Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridges ratchet (BBR) is one mechanism used to achieve superdiffusive molecular motion over long distances through the successive cleavage of surface-bound energy-rich substrate sites. The BBR mechanism is utilized throughout Nature: it can be found in bacteria, plants, humans, as well as non-life forms such as influenza. Motivated to understand how fundamental design principles alter BBR kinetics, we have built both computer models as well as synthetic experimental systems to understand BBR kinetics. In this talk I will present the results of our modelling work where we explore how multivalency, leg length, hub topology, landscape dimension, and landscape elasticity affect BBR kinetics. I will also present the preliminary results of our experimental work where we have created a micron-sized BBR that has achieved superdiffusive motion on a two-dimensional landscape. Our work provides insight into the mechanistic origin for the observed velocities and persistence found in both synthetic and biological (eg. Influenza and ParA/ParB) systems.

In general, the mechanisms by which walled cells specify their shapes are not fully understood. This project aims to understand the cell-shape formation during tip-cell elongation at the early developmental stage of moss. To do so, we have developed a mathematical method that decomposes cell wall “active” growth and cell wall “passive” stretching due to turgor pressure. We demonstrate that it is possible to map the active and passive physical effects using cell outline data and cell-wall marker techniques such as quantum dots. Joint work with: Luis Vidali, Giulia Galotto, Danush Chelladurai, Yaqi Deng, Chaozhen Wei, and Kamryn Spinelli.

Election dynamics are a rich complex system, and forecasting next months U.S. elections is an exciting, high-stakes problem with many sources of subjectivity and uncertainty. In this talk, we take a dynamical-systems perspective on election forecasting, with the goal of helping to shed light on the forecast process and raise questions for future work. By adapting a well-studied model from epidemiology, we show how to combine a compartmental approach with polling data to produce forecasts of presidential, senatorial, and gubernatorial elections at the state level. Our results for the last 16 years of U.S. elections are largely in agreement with those of popular analysts, and we apply our model to forecast the upcoming U.S. elections on 3 November 2020. We also use our modeling framework to explore how different methods for handling polling data and accounting for uncertainty affect forecasts. This is joint work with Samuel Chian, William He, Christopher Lee, Daniel Linder, Mason Porter, and Grzegorz Rempala.

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