SUMMER RESEARCH: THE SUPERSTRING PROBLEM

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SUMMER RESEARCH THE SUPERSTRING PROBLEM

• Charles Mullins
• DIMACS Biomaths Conference
• April 30, 2005

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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

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A SUPERSTRING CONTAINS ALL THE ORIGINAL STRINGS

• Occams razor
• Nature is efficient
• LOOK FOR SHORTEST SUPERSTRING SS!
• Greedy Algorithm proceed pairwise to get
  maximal overlap at each stage
• Greedy doesnt always give SS

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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

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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

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

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CONJECTURE

• In general, Greedy will never produce a
  result more than twice the length of a
  
• shortest superstring

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TEACHING RESEARCH METHODS AT ASMSA

• Charles Mullins
• Arkansas School for Mathematics,
• Science and the Arts
• Hot Springs AR 71910
• Mullinsc_at_asmsa.org

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Topics

• Research Through Technology
• Junior FIRM
• Senior FIRM

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RTT

• Required course for all entering juniors
• Fall semester
• Objectives in
• Technology
• Science
• Math
• Writing

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Technology objectives

• Learn to use
• TI calculator
• GraphLink TI-Interactive
• Office
• E-mail, Web, HTML
• Turnitin.com

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Math Objectives

• Get introduced to
• Regressions and data modeling
• Probability
• Descriptive statistics
• Inferential statistics

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Structure

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

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Science Objectives

• Learn
• How to design do experiments
• How to present model data

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Writing objectives

• Learn
• Our lab report format style
• How to paraphrase cite
• How to integrate data, graphs, equations, etc.

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Text

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

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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.

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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

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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

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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

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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

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Assignments

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

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Summer work

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

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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

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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

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End products

• Science paper
• Project display for science fair
• Oral presentation Junior Academy of Science

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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

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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.

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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