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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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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
- 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?”
- 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
- XABAB ABABY BABA
- FIRST, SECOND: ABAB
- FIRST, THIRD: BAB
- SECOND,THIRD: ABA
- REPLACE FIRST PAIR WITH XABABY
- XABABY,BABA YIELD XABABYBABA
- SS IS XABABABY
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
In general, “Greedy” will never produce a result more than twice the length of a
shortest superstring
TEACHING RESEARCH METHODS AT ASMSA
Charles Mullins
Arkansas School for Mathematics,
Science and the Arts
Hot Springs AR 71910
Mullinsc@asmsa.org
Topics
- Research Through Technology
- Junior FIRM
- Senior FIRM
RTT
- Required course for all entering juniors
- Fall semester
- Objectives in:
- Technology
- Science
- Math
- Writing
Technology objectives
- Learn to use:
- TI calculator
- GraphLink & TI-Interactive
- Office
- E-mail, Web, HTML
- Turnitin.com
Math Objectives:
- Get introduced to :
- Regressions and data modeling
- Probability
- Descriptive statistics
- Inferential statistics
Structure
- Introductory lessons & activities
- Four mini projects
- The Ideal Weight
- The Dubl Stuf Dilemma
- Pop Off
- M & Ms
Science Objectives
- Learn:
- How to design & do experiments
- How to present & model data
Writing objectives
- Learn:
- Our lab report format & style
- How to paraphrase & cite
- How to integrate data, graphs, equations, etc.
Text
- http://165.29.91.7/math/Rizzle/Final.pdf
- PDF-formatted copy of the text we wrote for RTT
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.
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
- 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
- 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
- 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
Assignments
- Critique seniors project displays and oral presentations
- Present their planned experiment to a panel of faculty & seniors
Summer work
- Ideally they should start their experiment if possible
- Minimum requirement is to be ready to start in August
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
- 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
- Science paper
- Project display for science fair
- Oral presentation Junior Academy of Science
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
- 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
- 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
