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We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
Many networked systems such as electric networks, the brain, and social networks of opinion dynamics are known to obey conservation laws. Examples of this phenomenon include the Kirchoff laws in electric networks and opinion consensus in…
Rotor walks are cellular automata that determine deterministic traversals of particles in a directed multigraph using simple local rules, yet they can generate complex behaviors. Furthermore, these trajectories exhibit statistical…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…
Given two subsets A and B of nodes in a directed graph, the conduciveness of the graph from A to B is the ratio representing how many of the edges outgoing from nodes in A are incoming to nodes in B. When the graph's nodes stand for the…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components…
Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches, random walks have been leveraged to capture such…
The increasing penetration of intermittent distributed energy resources in power networks calls for novel planning and control methodologies which hinge on detailed knowledge of the grid. However, reliable information concerning the system…
The support of a flow $x$ in a network is the subdigraph induced by the arcs $uv$ for which $x(uv)>0$. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Power flow analysis is used to evaluate the flow of electricity in the power system network. Power flow calculation is used to determine the steady-state variables of the system, such as the voltage magnitude/phase angle of each bus and the…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in…