UC Merced Applied Mathematics
2014-2016 NSF Summer Undergraduate Research Program
(The program will not be offered in Summer 2017)
The Applied Math Summer Undergraduate Research Program at UC Merced is called the ARCHIMEDES Summer Program, and it stands for Applied ResearCH In ModEling and Data-Enabled Science. The objectives of the program are to:
- Introduce students to scientific computing to strengthen programming skills,
- Use mathematical models to solve real-world problems,
- Apply computational tools to research level problems, and
- Analyze results using data and translate into scientific context.
The ARCHIMEDES Summer Program ran for 9 weeks. In the first week, students participated in a computational "bootcamp" designed to develop fundamental computational skills, preparatory to doing research during the rest of their summer program. The students then worked intensely for the remaining eight weeks, in teams of four and with a faculty mentor, on projects with strong computational and modeling components. Students actively participated in weekly workshops and presentations to practice and improve their oral communication skills. They also produced a technical report and a poster, and presented at a public research symposium at the end of the program.
ARCHIMEDES participants received a $4,500 summer stipend, paid travel to and from UC Merced, free on-campus housing, and meal allowance for the duration of the program.
CONTACT
Program Co-Director: Prof. Roummel Marcia (rmarcia at ucmerced dot edu)
Program Co-Director: Prof. Karin Leiderman (kleiderman at ucmerced dot edu)
2016 ARCHIMEDES PROGRAM
RESEARCH TOPICS
Research Topic 1: Optimization methods for computational genomics.
Faculty Mentors: Prof. Roummel Marcia and Prof. Suzanne Sindi
Abstract: For this project we will learn optimization methods for predicting rearrangements in genomic sequences. These data-driven problems from computational genomics are very challenging because (1) the data sets are massive, (2) the data are noisy or inexact, and (3) the problem formulation is ill-posed. To address these challenges, we leverage recent work in large-scale optimization and sparse signal recovery to detect variations in genomic structural sequences by incorporating a priori information about the data. In this project, students will be introduced to statistics, numerical linear algebra, and optimization in the context of computational biology.
Research Topic 2: Modeling of biological invasions.
Faculty Mentors: Prof. Shilpa Khatri and Prof. Karin Leiderman
Abstract: Biological invasions can be described as the spatial spread of species, diseases, and genes. The presence of roads and/or rivers can significantly affect how these species spread. One specific example is the plant pathogen, Phytophthora lateralis that is fatal to the Port Orford cedar, a tree native to northern California and southern Oregon. The deadly pathogen is carried by vehicle and foot traffic along roads and trails, which increases the range of its impact. Biological invasions are often modeled with reaction-diffusion partial differential equations. In this project, students will learn how to formulate, analyze, and numerically simulate systems of these equations in the presence of interfaces that represent roads/rivers. We will explore the impact of different parameters on the spread of species and if time permits, we will model specific biological examples from the literature.
2016 ARCHIMEDES SCHOLARS
Team GenOpt
Andrew Fujikawa Cal State Sacramento |
Jonathan Sahagun Cal State Los Angeles |
Katie Sanderson Montana State University |
Melissa Spence University of California, Davis |
Team BioInvasion
Shayna Bennett Johnson State College |
Roberto Bertolini University of Rochester |
Alyssa Fortier University of Arizona |
Jessica Linton Benedictine College |
Patricia Roberts Medgar Evers College |
2015 ARCHIMEDES PROGRAM
RESEARCH TOPICS
Research Topic 1: Computational Modeling of Multiple Scattering of Light.
Faculty Mentors: Prof. Boaz Ilan and Prof. Arnold Kim
Abstract: For this project we will learn the computational methods needed to study light propagation in a multiple scattering medium. This fundamental problem has several applications including light in biological tissues for imaging and diagnosis, sunlight propagation in concentrators for solar energy harvesting, light in cloudy atmospheres for environmental remote sensing, light in the ocean for underwater wireless optical communications, and many others. There are several mathematical models describing different situations and settings. The key to research in this field lies in a comprehensive approach to study all of these different models, which requires advanced skills in linear algebra and numerical analysis. Students participating in this project will develop these skills and gain knowledge in the physics of multiple scattering theory along with its applications.
Research Topic 2: Simulating Fluid Flow Using Exponential Time Integrators.
Faculty Mentors: Prof. François Blanchette and Prof. Mayya Tokman
Abstract: Simulating and predicting behavior of large scale fluid flows, such as gravity currents (see figure on the right), have long been one of the major challenges in applied mathematics as well as in many branches of science and engineering. At first, simple ordinary differential equations models were used to describe the dynamics of fluids. These initial models later gave way to shallow-water and Navier-Stokes equations in two and three-dimensions. The complexity of these models requires high computational efficiency from the numerical methods used to solve these equations. Our ability to numerically simulate such phenomenon as gravity currents depends on the efficiency of the computational techniques employed. In this project, we will focus on exploring how the latest techniques in numerical time integration, particularly exponential methods, can further progress in simulating large scale fluid flow.
2015 ARCHIMEDES SCHOLARS
Team Fluids
Julia Afeltra Stonehill College |
David Hesslink MIT |
Alina Levine Queens College |
Theresa Morrison San Diego State University |
Team Light |
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Colton Bryant Colorado School of Mines |
Austin Sagan Rochester Institute of Technology |
Micahel Siozios College of Staten Island |
Dustin Story Northern Arizona University |
2014 ARCHIMEDES SCHOLARS
Team Coag
Ben Guth University of Tennessee, Knoxville |
Joana Perdomo Harvey Mudd College |
Kristen Kohler Binghamton University |
Sabrina Lynch Tulane University |
Team ImOp |
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Abbey Benzine Coe College |
Ben Bogard Wartburg College |
Jimmy Nguyen Wesleyan University |
Aramayis Orkusyan Fresno State |
Visiting places...
Some silliness...
This program is supported by NSF Grant DMS-1359484. Any opinions, findings and conclusions or recommendations expressed in the publications supported by this grant are those of the author(s) and do not necessarily reflect the views of the NSF.
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