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Mathematics Department

Applied Math Seminar

Spring 2022

All talks are from 12:00-1:00 p.m. in the Seminar Room CH351, unless otherwise specified.

  • Apr
    29
  • TBA
    Ana Maria Soane
    USNA Math
    Location: CH351
    Time: 12:00 PM
  • Apr
    21
  • Existence theory and propagation of oscillations for the system of viscoelasticity of strain-rate type
    Athanasios Tzavaras
    King Abdullah University of Science and Technology
    Location: Virtual
    Time: 12:00 PM
  • Apr
    15
  • Thou Shalt Not Throw Away Perfectly Good Data: How Using Repeated Measurements Improves Estimation of Mortality Risk in Liver Transplant Candidates
    Douglas Vanderwerken
    USNA Math
    Location: CH351
    Time: 12:00 PM

    View Abstract

    In the United States, approximately 17,000 people are waiting for a liver transplant. These patients are prioritized for transplant according to medical need, as characterized by a composite score of liver functionality called MELD. The MELD score is an integer from 6 to 40, with higher scores indicating poorer liver function and hence higher short-term mortality in the absence of transplant. Estimating the precise relationship between MELD and mortality is challenging for a number of reasons: (1) survival times are censored, (2) censoring by transplant is informative of survival time in violation of a traditional assumption, (3) data are collected as repeated measurements, and (4) very high MELD scores are rare. I introduce a fully nonparametric approach for repeated-measurements survival data that combines bootstrapping and inverse probability censoring weighted Kaplan-Meier modeling. I use it to estimate the bias-corrected 90-day without-transplant survival probability (with confidence bands) as a function of MELD score. This function has an important role to play in determining exception scores, defining the pediatric MELD score, and optimizing geographic allocation districts. This is joint work with Dave Ruth and Nick Wood.
  • Apr
    08
  • End Behaviour Of A Flutter Model.
    Abhishek Balakrishna
    UMBC Math
    Location: CH351
    Time: 12:00 PM

    View Abstract

    We will be looking at the problem of flutter in a panel placed horizontally along a subsonic flow. The system is modelled as a coupled wave-plate system. Empirical observations indicate that intrinsic panel damping stabilizes the subsonic wave-plate system to equilibria. This means that eventually, there is no panel flutter when the fluid flow is subsonic. The mathematical proof of the statement has remained open for a while. Several partial results have been previously established through regularization of the model; without doing this, classical approaches which decouple the plate and wave dynamics have fallen short. This is due to the regularity defects of the hyperbolic Neumann map. I will discuss how we may operate on the model as it appears in the engineering literature with no regularization and achieve stabilization by “microlocalizing” the wave data itself (given by the plate). This is achieved by observing that there is a compensation by the plate dynamics precisely where the regularity of the 3D wave is compromised (in the “characteristic” sector).
  • Apr
    01
  • An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence
    Evelyn Lunasin
    USNA Math
    Location: CH351
    Time: 12:00 PM

    View Abstract

    Complex nonlinear turbulent dynamical systems are ubiquitous in many areas of research. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this talk I will present an efficient continuous in time data assimilation scheme which exploits closed analytic formulae for updating the unobserved state variables. It is computationally efficient and accurate. The new data assimilation scheme is combined with a simple reduced order modeling technique that involves a cheap closure approximation and a noise inflation. In such a way, many complicated turbulent dynamical systems can satisfy the requirements of the mathematical structures for the proposed efficient data assimilation scheme. The new data assimilation scheme is then applied to the Sabra shell model, which is a conceptual model for turbulence. The goal is to recover the unobserved shell velocities across different spatial scales. It is shown that the new data assimilation scheme is skillful in capturing the nonlinear features of turbulence including the intermittency and extreme events in both the chaotic and the turbulent dynamical regimes. It is also shown that the new data assimilation scheme is more accurate and computationally cheaper than the standard ensemble Kalman filter and nudging data assimilation schemes for assimilating the Sabra shell model with partial observations.
  • Mar
    25
  • A Computationally Efficient Approach to Estimating Species Richness and Rarefaction Curve
    Location: Virtual
    Time: 12:00 PM

    View Abstract

    In ecological and educational studies, estimators of the total number of species and rarefaction curve based on empirical samples are important tools. We propose a new method to estimate both rarefaction curve and the number of species based on a ready-made numerical approach such as quadratic optimization. The key idea in developing the proposed algorithm is based on nonparametric empirical Bayes estimation incorporating an interpolated rarefaction curve through quadratic optimization with linear constraints based on g-modeling in Efron (2014). Our proposed algorithm is easily implemented and shows better performances than existing methods in terms of computational speed and accuracy. Furthermore, we provide a criterion of model selection to choose some tuning parameters in estimation procedure and the idea of confidence interval based on asymptotic theory rather than resampling method. We present some asymptotic result of our estimator to validate the efficiency of our estimator theoretically. A broad range of numerical studies including simulations and real data examples are also conducted, and the gain that it produces has been compared to existing methods.
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