Related papers: Transition State Theory for Network Dynamics
Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world,…
Network scientists often use complex dynamic processes to describe network contagions, but tools for fitting contagion models typically assume simple dynamics. Here, we address this gap by developing a nonparametric method to reconstruct a…
The changing topology of a network is driven by the need to maintain or optimize network function. As this function is often related to moving quantities such as traffic, information, etc. efficiently through the network the structure of…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
Network control theory has recently emerged as a promising approach for understanding brain function and dynamics. By operationalizing notions of control theory for brain networks, it offers a fundamental explanation for how brain dynamics…
Building upon the findings presented in the first three papers of this series, we formulate an effective field theory for interacting collective states. These states consist of a large number of interconnected neurons and are distinguished…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
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…
Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard…
In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
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…
Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur…