Zoom link: uiowa.zoom.us/j/97719726447?pwd=EFWXnhfXYxIOp1TPe8kzk6ka7N64cN.1
Meeting ID: 977 1972 6447
Passcode: 687960
Abstract: In the study of dynamical systems, one comes across the Lyapunov Exponent, a quantity that characterizes the exponential rate of separation of infinitesimally close trajectories. One of the interesting applications of this is in the study of the discrete Schrodinger Equation with random potential function. In this case, the Lyapunov exponent holds information about the exponential decay of the fundamental solution of the Schrodinger Equation, with it either being positive or zero. Any zero of the Lyapunov Exponent is called critical energy. In 1999, Germinet and De Bièvre proved that if the random potential has Bernoulli random variables, and the random variables repeat every two consecutive nodes, then there exist critical energies and they compute them. We discuss how to extend this result to any number of consecutive repetitions and compute the roots explicitly.
Abstract:
Abstract: MUC5B is a major component of mucus in the human airway and plays a significant role in removing pathogens and debris out of the lungs. However, a genetic variant in the MUC5B gene is enriched in a rare disease called idiopathic pulmonary fibrosis (IPF) which led to its discovery. It is still unknown why the variant is enriched in IPF. Interestingly however, while IPF remains rare even in those with the genetic variant, the variant is common in the northwestern region of the globe (about ~1/5 people have at least one variant). Why is this variant so common? Could it have a beneficial effect? In this talk, we use survival analysis techniques with data from the All of Us database to show that the MUC5B variant is protective against COVID-19 hospitalization, perhaps suggesting some protective effect against viral respiratory pathogens. Further results will suggest a trend toward a protective effect against all-cause mortality.
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