Related papers: Small-World Network Effect in Competing Glauber- a…
In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a…
We study the domain growth of the one-dimensional kinetic Ising model under the competing influence of Glauber dynamics at temperature T and Kawasaki dynamics with a configuration-independent rate. The scaling of the structure factor is…
Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at…
Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link…
We study the dynamics of the Bak-Sneppen model on small-world networks. For each site in the network, we define a ``connectance,'' which measures the distance to all other sites. We find radically different patterns of activity for…
Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
We compare equilibrium probability distributions obtained from Monte Carlo simulations for different spin exchange dynamics with the exact Boltzmann distribution for the fixed magnetization Ising model on small lattices. We present simple…
The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising…
The Kuramoto model of coupled phase oscillators on small-world (SW) graphs is analyzed in this work. When the number of oscillators in the network goes to infinity, the model acquires a family of steady state solutions of degree q, called…
We present a simple mathematical framework for the description of the dynamics of glassy systems in terms of a random walk in a complex energy landscape pictured as a network of minima. We show how to use the tools developed for the study…
While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory…
We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…
We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories. In this approach trajectories are classified according to a dynamical…
We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the…
Motivated by the ability of triangular spin ladders to implement quantum information processing, we propose a type of such systems whose Hamiltonian includes the XX Heisenberg interaction on the rungs and DzyaloshinskiiMoriya (DM) coupling…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential…