Related papers: Self-avoiding walks and connective constants in sm…
We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is…
The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a graph and $t$ is a sufficiently small positive…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
Simulations of the self-avoiding walk (SAW) are performed in a half-plane and a cut-plane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
We consider a self-avoiding walk on the dual $\mathbb{Z}^2$ lattice. This walk can traverse the same square twice but cannot cross the same edge more than once. The weight of each square visited by the walk depends on the way the walk…
We have analyzed geometric and topological features of self-avoiding walks. We introduce a new kind of walk: the loop-deleted self-avoiding walk (LDSAW) motivated by the interaction of chromatin with the nuclear lamina. Its critical…
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
A celebrated problem in numerical analysis is to consider Brownian motion originating at the centre of a $10 \times 1$ rectangle, and to evaluate the ratio of probabilities of a Brownian path hitting the short ends of the rectangle before…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
We define a new ensemble for self-avoiding walks in the upper half-plane, the fixed irredicible bridge ensemble, by considering self-avoiding walks in the upper half-plane up to their $n$-th bridge height, $Y_n$, and scaling the walk by…
The model of self-avoiding lattice walks and the asymptotic analysis of power-series have been two of the major research themes of Tony Guttmann. In this paper we bring the two together and perform a new analysis of the generating functions…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
Temporal networks serve as abstractions of many real-world dynamic systems. These networks typically evolve according to certain laws, such as the law of triadic closure, which is universal in social networks. Inductive representation…
The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…