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SUMMER RESEARCH: THE SUPERSTRING PROBLEM . Charles Mullins DIMACS Biomaths Conference April 30, 2005. THE SUPERSTRING PROBLEM. Human genome consists of billions of bases: A,C,G,T Current technology can only sequence “short” strings from 500-1000 bases

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summer research the superstring problem

SUMMER RESEARCH: THE SUPERSTRING PROBLEM

Charles Mullins

DIMACS Biomaths Conference

April 30, 2005

the superstring problem
THE SUPERSTRING PROBLEM
  • Human genome consists of billions of bases: A,C,G,T
  • Current technology can only sequence “short” strings from 500-1000 bases
  • Genome is cut into smaller strings that are sequenced
  • How to recover the original superstring
a superstring contains all the original strings
A SUPERSTRING CONTAINS ALL THE ORIGINAL STRINGS
  • Occam’s razor
  • Nature is efficient
  • LOOK FOR SHORTEST SUPERSTRING SS!
  • Greedy Algorithm: proceed pairwise to get maximal overlap at each “stage”
  • Greedy doesn’t always give SS
how good is greedy
HOW GOOD IS “GREEDY?”
  • Early results proved resulting SS was never worse than 3 times as long
  • This factor was slowly reduced by others
  • Our mentor Elizabeth “Z” Sweedyk obtained a factor of 2.5
example of greedy
EXAMPLE OF GREEDY
  • XABAB ABABY BABA
  • FIRST, SECOND: ABAB
  • FIRST, THIRD: BAB
  • SECOND,THIRD: ABA
  • REPLACE FIRST PAIR WITH XABABY
  • XABABY,BABA YIELD XABABYBABA
  • SS IS XABABABY
slide6
Our research considered strings consisting of m zeros followed by n ones followed by p zeros:

01100

000111100

etc

Key result: Greedy gives SS

conjecture
CONJECTURE

In general, “Greedy” will never produce a result more than twice the length of a

shortest superstring

teaching research methods at asmsa
TEACHING RESEARCH METHODS AT ASMSA

Charles Mullins

Arkansas School for Mathematics,

Science and the Arts

Hot Springs AR 71910

Mullinsc@asmsa.org

topics
Topics
  • Research Through Technology
  • Junior FIRM
  • Senior FIRM
slide10
RTT
  • Required course for all entering juniors
  • Fall semester
  • Objectives in:
    • Technology
    • Science
    • Math
    • Writing
technology objectives
Technology objectives
  • Learn to use:
    • TI calculator
    • GraphLink & TI-Interactive
    • Office
    • E-mail, Web, HTML
    • Turnitin.com
math objectives
Math Objectives:
  • Get introduced to :
    • Regressions and data modeling
    • Probability
    • Descriptive statistics
    • Inferential statistics
structure
Structure
  • Introductory lessons & activities
  • Four mini projects
    • The Ideal Weight
    • The Dubl Stuf Dilemma
    • Pop Off
    • M & Ms
science objectives
Science Objectives
  • Learn:
    • How to design & do experiments
    • How to present & model data
writing objectives
Writing objectives
  • Learn:
    • Our lab report format & style
    • How to paraphrase & cite
    • How to integrate data, graphs, equations, etc.
slide16
Text
  • http://165.29.91.7/math/Rizzle/Final.pdf
  • PDF-formatted copy of the text we wrote for RTT
scheduling
Scheduling
  • All our classes meet 3 times per week
  • Monday all 7 classes for 55 mins
  • Tuesday periods 1 - 4 for 75 mins
  • Wed. periods 5 - 7 for 75 mins.
  • Thur & Fri are repeats but for 90 mins.
scheduling1
Scheduling
  • Gives us Tues. & Wed. afternoon w/o classes
  • Tuesday for Junior FIRM
  • Wednesday for senior FIRM
  • 2 hour blocks to work with our students on their projects
junior firm
Junior FIRM
  • Prelude during November
  • Faculty post database of problem statements and interest areas
  • Students review database
  • Choose faculty ideas they like
  • Formulate their own that overlaps w/ faculty interest
project matching
Project matching
  • Students interview w/ chosen faculty to:
    • Compete for a faculty-chosen problem
    • Sell their idea to a mentor
  • Goals:
    • Match each junior w/ mentor by end of Jan.
    • Distribute juniors, 5 per teacher
assignments
Assignments
  • Be ready to start experiment on 1 June
  • Formulate problem statement & hypothesis (design goal)
  • Collect sources & start bibliography
  • Study background science
  • Start thinking about required materials
  • Plan experimental techniques
assignments1
Assignments
  • Critique seniors project displays and oral presentations
  • Present their planned experiment to a panel of faculty & seniors
summer work
Summer work
  • Ideally they should start their experiment if possible
  • Minimum requirement is to be ready to start in August
senior firm
Senior FIRM
  • More of the same
  • Continue to study background
  • Refine method
  • Collect data, obtain results, & draw a conclusion
  • Early Dec. deadline for preliminary results
cooperation
Cooperation
  • All writing assignments submitted to mentor and in composition class
  • Graded by differing criteria:
    • Mentor looks for quality science
    • Comp. teacher looks at writing
  • Math teachers help w/ statistics
end products
End products
  • Science paper
  • Project display for science fair
  • Oral presentation Junior Academy of Science
benefits
Benefits
  • Students leave school:
    • with lab skills
    • knowing how to write lab reports
    • Knowing how to present results
  • Students do well in state and international science fairs
science fair
Science fair
  • We have enough students to have our own ISEF-affiliated regional fair
  • Must have 50 students
  • $500 affiliation fee
  • Must send at least one finalist and adult to International fair.
acknowledgements
ACKNOWLEDGEMENTS
  • The presentation on implementing research at ASMSA was first given at the NCSSSMST Expedition 2005 conference in St. Louis, March 9-12, 2005, by my colleagues, Dr. Brian Monson, Dept of Science Chair, and Bruce Turkal, Dept of Mathematics