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We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy for finite {M}arkov chains,'' J. Funct. Anal. 261(8), 2011)…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
This thesis examines linearly edge-reinforced random walks on infinite trees. In particular, recurrence and transience of such random walks on general (fixed) trees as well as on Galton-Watson trees (i.e. random trees) is characterized, and…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
Given a graph with non-negative edge weights, there are various ways to interpret the edge weights and induce a metric on the vertices of the graph. A few examples are shortest-path, when interpreting the weights as lengths; resistance…
The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical…
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
Finding the dominant direction of flow of information in densely interconnected regulatory or signaling networks is required in many applications in computational biology and neuroscience. This is achieved by first identifying and removing…
Understanding how users navigate in a network is of high interest in many applications. We consider a setting where only aggregate node-level traffic is observed and tackle the task of learning edge transition probabilities. We cast it as a…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Reinforced random walks are random walks on graphs whose transition probabilities along edges from a vertex are proportional to the weights of those edges, but where the weight of an edge evolves in a way that depends on the past traversals…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…
Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…