Joseph D. Johnson, a PhD candidate at Engineering Sciences and Applied Mathematics, Northwestern University, whose research is in using the dynamical systems to model social and biological phenomena, reports on Dynamics Days 2020.
Dynamics Days 2020 was held in Hartford, Connecticut, January 3-5. This conference truly showed the flexibility and power of dynamical systems, displaying variety in theory and application. Applications spanned topics such as collective behavior of swarms to fluid dynamics to mathematical biology to social media analytics.
Flavio Fenton (Georgia Institute of Technology) kicked off the conference. Fenton demonstrated WebGL code to simulate large sets of nonlinear differential equations in 2D and 3D over a web browser. This allows anyone to solve complex nonlinear differential equations on a computer, a tablet, or even a cellphone!
Those who were interested in cardiac dynamics received two great talks from Leon Glass (McGill University) and Matthew Hoffman (Rochester Institute of Technology). Glass presented on the universality of nonlinear dynamical processes in cardiac dynamics. Glass provided examples from theory, experiments, and clinical data that nonlinear processes such as paroxysmal rhythms arise in various organisms. Hoffman talked about his work on reconstructing cardiac electrical dynamics using data-assimilation methods. He combined data with numerical model simulations to estimate state variables. He also addressed the system’s parameter sensitivity when there are errors in the model or the data.
Coupled oscillators also got their time to shine. Dan Wilson (University of Tennessee Knoxville) went beyond the standard phase reduction for weakly interacting oscillators and used a novel phase-amplitude coordinate system to increase the accuracy of phase reduction. Rennie Mirollo (Boston College) made a fascinating tie between hyperbolic geometry and coupled oscillator networks. Mirollo demonstrated that the space of possible phase configurations was equivalent to a 2D disc and gave a complete description of the long-term network dynamics using the geometry of the space. Danny Abrams (Northwestern University) laid out a surprisingly intuitive theory on the development of multimodality in physical, biological, or social systems using a variant of the Kuramoto model as a testbed. He showed that for a wide class of interaction functions one only needs to compare the slopes at the zeros of the interaction function to determine the stability of a multimodal phase distribution.
As a person who spends too much time on Twitter, I enjoyed the talks on social media, social networks, and social categorization. I found Chris Danforth’s (University of Vermont) presentation captivating. He demonstrated an assortment of instruments to explore Twitter data, showing results such as people used the word “Trump” more than the word “God.” William Oakley (UCLA) talked about how decision-making processes made within a social network could lead to an inharmonious belief state if individuals within the network have to balance their own stubbornness against their desire to conform. He also proposed strategies to bring the social network to a consensus. Vicky Yang (Santa Fe Institute) gave a fascinating talk on social categorization, where she developed a dynamical systems model for the formation of two social groups based on a continuous attribute. She found an astonishing result: two groups form at the extreme ends of the spectrum and both groups deem the individuals in the middle outsiders.
Jessica Conway (Pennsylvania State University), Christopher Kulp (Lycoming College), and Subekshya Bidari (University of Colorado Boulder) gave some of my favorite talks. Conway presented her work on HIV dynamics within a patient who has stopped antiretroviral therapy (ART). She used a system of differential equations to model interactions between target cells, productively infected cells, latently infected cells, virus, and cytotoxic T lymphocytes (CTL). She found that if the viral load is small compared to the killing rate of the CTL then the viral load will remain low. Kulp spoke on his analysis of various tax systems, where he applied various tax models within the framework of an agent-based exchange game. Intriguingly, he found that redistribution via income taxes did little to change income inequality, but wealth taxes worked quite well to alleviate the inequality in the income distribution. Bidari taught us how honeybee colonies use a dance language to communicate the quality and location of foraging or nest sites in order to come to a consensus within the hive. She found that the spatial structure of the hive and the bees’ motion statistics affect the recruitment process, and hence how fast the hive comes to a consensus.
Flash and poster sessions gave an opportunity for young researchers to advertise their work. This further diversified the work presented at Dynamics Days, where topics ranged from C. elegans locomotion, gang membership dynamics, virus competition, and nonlinear correlations in financial markets. I personally enjoyed my time presenting my work on the development of sex cell size dimorphism at one of the two poster sessions, gaining valuable insight and questions from those who spent time talking to me about my research.
Dynamics Days has proven repeatedly to benefit the dynamical systems community, providing opportunities to see fresh and exciting research. This conference always has a talk for everyone and I am eager to see what comes next at Dynamics Days 2021.