Related papers: Enhanced Random Walk with Choice: An Empirical Stu…
How to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online…
Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
Consider a continuous time random walk in $\mathbb{Z}$ with independent and exponentially distributed jumps $\pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of…
We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of…
We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\subseteq V$, we aim to identify the $k$ most central nodes in $G$ with respect to $Q$. Specifically, we consider…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility,…
In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…