Related papers: Dynamic System of Neurons on a Complete Graph: Syn…
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…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
Why do neurons communicate through spikes? By definition, spikes are all-or-none neural events which occur at continuous times. In other words, spikes are on one side binary, existing or not without further details, and on the other can…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…
Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
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…
Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network with given…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites,…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…
Can Spiking Neural Networks (SNNs) approximate the dynamics of Recurrent Neural Networks (RNNs)? Arguments in classical mean-field theory based on laws of large numbers provide a positive answer when each neuron in the network has many…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…