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 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

1. The Ideal Weight2. The Dubl Stuf Dilemma3. Pop Off4. 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