Related papers: Duality between equilibrium and growing networks
We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…
It is still common wisdom amongst economists, politicians and lay people that economic growth is a necessity of our social systems, at least to avoid distributional conflicts. This paper challenges such belief moving from a purely physical…
We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
We draw attention to a clear dichotomy between small-world networks exhibiting exponential neighborhood growth, and fractal-like networks where neighborhoods grow according to a power law. This distinction is observed in a number of…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges.…
Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
This paper studies a special kind of equilibrium termed as "balanced equilibrium" which arises in the power allocation game defined in \cite{allocation}. In equilibrium, each country in antagonism has to use all of its own power to…
We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent…
Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of the nonlinearly growing networks into free-scale structures. We find that the accelerating growth of the networks…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…