相关论文: Scaling Concepts in Graph Thoery: Self-Avoiding Wa…

We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…

We present a new family of graphs with remarkable properties. They are obtained by connecting the points of a random walk when their distance is smaller than a given scale. Their degree (number of neighbors) does not depend on the graph's…

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for…

Walks in a directed graph can be given a partially ordered structure that extends to possibly unconnected objects, called hikes. Studying the incidence algebra on this poset reveals unsuspected relations between walks and self-avoiding…

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph $C_n$,…

The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…

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…

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…

We present Walklets, a novel approach for learning multiscale representations of vertices in a network. In contrast to previous works, these representations explicitly encode multiscale vertex relationships in a way that is analytically…

We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of $N$ steps is of order $3^{N/4}$ times a polynomial in $N$, and so the approach is…

In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…

In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can…

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in…

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its…

Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…