Tales from the ArXiv: Everybody Loves Coupled Oscillators (and the Michigan Rag)

If this were my study and I were giving a talk about it, Michigan J. Frog would surely make an appearance.

New on arXiv: "Interaction Mechanisms Quantified from Dynamical Features of Frog Choruses" (by Kaiichiro Ota, Ikkyu Aihara, Toshio Aoyagi): https://t.co/TUWa7wbXwB

[a phase-oscillator model of interactions underlying the choruses of male Japanese tree frogs]

— DynamicalSystemsSIAM (@DynamicsSIAM) July 29, 2019

The Mathematical Biosciences Institute (MBI) Refrigerator is Tweeting Again

It's baaaaaack: the MBI refrigerator is up and tweeting again.

What Happens in San José (Costa Rica) Stays in San José (Costa Rica)

I am heading off to Costa Rica for a visit related to an epidemiology project related to combatting Dengue Fever, Zika, and Chikungunya using mathematical modeling and network analysis.

Opinion: "Are Theoretical Results 'Results'?"

I agree strongly with Ray Goldstein: YES!!!!!!

Moreover: Hell yes!

This is a major issue for interdisciplinary students and postdocs (and more senior scholars), and this is a very helpful paper for them to read as they navigate these waters. I also really like the fact that Ray included two different versions of a 'Results' section in his opinion article.

This guy knows how to write an abstract https://t.co/D8tWZi7VCn pic.twitter.com/980OFvCv3U

— Adam J Calhoun (@neuroecology) July 23, 2018

A Harsh Review of Lotka's Work in Mathematical Biology

Wow!

This review of work by , who was famous for his work in population dynamics, is both harsh and astounding.

Mathematic biology, alternative perpsective pic.twitter.com/HdskKTFazX

— Hong Qin (@hongqin) May 17, 2017

(Tip of the cap to Kit Yates.)

"A Predator–2 Prey Fast–Slow Dynamical System for Rapid Predator Evolution"

One of my papers has now been posted in final form. (A second one appeared online today, but it joins a long list of papers that are still awaiting their coordinates. I will blog about those papers when they have those coordinates.)

Anyway, let's talk about the paper that does have its coordinates. It's about plankton modeling, and here are the details.

Title: A Predator–2 Prey Fast–Slow Dynamical System for Rapid Predator Evolution

Authors: So a H. Piltz, Frits Veerman, Philip K. Maini, and Mason A. Porter

Abstract: We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast–3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator's diet choice. The two extremes at which the predator's diet is composed solely of one prey correspond to two branches of the three-branch critical manifold of the fast–slow system. By calculating the points at which there is a fast transition between these two feeding choices (i.e., branches of the critical manifold), we prove that the system has a two-parameter family of periodic orbits for su ciently large separation of the time scales between the evolutionary and ecological dynamics. Using numerical simulations, we show that these periodic orbits exist, and that their phase di erence and oscillation patterns persist, when ecological and evolutionary interactions occur on comparable time scales. Our model also exhibits periodic orbits that agree qualitatively with oscillation patterns observed in experimental studies of
the coupling between rapid evolution and ecological interactions.

Is A Chicken a Dirac Limit of a Dinosaur?

This paper has a lovely line in its concluding section: "In such a cartoon description, a chicken is a Dirac limit of a tyrannosaur, in which many of its genetic parameters tend to zero."

(Tip of the cap to Lior Pachter.)

"Null Models for Community Detection in Spatially Embedded, Temporal Networks"

Another one of my papers finally got its volume, issue, and page numbers last week. (It came out in advanced access in November 2015.) I finally got my own copy of the document today, so here are some details.

Title: Null Models for Community Detection in Spatially Embedded, Temporal Networks

Authors: Marta Sarzynska, Elizabeth A. Leicht, Gerardo Chowell, and Mason A. Porter

Abstract: In the study of networks, it is often insightful to use algorithms to determine mesoscale features such as 'community structure', in which densely connected sets of nodes constitute 'communities' that have sparse connections to other communities. The most popular way of detecting communities algorithmically is to maximize the quality function known as modularity. When maximizing modularity, one compares the actual connections in a (static or time-dependent) network to the connections obtained from a random-graph ensemble that acts as a null model. The communities are then the sets of nodes that are connected to each other densely relative to what is expected from the null model. Clearly, the process of community detection depends fundamentally on the choice of the null model, so it is important to develop and analyse novel null models that take into account appropriate features of the system under study. In this paper, we investigate the effects of using null models that incorporate spatial information, and we propose a novel null model based on the radiation model of population spread. We also develop novel synthetic spatial benchmark networks in which the connections between entities are based on the distance or flux between nodes, and we compare the performance of static and time-dependent versions of the radiation null model to the standard ('Newman–Girvan') null model for modularity optimization and to a recently proposed gravity null model. In our comparisons, we use both the above synthetic benchmarks and time-dependent correlation networks that we construct using countrywide dengue fever incidence data for Peru. Our findings illustrate the need to use appropriate generative models for the development of spatial null models for community detection.

Limit-Cycle-Oscillator Models of Bipolar Disorder: Revisited

Years ago, Steve Wirkus and I coauthored (with several undergraduate students) a paper that first introduced the idea of using limit-cycle oscillators to model bipolar patients. Our model was a toy model, but years later several of my colleagues at Oxford have been doing amazing things from a more data-centric perspective. Their latest paper is especially exciting for me. It does what we dreamed about and speculated about 12 years ago in our paper: taking the basic idea of a limit-cycle oscillator and combining it with clinical data in a realistic way. (The authors of this work understandably also incorporate noise into their model.)

Quoting the last few lines of our conclusions: "In this respect, we view our work as a first step in developing mathematical models of the mood swings of bipolar individuals. Our intent is to provide a mathematical framework that ultimately leads to the development of more detailed models of bipolar disorder that incorporate clinical data. With this work, we hope to motivate the collection of time-series data from clinical trials that will lead to refinements of our model that incorporate such data. In our view, dynamical systems theory and mathematical modeling in general can lead to important advancements in the understanding of bipolar disorder."

(Tip of the cap to Society for Industrial and Applied Mathematics, who shared a popular account of the work on Facebook.)

Official Congratulations to Drs. Sofia Piltz and Marta Sarzynska!

My doctoral students Sofia Piltz (co-supervised with Philip Maini), who started a postdoc in ecology at DTU in June 2014, and Marta Sarzynska, who will be working at Bain & Company starting next month, both have gotten the revised versions of their doctoral theses approved in final form. Thus, they are now both officially done! Sofia's thesis is called "Models for Adaptive Feeding and Population Dynamics in Plankton", and some of her thesis work (with a couple more papers on the way) was published in SIADS. Marta's thesis is about "Spatial Community Structure and Epidemics", and you can read about some of it in this paper (whose sequel is on the way).