"Random-Graph Models and Characterization of Granular Networks"

A paper of mine from 2020 now has its final coordinates listed on the published file itself. Here are some details.

Title: Random-Graph Models and Characterization of Granular Networks

Authors: Silvia Nauer, Lucas Böttcher, and Mason A. Porter

Abstract: Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we examine a variety of common network measures and study their ability to characterize various two-dimensional and three-dimensional spatial random-graph models and empirical two-dimensional granular networks. We identify network measures that are able to distinguish between physically plausible and unphysical spatial network models. Our results also suggest that there are significant differences in the distributions of certain network measures in two and three dimensions, hinting at important differences that we also expect to arise in experimental granular networks.

"Topological Data Analysis of Continuum Percolation with Disks"

One of my papers came out in final form today. Here are some details and a story.

Title: Topological Data Analysis of Continuum Percolation with Disks

Authors: Leo Speidel, Heather A. Harrington, S. Jonathan Chapman, and Mason A. Porter

Abstract: We study continuum percolation with disks, a variant of continuum percolation in two-dimensional Euclidean space, by applying tools from topological data analysis. We interpret each realization of continuum percolation with disks as a topological subspace of [0,1]^2 and investigate its topological features across many realizations. Specifically, we apply persistent homology to investigate topological changes as we vary the number and radius of disks, and we observe evidence that the longest persisting invariant is born at or near the percolation transition.


And to give a story, or at least the hint of the interesting relationship that I sometimes have with typesetters and editors, here is a note that I received from them while we were working on the galley proofs.

Update (8/05/18): A nice way of phrasing things is that we're in a nonassociative situation, and hyphens are a great tool to indicate exactly (and tersely) where the parentheses should be to group terms in a way that renders their meaning unambiguous. (And, naturally, if somebody makes a change in my text that I don't like, my immediate desire is to change it back.)

"Dynamics on Modular Networks with Heterogeneous Correlations"

Another one of my papers came out in final form today. (That's two days in a row, and there is a third that will be out imminently.) Here are the details.

Title: Dynamics on Modular Networks with Heterogeneous Correlations

Authors: Sergey Melnik, Mason A. Porter, Peter J. Mucha, and James P. Gleeson


Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree- degree correlations across modules, which is important for the consideration of nonidentical interactingnetworks.


The basic idea is that we have developed a new random-graph ensemble that allows one to consider heterogeneous levels of homophily (which, in this paper, we use as degree homophily) in different parts of a network. You can also relate this to metapopulations in biology. We examine some simple dynamical processes on such ensembles.