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September 2020
Applied Math Talk: Variable Selection via Arbitrary Rectangle-Range Generalized Elastic Net given by Yujia Ding (CGU)
We propose a regularization and variable selection method, named arbitrary rectangle-range generalized elastic net (ARGEN). It can be applied in high dimensional sparse linear regression models. We propose an algorithm to solve ARGEN; it is an extension of multiplicative updates. Multiple simulation studies and a real-world application in the stock market show that ARGEN applies to more complicated problems, outperforms and extends the lasso, ridge, and elastic net.
Find out more »Applied Math Talk: Nonlocal Helmholz-Hodge decompositions for nonlocal operators given by Prof. Petronela Radu (University of Nebraska – Lincoln)
Nonlocal theories have emerged with powerful models and methods to analyze and predict complex phenomena. Different versions of nonlocal operators have been proposed, each with its advantages and challenges. In this talk I will give an introduction to main ideas in the nonlocality framework and present two sets of results for Helmholtz-Hodge type decompositions.
Find out more »October 2020
Applied Math Talk: Multiwavelet discontinuous Galerkin methods and automated parameters for troubled cell indication given by Professor Jennifer Ryan (Colorado School of Mines)
This talk focuses on using a multiwavelet representation of the discontinuous Galerkin (DG) approximation for trouble cell indication. The multiwavelet representation is related to the jumps in the (derivatives of) the DG approximation. We then compare this indicator with other, more established indicators as well as machine learning approaches and demonstrate that it is possible to choose the parameters for troubled cell indicators automatically and appropriately.
Find out more »Applied Math Talk: Bounded-confidence models for opinion dynamics on online social networks given by Professor Heather Zinn Brooks (HMC)
Online social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online, the content that spreads on online social networks can have important consequences on public opinion, policy, and voting. To better understand the online content spread, mathematical modeling of opinion dynamics is becoming an increasingly popular field of study. In this talk, I will introduce you to a special class of models of opinion dynamics on networks called bounded-confidence…
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