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December 2019
Applied Math Talk: Set your parasites low (or high) given by Professor Maryann Hohn (Pomona College)
Individuals may choose to create social groups where their individual fitness and success is influenced by those around them. A group may increase an individual's success in finding food, shelter, and safety; however, if the group fails, so does the individual. In this talk, we will explore how choices of individuals influence group dynamics using both agent-based modeling and partial differential equations. In particular, we will examine individuals who live in close, collaborate groups who are susceptible to infectious diseases such as pathogens and parasites through…
Find out more »January 2020
Applied Math Talk: Statistical Mechanics of Molecular Evolution and its Role in the SELEX Protocol given by Prof. Bhaven Mistry (CMC)
Antibodies are the standard biomolecule for marking molecular structures and delivering drugs due to their specific binding capabilities. However, they are expensive to produce and their relatively large size prevents their easy traversal of bi-lipid membranes. Over the past 30 years, molecular recognition has also been achieved through the use of aptamers, short oligonucleotide sequences that fold in conformations that allow them to specifically bind to targets. These aptamers are produced rapidly and efficiently through a process known as Systematic…
Find out more »February 2020
Applied Math Talk: Robust Estimators for Monte Carlo data given by Prof. Mark Huber (CMC)
Data coming from Monte Carlo experiments is often analyzed in the same way as data from more traditional sources. The unique nature of Monte Carlo data, where it is easy to take a random number of samples, allows for estimators where the user can control the relative error of the estimate much more precisely than with classical approaches. In this talk I will discuss three such estimators useful in different problems. The first is a user-specified-relative-error (USRE) estimate for the…
Find out more »Applied Math Talk: Information Theory, Archetypal Analysis and MT Flu given by Professor Emily Stone (University of Montana-Missoula)
In this talk I will discuss a rather unique collection of tools and how they have been used to understand the spread of Influenza virus in the State of Montana. With flu counts from each county over a 10 year period some patterns emerge, which explain some vectors of the disease spread. Archetypal analysis then creates reduced dimension sets, and the dynamics of the flu spread can be understood by parameterizing SIR models with the reduced data.
Find out more »March 2020
Applied Math Talk: Approaches to modeling dispersal and swarm behavior at multiple scales given by Prof. Christopher Strickland ( The University of Tennessee, Knoxville)
Biological invasions often have outsized consequences for the invaded ecosystem and represent an interesting challenge to model mathematically. Landscape heterogeneity, non-local or time-dependent spreading mechanisms, coarse data, and air or water flow transport are but a few of the complications that can greatly affect our understanding of small organism movement – a critical component of both invasion success and the ability of native organisms to persist at a location. In this talk, I will look at dispersal and swarm behavior…
Find out more »(Cancelled!!) Applied Math Talk: Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems given by Prof. Paul Carter (University of Minnesota)
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms representing the downhill flow of water. We focus on one such model in the 'large-advection' limit, and we prove the existence of traveling planar stripe…
Find out more »April 2020
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.
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