In the setting of finite-dimensional C∗-algebras A we define what we call a Riemannian metric for A, which when A is commutative is very closely related to a finite resistance network. We explore the relationship with Dirichlet forms and corresponding seminorms that are Markov and Leibniz, with corresponding matricial structure and metric on the state space. We also examine associated Laplace a...

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.

We calculate resistance distances between papers in a nearly bipartite citation network of 492 papers and the sources cited by them. We validate that this is a realistic measure of thematic distance if each citation link has an electric resistance equal to the geometric mean of the number of the paper’s references and the citation number of the cited source.

We study the performance of leader-follower noisy consensus networks, and in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered (1) noise-free leaders, in which leaders dictate the trajectory exactly and followers are subject to external disturbances, and (2) noise-corrupted leaders, in which both leaders and followe...

Least-cost modelling and circuit theory are common analogs used in ecology and evolution to model gene flow or animal movement across landscapes. Least-cost modelling estimates the least-cost distance, whereas circuit theory estimates resistance distance. The bias added in choosing one method over the other has not been well documented. We designed an experiment to test whether both methods wer...

Fusarium head blight is one of the most important and most common diseases of winter wheat. In order to better understanding this disease and to assess the correlations between different factors, 30 cultivars of this cereal were evaluated in a two-year period. Fusarium head blight resistance was evaluated and the concentration of trichothecene mycotoxins was analysed. Grain samples originated f...