1 / 29

SUMMER RESEARCH: THE SUPERSTRING PROBLEM

This research focuses on finding the shortest superstring for the human genome, using the greedy algorithm. Results show that the greedy algorithm yields a superstring that is never more than twice the length of the shortest superstring.

sgaither
Download Presentation

SUMMER RESEARCH: THE SUPERSTRING PROBLEM

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SUMMER RESEARCH: THE SUPERSTRING PROBLEM Charles Mullins DIMACS Biomaths Conference April 30, 2005

  2. 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

  3. 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

  4. 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

  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

  6. Our research considered strings consisting of m zeros followed by n ones followed by p zeros: 01100 000111100 etc Key result: Greedy gives SS

  7. CONJECTURE In general, “Greedy” will never produce a result more than twice the length of a shortest superstring

  8. TEACHING RESEARCH METHODS AT ASMSA Charles Mullins Arkansas School for Mathematics, Science and the Arts Hot Springs AR 71910 Mullinsc@asmsa.org

  9. Topics • Research Through Technology • Junior FIRM • Senior FIRM

  10. RTT • Required course for all entering juniors • Fall semester • Objectives in: • Technology • Science • Math • Writing

  11. Technology objectives • Learn to use: • TI calculator • GraphLink & TI-Interactive • Office • E-mail, Web, HTML • Turnitin.com

  12. Math Objectives: • Get introduced to : • Regressions and data modeling • Probability • Descriptive statistics • Inferential statistics

  13. Structure • Introductory lessons & activities • Four mini projects • The Ideal Weight • The Dubl Stuf Dilemma • Pop Off • M & Ms

  14. Science Objectives • Learn: • How to design & do experiments • How to present & model data

  15. Writing objectives • Learn: • Our lab report format & style • How to paraphrase & cite • How to integrate data, graphs, equations, etc.

  16. Text • http://165.29.91.7/math/Rizzle/Final.pdf • PDF-formatted copy of the text we wrote for RTT

  17. 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.

  18. 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

  19. 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

  20. 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

  21. 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

  22. Assignments • Critique seniors project displays and oral presentations • Present their planned experiment to a panel of faculty & seniors

  23. Summer work • Ideally they should start their experiment if possible • Minimum requirement is to be ready to start in August

  24. 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

  25. 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

  26. End products • Science paper • Project display for science fair • Oral presentation Junior Academy of Science

  27. 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

  28. 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.

  29. 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

More Related