Mullins rev

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Published on January 17, 2008

Author: Bertrando


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 Topics:  Topics Research Through Technology Junior FIRM Senior FIRM RTT:  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 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. Text:  Text 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. Scheduling:  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 Assignments:  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

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