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Summer Undergraduate Research Program

UC Merced Applied Mathematics
2014 NSF Summer Undergraduate Research Program
June-August, 2014

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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 Program will run for 9 weeks. In the first week, students will participate in a computational "bootcamp" designed to develop fundamental computational skills, preparatory to doing research during the rest of their summer program. The students will then work intensely for the remaining eight weeks, in teams of four and with a faculty mentor, on projects with strong computational and modeling components. Students will actively participate in weekly workshops and presentations to practice and improve their oral communication skills. They will also produce a technical report and a poster, and present at a public research symposium at the end of the program.

PROJECTS

1. Sensitivity Analysis of a Mathematical Model of Blood Coagulation. Blood coagulation is a large network of biochemical reactions that produces an enzyme necessary to clot formation and the cessation of bleeding. Mathematical models have been developed to better understand blood coagulation and to predict outcomes of perturbations to the reaction network. Assessing the predictive capability of such models is crucial if they are to be used to inform clinicians. In this project, students will first learn the biology of blood coagulation, basic theory of ODEs and methods to solve them using MATLAB, and core methodology of sensitivity analyses. They will incorporate cellular-surface binding into a current mathematical model of coagulation, perform sensitivity analysis of the model to its kinetic rate constants, and determine the predictive capability of the model. They will compare results from the mathematical model with those from other models and experiments published in biological literature. Project Mentors: Prof. Karin Leiderman and Prof. Suzanne Sindi.

2. Optimization Methods in Imaging. With the advent of cheaper cameras, large volumes of data in the form of images are generated everyday. To process such data, fast, robust, accurate, and scalable computational methods are needed. This research project will focus on optimization methods for extracting information from noisy and inexact observations from imaging. In particular, we are interested in applications where a sequence of measurements are obtained, such as videos. These problems are high-dimensional. Thus, large-scale optimization methods are needed to solve these problems. For this project, students will (1) model how the signal is projected onto the observed data, (2) solve the recovery problem using large-scale optimization algorithms, and (3) analyze the results and compare them to known data to evaluate the model and the optimization methods. This project will consider different types of approaches for optimization, such as first-order methods and matrix-free methods. Project Mentor: Prof. Roummel Marcia.

APPLICATION
Applications will be due on March 15, 2014. They will consist of the following:

  1. Application form (download here)
  2. One letter of recommendation from a faculty member (download form here)
  3. Transcript from current institution (non-official transcripts will be acceptable).

Email application forms and transcripts to archimedes at ucmerced dot edu. All applicants must a United States citizen or permanent U.S. resident.

All qualified undergraduate students are encouraged to apply to this summer program. Particular emphasis will be placed on broadening the participation of members of groups historically underrepresented in science and engineering: women, African Americans, Alaska natives, American natives, Hispanic Americans, Native Pacific Islanders, and persons with disabilities.

CONTACT
If you are interested in this program, send an email for further information:
Program Director: Prof. Roummel Marcia (rmarcia at ucmerced dot edu)
Program Co-Director: Prof. Karin Leiderman (kleiderman at ucmerced dot edu)

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.