An American Mathematician (and Physicist) in Stockholm

Tomorrow I will be flying directly from WorldCon to Stockholm for my next adventure on the faculty of Nordita (the Nordic Institute for Theoretical Physics) and the Department of Mathematics at Stockholm University. In the latter, my title is Professor in Complex Systems.

I hardly ever write long blog posts these days, but the title of this post is an homage to my post from when I moved to Oxford in 2007.

A new adventure awaits!

"Bounded-Confidence Models of Opinion Dynamics with Neighborhood Effects"

One of my papers just came out in final form. Here are some details.

"Dynamical Processes on Metric Networks"

A paper of mine was just published in final form. Here are some details.

Title: Dynamical Processes on Metric Networks

Authors: Lucas Böttcher and Mason A. Porter

What Happens in Stockholm Stays in Stockholm (2025 Edition)

I am off to Stockholm to give a talk and visit Nordita!

What Happens in Dresden Stays in Dresden (2025 Edition)

I'm heading to Dresden to give a colloquium at the Max Planck Institute for the Physics of Complex Systems.

"Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions"

The published version of one of my papers just came out today. Here are some details.

Title: Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

Authors: Corbit R. Sampson, Juan G. Restrepo, and Mason A. Porter

Abstract:

"Competition Between Group Interactions and Nonlinearity in Voter Dynamics on Hypergraphs"

One of my papers just came out in final form. Here are some details.

Title: Competition Between Group Interactions and Nonlinearity in Voter Dynamics on Hypergraphs

Authors: Jihye Kim, Deok-Sun Lee, Byungjoon Min, Mason A. Porter, Maxi San Miguel, and Kwang-Il Goh

What Happens at the Global Physics Summit Stays at the Global Physics Summit

Later this afternoon, I will be taking a train to Anaheim to go to the Global Physics Summit, where I will be participating in the March-Meeting wing of this summit. I'll only be around for about a day and a half or so, but nevertheless I will be making my triumphant return to the March Meeting (which I last attended in 2016).

Update: I ended up just taking a Lyft directly to my hotel and not bothering with the train.

What Happens in Denver Stays in Denver (2025 Edition)

I am flying to Denver for the US Dynamics Days 2025 conference. I really love this conference series! This year, the conference hotel is actually about half a mile from the 2025 Snowbird-conference hotel.

I am really looking forward to this year's Dynamics Daze conference!

"Dynamical Importance and Network Perturbations"

One of my papers was just published in final form. Here are some details.

Title: Dynamical Importance and Network Perturbations

Authors: Ethan Young and Mason A. Porter

Abstract: The leading eigenvalue λ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of importance of network structures to λ and its associated eigenvectors. We study a previously derived measure of edge importance known as “dynamical importance,” which estimates how much λ changes when one removes an edge from a graph or adds an edge to it. We examine the accuracy of this estimate for several undirected network structures and compare it to the relative change in λ after an edge removal or edge addition. We then derive a first-order approximation of the change in the leading eigenvector. We also consider the effects of edge additions on Kuramoto dynamics on networks, and we express the Kuramoto order parameter in terms of dynamical importance. Through our analysis and computational experiments, we find that studying dynamical importance can improve understanding of the relationship between network perturbations and dynamical processes on networks.

What Happens in Boston Stays in Boston

I'm on my way to Boston for the workshop to celebrate David Campbell's 80th birthday! It will surely be chaotic. :)

2024 Nobel Prize in Physics Awarded for Applications of Statistical Physics to Machine Learning!

The 2024 Nobel Prize in Physics has been awarded to physicist John Hopfield and computer scientist Geoffrey Hinton.

The official prize citation is "for foundational discoveries and inventions that enable machine learning with artificial neural networks". However, I strongly prefer the phrasing along the lines of "for the statistical-physics basis of neural networks", which is how mathematical physicist Barry Simon described it.

Here is the information, press release, and other materials from The Nobel Foundation.

Naturally, I am strongly in favor of more Nobel Prizes being awarded for foundational interdisciplinary work, as that is the world in which I live. Unsurprisingly, many traditional physicists are arguing against and doing their common practice of staking territorial claim (as we also often see on the job market and in other arenas). This is an old battle, and we can look forward to a later phase when somebody gets a physics Nobel Prize for work in networks. That said, I am grateful to see people arguing about science, rather than about other ideological things!

What Happens in Frankfurt Stays in Frankfurt

I am going to be in Frankfurt for a few days for a workshop on metric networks that I coorganized.

RIP Martin Mull (1943–2024)

Comedic actor, musician, and painter Martin Mull dies yesterday.

I found out about him via the song "Dueling Tubas", which I first learned about in Physics 2a through an acoustics demo by now-Nobel Laureate David Politzer.

My musically-inclined classmates were in emotional pain.

RIP David Goodstein (1939–2024)

David Goodstein (an emeritus physics professor at Caltech) died yesterday. This is the end of an era.

I watched many of The Mechanical Universe videos in high school. The beginning and end of each video showed Goodstein lecturing to students in the big Caltech physics lecture hall. I had Goodstein for Physics 1a (mechanics) in fall of my frosh year in that same lecture hall, and I remember how surreal it felt. That was one of my big "Wow, I am now at Caltech." things. Also, I came out of lectures feeling that I understood the material — but then I tried the homework and saw that I didn't actually yet understand it.

(h/t Barry Simon)

"Complex Networks with Complex Weights"

The published version of one of my papers came out today. Its title is one of my favorites among all of the papers that I've ever written. Here are some details about the paper.

Title: Complex Networks with Complex Weights

Authors: Lucas Böttcher and Mason A. Porter

Abstract: In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to encode node–node interactions with heterogeneous intensities or frequencies (e.g., in transportation networks, supply chains, and social networks). Most such studies have considered real-valued weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information, quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we examine how standard network-analysis methods fail to capture structural features of networks with complex edge weights. We then generalize several network measures to the complex domain and show that random-walk centralities provide a useful approach to examine node importances in networks with complex weights.

"The Topology of Data"

Our introduction to a topological data analysis (TDA) for a general physics audience was published today in Physics Today. Here are some details.

Title: The Topology of Data

Authors: Mason A. Porter, Michelle Feng, and Eleni Katifori

Lede: Topological data analysis, which allows systematic investigations of the “shape” of data, has yielded fascinating insights into many physical systems.

"Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition"

One of my papers just came out in final form last week. Here are some details.

Title: Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition

Abstract: Dynamic-mode decomposition (DMD) is a versatile framework for model-free analysis of time series that are generated by dynamical systems. We develop a DMD-based algorithm to investigate the formation of functional communities in networks of coupled, heterogeneous Kuramoto oscillators. In these functional communities, the oscillators in a network have similar dynamics. We consider two common random-graph models (Watts–Strogatz networks and Barabási–Albert networks) with different amounts of heterogeneities among the oscillators. In our computations, we find that membership in a functional community reflects the extent to which there is establishment and sustainment of locking between oscillators. We construct forest graphs that illustrate the complex ways in which the heterogeneous oscillators associate and disassociate with each other.

"Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices"

One of my papers just came out in final form. Here are some details.

Title: Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Authors: Christopher Chong, Yifan Wang, Donovan Maréchal, Efstathios G. Charalampidis, Miguel Molerón, Alejandro J. Martínez, Mason A. Porter, Panayotis G. Kevrekidis, and Chiara Daraio

Abstract: We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi–Pasta–Ulam–Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs.

"Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection"

Another of my papers just came out in final form today. Here are some details.

Title: Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection

Authors: Xinzhe Zuo and Mason A. Porter

Abstract: The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the moments of the tie strength evolve with time in several models, and we explore—both numerically and analytically—criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible–infected–recovered model of an infectious disease.