-Rose model of neuronal bursting using burst phase response curves (BPRCs) computed with an infinitesimal perturbation approximation and by direct simulation of synaptic input.…
Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize…
Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…
Brain networks are typically represented by adjacency matrices, where each node corresponds to a brain region. In traditional brain network analysis, nodes are assumed to be matched across individuals, but the methods used for node matching…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
Mathematical modeling is an important tool to study the role of delay in neural systems and to evaluate its effects on the signaling activity of coupled neurons. Models for delayed neurons are often used to represent the dynamics of real…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
Regularization can mitigate the generalization gap between training and inference by introducing inductive bias. Existing works have already proposed various inductive biases from diverse perspectives. However, none of them explores…
Distributed consensus has been widely studied for sensor network applications. Whereas the asymptotic convergence rate has been extensively explored in prior work, other important and practical issues, including energy efficiency and link…
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…
We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in…
A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system…
Experiments in the human brain reveal switching between different activity patterns and functional network organization over time. Recently, multilayer modeling has been employed across multiple neurobiological levels (from spiking networks…