computational science internships: applying mathematics and

Computational Science

Coursework and Internships:

Applying Mathematics and Computer Science

to Important Scientific Problems

Angela Shiflet, Ph. D.Wofford College

LaGrange CollegeOctober 22, 2009

http://www.wofford.edu/ecs/


Overview

• Computational Science

– Definition

– Recommendations

– Content areas

– Internships

– Applications


Computational Science

Mathematics

Computer Science

Physical Sciences

Biological and


Science Today

• Theory

• Experimentation

• Computation


Interdisciplinary example

• Virginia Commonwealth U. NSF REU

– Bioinformatics & Bioengineering

Summer Institute

– Center for the Study of Biological

Complexity

• Trypanosoma cruzi (T. cruzi)

– Causes Chagas’ disease

– 14 million people are affected


Interdisciplinary example

• Integrated mathematical and computational model of lifecycle– Newtonian equations, fluid dynamics

– New paradigms for understanding infectious disease process

– Novel public health strategies

• “Wet” and “dry” lab teams– Theory, experiment, computation


A SIAM Working Group Report, 2007

• Undergraduate Computational Science and Engineering Education

• http://www.siam.org/about/pdf/CSE_Report.pdf• Sponsored by SIAM Education Committee• Working Group Members

– Peter Turner (Clarkson University, Chair)– Kirk Jordan (IBM)– Linda Petzold (UC Santa Barbara)– Angela Shiflet (Wofford College)– Ignatios Vakalis (Capital University, OH)


Common Curriculum Content Components (1)

• Simulation and modeling• Programming and algorithms

– A high level language, elementary data structures, analysis

• Applied mathematics– Calculus and differential equations, linear algebra, (discrete)

dynamical systems

• Numerical methods– Errors, nonlinear equations, solving systems of linear

equations, interpolation and curve fitting, optimization, Monte Carlo, ODEs, PDEs

• Parallel programming• Scientific visualization


Common Curriculum Content Components (2)

• Application domain content

– At least one major application area of science or engineering

• Team-based projects

• Effective technical analysis and presentation

• Research or Professional Experience

– Independent research, presentation of solution

methodologies, internship


Wofford’s Emphasis in Computational Science (ECS)• One of first undergraduate programs• Requirements

– Bachelor of Science– 5 courses

• Programming• Data Structures• Calculus I• Data and Visualization• Modeling and Simulation

– Summer internship involving computation in the sciences


Content Area:Programming & Algorithms

• Examples

• Genomic Sequence Comparison

• Space

• Science of Music


Internship:Programming

• Extensible Framework for the Mathematical

Manipulation Of Music

• Mathematica

• Fullerton Foundation Community of Scholars

at Wofford

• U. OK graduate school in theoretical physics


• Jet Propulsion Laboratory

• Software for Mars Rover Operations

• NSF Graduate Research Fellowship– Computer Graphics - Columbia U. in NY

– Physics, applied math & CS– Cloth simulation

– Disney Studios

– Weta Digital, a movie special FX company in NZ• Special effects for “Lord of the Rings “



Content Area: Web Assessable Databases

• UNIX

• Accessing and creating databases with SQL

• Creating web forms, HTML

• Interfacing, Perl

• Teams


• Genetic epidemiology at Greenwood Genetic Center

• Developed Perl program to automate linkage analysis on disease genes

• Created database on diets of Honduran women

• Used SAS (Statistical Analysis System) to examine relationship between diet and birth defects

Excitement to Experience to Expertise


Excitement to Experience to Expertise

• SIAM Minisymposium on Undergrad Research • Massachusetts General Hospital/Harvard • National Institutes of Health• NIH research fellowship, then graduate school

in genetics– Finding genetic associations with obesity

• Statistical analysis• Perl programs• Database to store our genotypes• Work with many software programs

http://polaris.med.unc.edu/wiki/index.php/Image:Marie-holiday-party-2007.jpg


Content Area:Scientific Visualization

• 3D Interactive Computer Animations with all

science examples

• Programming and OpenGL

• Computer Graphics: Programming, Problem

Solving, and Visual Communication by Steve

Cunningham, Prentice Hall, 2007


Visualization Applications

• DNA and other molecules

• Movement of ocean waves

• Diffusion across membrane

• Heat diffusion

• Spread of disease

• Lorenz equations


Lorenz Equations

• Modeling of convection rolls in atmosphere

ﾠ

dx

dt= - s x +s y

dy

dt= - x z + r x - y

cz

dt= x y - b z

Figures from http://en.wikipedia.org/wiki/Lorenz_attractorProgram from Steve Cunningham, revised by Angela Shiflet


Internship:Scientific visualization


Internship:Medical Imaging

• Wadsworth Center, NY Dept. of Health, HHMI

• 3D Computer Image Processing of Ribosome

– Structure

– Mechanism of protein synthesis

• Nat’l Center for Biotechnology in Madrid

• CSE talk

• NIH, medical school


Content Area:Modeling and Simulation

• System dynamics models • Global view

• Differential/difference equations

• Cellular automata simulations• Local view

• Stochastic

• Mathematica, Maple, MATLAB, Excel, programming languages


Modeling and Simulation:Cellular Automata Applications• Brownian motion• Movement of ants• Spread of fire• HIV in body• Foraging behavior• Spread of disease• Fish schooling• Pit vipers and heat diffusion• Snow flakes - solidification


Modeling and Simulation:Mushroom fairy rings


Modeling and Simulation:System Dynamics Tools

• Dynamic systems usually

– Very complex

– Many components

– Involved relationships

• Tool can lower barriers and increase understanding of mathematical concepts and application

– STELLA, Vensim, Berkeley Madonna


Modeling and Simulation:System Dynamics Applications

• Drug dosage• Scuba diving - ideal gas laws• Enzyme kinetics• Defibrillators - electrical circuits• Cardiovascular system• Global warming• Carbohydrate metabolism• Predator-prey and competition• Radioactive chains• Malaria and other diseases


Example: Spread of Disease

• SIR model– S - susceptibles– I - infecteds– R - recovereds– Simplifying assumptions

• Closed environment

• No deaths


Diagram of model with reservoirs and flows


Rate of change of recovereds (R) proportional to infecteds (I):

ﾠ

dR

dt= kI

ﾠ

dR

dta I


Rate of change of susceptibles proportional to SI

ﾠ

dS

dt= - cSI

ﾠ

dR

dt= kI

ﾠ

dI

dt= cSI - kI


Typical graph

• Transmission constant = 0.00218• Recovery rate = 0.5

3:02 PM Sat, Mar 18, 2006

SIR Populations

Page 10.00 3.50 7.00 10.50 14.00

Days

1:

1:

1:

2:

2:

2:

3:

3:

3:

0

381

762

1: susceptibles 2: infecteds 3: recovereds

1

1

1

12

2

2

2

3

3

3

3


Internship: HIV

• Los Alamos National Laboratory• Dr. Alan Perelson, Laboratory

Fellow with Theoretical Biology and Biophysics Develop– Scientists “with interdisciplinary skills

in computation, modeling, and statistics”

– Model changed view of HIV– Combination drug therapy


Internship

• Oak Ridge National Laboratory, Research Alliance for Math & Science

• Computational model of biochemical pathways

• Differential equations with only one semester of calculus and computational science


Achievements

• Supercomputing Conference

• Continuation of research

• Biomedical research at ORNL

• Vanderbilt U. Medical School

– Modeling biomechanical properties of bone

• MUSC

– Heart modeling


Textbook for Modeling and Simulation

• Introduction to Computational Science:

Modeling and Simulation for the Sciences

– Angela Shiflet and George Shiflet

– Princeton University Press, 2006

• Files & tutorials on website in

– STELLA, Vensim, Madonna

– Maple, Mathematica, MATLAB

– Python, Excel


Undergraduate computational science programs with internships can help fill critical need

• Computers – fast & cheap enough

• Networks– sophisticated enough

• Internet – pervasive and friendly enough

• Scientific visualization– mature enough

• Computational tools– Useful, yet simple, enough


The sky is not the limit

NASA / JPL-Caltech / Univ. of Ariz.

• JPL - Near Asteroid Team• LA, database, computation

– Found asteroid

• Ph.D. in Earth & Planetary Sciences– Rate of transfer of light through Martian atmosphere– Simulations– Numerical solutions to DEs

• Johns Hopkins U. Applied Physics Lab – Compact Reconnaissance Imaging Spectrometer for Mars

(CRISM)– Water on Mars


How did you get interested in space exploration?

In 1997 I had a summer undergraduate fellowship at JPL - this just happed to be the summer when Mars Pathfinder landed. It was an incredibly exciting time to be at the lab and it sparked my interest in planetary exploration. I interned at JPL the following summer as well - more than any other experience it was those summer internships that pointed me toward a career in planetary science.http://crism.jhuapl.edu/team/profiles/SeelosF.php


Internship:Scientific visualization

• Molecular Graphics Laboratory at

The Scripps Research Institute

• ”Tangible models”

– 3D models of molecules, such as

hemoglobin


• Oak Ridge National Lab

• Modeling the electrical grid – To display outage areas in large

storms for FEMA– To predict electrical customer

outages


computational science internships: applying mathematics and

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