Related papers: From Neuron to Neural Networks dynamics

This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…

This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series…

The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signalling activity of neurons a challenge of practical interest. Neuron models are frequently used to…

By means of the concept DE we analyze the responses of a HH neuron to two types of spike-train inputs. Two characteristic quantities can be extracted, which can reflect partially the dynamical process of a HH neuron.

When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…

We consider the implications of the mathematical analysis of neurone-to-neurone dynamical complex networks. We show how the dynamical behaviour of small scale strongly connected networks lead naturally to non-binary information processing…

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…

A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…

This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…

Reverberating dynamics of neural network is modelled on PC in order to illustrate possible role of inhibition as binding controller in the network. The network is composed of binding neurons. In the binding neuron model the degree of…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

We study a mathematical model of biological neuronal networks composed by any finite number $N \geq 2$ of non necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential…

We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…

Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…

There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond to neurons (or nerve cells, to avoid confusion) in the…

Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…

Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…