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ARCHIMEDES Summer REU Program for Undergraduates

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:

  1. Introduce students to scientific computing to strengthen programming skills,
  2. Use mathematical models to solve real-world problems,
  3. Apply computational tools to research level problems, and
  4. 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.


Program Co-Director: Prof. Roummel Marcia (rmarcia at ucmerced dot edu)
Program Co-Director: Prof. Karin Leiderman (kleiderman at ucmerced dot edu)



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. 



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



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.


Team Fluids

Julia Afeltra

Stonehill College

David Hesslink


Alina Levine

Queens College

Theresa Morrison

San Diego State University

Team Light

Colton Bryant

Colorado School of Mines

Austin Sagan

Rochester Institute of Technology

Micahel Siozios

College of Staten Island

Dustin Story

Northern Arizona University


Team Coag

Ben Guth

University of Tennessee, Knoxville

Joana Perdomo

Harvey Mudd College

Kristen Kohler

Binghamton University

Sabrina Lynch

Tulane University

Team ImOp

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.