Related papers: Detecting random walks on graphs with heterogeneou…
A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…
This paper considers the problem of simultaneous sensor fault detection, isolation, and networked estimation of linear full-rank dynamical systems. The proposed networked estimation is a variant of single time-scale protocol and is based on…
Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…
For $G$ a finitely generated group and $g \in G$, we say $g$ is detected by a normal subgroup $N \lhd G$ if $g \notin N$. The depth $D_G(g)$ of $g$ is the lowest index of a normal, finite index subgroup $N$ that detects $g$. In this paper…
It is natural to expect that nonbacktracking random walk will mix faster than simple random walks, but so far this has only been proved in regular graphs. To analyze typical irregular graphs, let $G$ be a random graph on $n$ vertices with…
The study of networks has emerged in diverse disciplines as a means of analyzing complex relationship data. Beyond graph analysis tasks like graph query processing, link analysis, influence propagation, there has recently been some work in…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
Assume that a graph $G$ models a detection system for a facility with a possible ``intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in $G$…
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…
We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…
We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the…
Random transvections generate a walk on the space of symplectic forms on $\mathbf{F}_q^{2n}$. The main result is establishing cutoff for this Markov chain. After $n+c$ steps, the walk is close to uniform while before $n-c$, it is far from…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
In this paper, we investigate the Gaussian graphical model inference problem in a novel setting that we call erose measurements, referring to irregularly measured or observed data. For graphs, this results in different node pairs having…
Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be…