Related papers: From Dyson to Hopfield: Processing on hierarchical…

Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…

The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by…

We consider a neural field model which consists of a network of an arbitrary number of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. We extend previous work on this…

Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

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…

We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph…

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for…

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…

It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we…

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

In this paper we develop conditions for various types of stability in social networks governed by Imitation of Success principle. Considering so-called Prisoner's Dilemma as the base of node-to-node game in the network we obtain well-known…

The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…

We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…

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…

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used.…

Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential…