Related papers: How to Store a Random Walk

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…

The problem of finding a resource residing in a network node (the \emph{resource location problem}) is a challenge in complex networks due to aspects as network size, unknown network topology, and network dynamics. The problem is especially…

Let $\mathcal{T}$ be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean $\mu >1$, conditioned to survive. Let $\varphi_{\mathcal{T}}$ be a random embedding of $\mathcal{T}$ into $\mathbb{Z}^d$ according…

We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…

We investigate the behavior of data structures when the input and operations are generated by an event graph. This model is inspired by Markov chains. We are given a fixed graph G, whose nodes are annotated with operations of the type…

We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…

The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…

In this paper we consider data storage from a probabilistic point of view and obtain bounds for efficient storage in the presence of feature selection and undersampling, both of which are important from the data science perspective. First,…

We study the problem of detecting a random walk on a graph from a sequence of noisy measurements at every node. There are two hypotheses: either every observation is just meaningless zero-mean Gaussian noise, or at each time step exactly…

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…

Following the recent work of Sznitman (arXiv:0805.4516), we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form G_N x Z, where G_N is a large finite connected weighted graph, and relate it to…

Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…

The rapid growth in feature dimension may introduce implicit associations between features and labels in multi-label datasets, making the relationships between features and labels increasingly complex. Moreover, existing methods often adopt…

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…

Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Many applications have requirements to…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

Node embeddings have become an ubiquitous technique for representing graph data in a low dimensional space. Graph autoencoders, as one of the widely adapted deep models, have been proposed to learn graph embeddings in an unsupervised way by…

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…