"Social Network Analysis for Social Neuroscientists"

A paper of mine that was posted in advanced access more than a year ago has now finally been posted in final form. It is a survey and perspective article on social network analysis for social neuroscientists. Here are some details.

Title: Social Network Analysis for Social Neuroscientists

Authors: Elisa C. Baek, Mason A. Porter, and Carolyn Parkinson

Abstract: Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to advance knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individual’s social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementations of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.

"Random Walks and Diffusion on Networks"

Our review article on random walks on networks has its final coordinates. Here are the details.

Title: Random Walks and Diffusion on Networks

Authors: Naoki Masuda, Mason A. Porter, and Renaud Lambiotte

Abstract: Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

Special Guest Star: A very weary random walker

"Nonlinear Coherent Structures in Granular Crystals"

My review article on granular crystals (and especially work on it during the last decade) just came out in final form. Here are the details.

Title: Nonlinear Coherent Structures in Granular Crystals

Authors: Chris Chong, Mason A. Porter, Panayotis G. Kevrekidis, and Chiara Daraio

Abstract: The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential
engineering applications that arise from the rich dynamic response of granular crystals.

My Blog Entry for Oxford University Press about "Multilayer Networks"

Here is a blog entry that I wrote for Oxford University Press to accompany a review article on multilayer networks by my collaborators and me.

There are also tutorial slides (from a 3-hour tutorial I gave at NetSci 2014) to help guide people through the review article.

Manlio De Domenico, Alex Arenas, and I also have developed software for analysis and visualization of multilayer networks. (There is also an article about our software.)

And if you want to learn more about multilayer networks, we're holding a workshop in July 2015 at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany.

(As a brief correction, "interaction oscillators" in the article should read "interacting oscillators". I didn't catch that typo until reading the published version of my blog entry a few minutes ago.)

"Multilayer Networks"

Our mega-review article on multilayer networks is finally out! The page proof stage was particularly painful, so it's great that the published version of our article is now available. (In my Facebook post, I wrote "After a long and painful bout with page proofs". Reading my words now, it's like "page proofs" are a disease, thought that allusion is not what I intended when I wrote that text.) We don't have things like page numbers yet, but those will come. (By the way, "our" equals the PLEXMATH team.)

Here are the details about the article.


Title: Multilayer Networks

Authors: Mikko Kivelä, Alex Arenas, Marc Barthelemy, James P. Gleeson, Yamir Moreno, and Mason A. Porter

Abstract: In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such ‘multilayer’ features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize 'traditional' network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other and provide a thorough discussion that compares, contrasts and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

"Limit Order Books"

Our review article on limit order books finally has official page numbers and all that, so I am finally going to blog about it. Here are the details of the article.

Title: Limit Order Books

Authors: Martin D. Gould, Mason A. Porter, Stacy Williams, Mark McDonald, Daniel J. Fenn, and Sam D. Howison

Abstract: Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.