computational science internships: applying mathematics and
TRANSCRIPT
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/
http://www.wofford.edu/ecs/
Overview
• Computational Science
– Definition
– Recommendations
– Content areas
– Internships
– Applications
http://www.wofford.edu/ecs/
Computational Science
Mathematics
Computer Science
Physical Sciences
Biological and
http://www.wofford.edu/ecs/
Science Today
• Theory
• Experimentation
• Computation
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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)
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Content Area:Programming & Algorithms
• Examples
• Genomic Sequence Comparison
• Space
• Science of Music
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
• 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 “
Internship:Programming
http://www.wofford.edu/ecs/
Content Area: Web Assessable Databases
• UNIX
• Accessing and creating databases with SQL
• Creating web forms, HTML
• Interfacing, Perl
• Teams
http://www.wofford.edu/ecs/
• 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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Visualization Applications
• DNA and other molecules
• Movement of ocean waves
• Diffusion across membrane
• Heat diffusion
• Spread of disease
• Lorenz equations
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Internship:Scientific visualization
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Modeling and Simulation:Mushroom fairy rings
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Example: Spread of Disease
• SIR model– S - susceptibles– I - infecteds– R - recovereds– Simplifying assumptions
• Closed environment
• No deaths
http://www.wofford.edu/ecs/
Diagram of model with reservoirs and flows
http://www.wofford.edu/ecs/
Rate of change of recovereds (R) proportional to infecteds (I):
ᅠ
dR
dt= kI
ᅠ
dR
dta I
http://www.wofford.edu/ecs/
Rate of change of susceptibles proportional to SI
ᅠ
dS
dt= - cSI
ᅠ
dR
dt= kI
ᅠ
dI
dt= cSI - kI
http://www.wofford.edu/ecs/
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:
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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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
Achievements
• Supercomputing Conference
• Continuation of research
• Biomedical research at ORNL
• Vanderbilt U. Medical School
– Modeling biomechanical properties of bone
• MUSC
– Heart modeling
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
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
http://www.wofford.edu/ecs/
http://www.wofford.edu/ecs/
Internship:Scientific visualization
• Molecular Graphics Laboratory at
The Scripps Research Institute
• ”Tangible models”
– 3D models of molecules, such as
hemoglobin
http://www.wofford.edu/ecs/
• Oak Ridge National Lab
• Modeling the electrical grid – To display outage areas in large
storms for FEMA– To predict electrical customer
outages
Internship:Programming