Transcript Researching the Superstring Problem

SUMMER RESEARCH: THE
SUPERSTRING PROBLEM
Charles Mullins
DIMACS Biomaths Conference
April 30, 2005
THE SUPERSTRING
PROBLEM
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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
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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?”
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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
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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
[email protected]
Topics
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Research Through Technology
Junior FIRM
Senior FIRM
RTT
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Required course for all entering juniors
Fall semester
Objectives in:
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Technology
Science
Math
Writing
Technology objectives
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Learn to use:
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TI calculator
GraphLink & TI-Interactive
Office
E-mail, Web, HTML
Turnitin.com
Math Objectives:
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Get introduced to :
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Regressions and data modeling
Probability
Descriptive statistics
Inferential statistics
Structure
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Introductory lessons & activities
Four mini projects
1.
2.
3.
4.
The Ideal Weight
The Dubl Stuf Dilemma
Pop Off
M & Ms
Science Objectives
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Learn:
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How to design & do experiments
How to present & model data
Writing objectives
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Learn:
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Our lab report format & style
How to paraphrase & cite
How to integrate data, graphs, equations,
etc.
Text
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http://165.29.91.7/math/Rizzle/Final.pdf
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PDF-formatted copy of the text we
wrote for RTT
Scheduling
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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
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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
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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
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Students interview w/ chosen faculty to:
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Compete for a faculty-chosen problem
Sell their idea to a mentor
Goals:
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Match each junior w/ mentor by end of Jan.
Distribute juniors, 5 per teacher
Assignments
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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
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Critique seniors project displays and
oral presentations
Present their planned experiment to a
panel of faculty & seniors
Summer work
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Ideally they should start their
experiment if possible
Minimum requirement is to be ready to
start in August
Senior FIRM
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More of the same
Continue to study background
Refine method
Collect data, obtain results, & draw a
conclusion
Early Dec. deadline for preliminary
results
Cooperation
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All writing assignments submitted to
mentor and in composition class
Graded by differing criteria:
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Mentor looks for quality science
Comp. teacher looks at writing
Math teachers help w/ statistics
End products
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Science paper
Project display for science fair
Oral presentation Junior Academy of
Science
Benefits
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Students leave school:
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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
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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
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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