Related papers: Effect of a static phase transition on searching d…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
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…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
The effect of particle overtaking on transport in a narrow channel is studied using a 1d model of a driven tracer in a quiescent bath. In contrast with the well-studied non-driven case, where the tracer's long-time dynamics changes from…
We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment. To this end, we consider a preferential-attachment-preferential-deletion…
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…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network;…
In this paper, we investigate the quest for a single target, that remains fixed in a lattice, by a set of independent walkers. The target exhibits a fluctuating behavior between trap and ordinary site of the lattice, whereas the walkers…
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…