MthSc 985, Fall 2011
MthSc 985, Fall 2011
"Mathematics is biology's next microscope, only better; Biology is
mathematics' next physics, only better." --Joel E. Cohen
About the class
Finding good research problems is a challenge, even for the most
experienced mathematicians. The course represents an introduction to a
new active research area in the theory of RNA pseudoknot structures,
in a non-traditional class setting. The author of our book, Christian
Reidys, pioneered this subfield within the last decade and has carved
a niche. In the process, he was honored as a Chang Jiang Scholar, the
Chinese national research prize in mathematics. Reidys has written
over fifty research articles on this topic with his collaborators
(including 7 PhD students) at the Center for Combinatorics, at Nankai
University. Reidys has written a book on this research, aimed at
researchers and graduates students who are interested in learning
about computational biology, RNA structures, and mathematics. The goal
of this class is to learn about this new and exciting field.
The content of this research area is truly transdisplinary, and draws
from all five subfaculty research areas in the mathematical science
department at Clemson. That said, no one (instructor included)
will be fully prepared in terms of having a solid grasp on all of the
prerequisites. However, the unique aspect is that the Clemson
graduates students, who are required to take multiple courses in all
five subfaculty areas, will have a more diverse and well-rounded
background than any of the Clemson faculty! Examples of how various
mathematical aspects of this research fall into the five subfaculty
areas is given below:
Algebra & Discrete Math: Enumerative combinatorics,
graph theory, group actions and Weyl groups.
Analysis: Singularity analysis, differential
equations for generating functions.
Computation: Algorithm design, thermodynamic models for RNA
pseudoknot structures.
Operations Research: Maximum weighted matching algorithms,
dynamic programming.
Probability & Statistics Branching processes,
central limit theorems for arcs in k-noncrossing structures.
We will take advantage of the diversity of the mathematical background
and strengths of the students taking this class. This course is not
intended to be one faculty member teaching eleven graduate students,
but rather, a dozen mathematicians with various backgrounds coming
together to learn a new area of research. As with any young
field, there are surely many unexplored areas, loose ends, and good
future research problems that we can discover, and one of our goals is
to find and propose these problems. In this class we will write a
self-contained research proposal as a final project, and give a
series of short presentations about what we've been studying and our
new ideas for future research. Everyone will contribute by either
writing a section in the proposal, or giving a presentation. These
presentations will be given in a research symposium that we
hold during our 2 1/2 hour final exam period. We will invite other
graduate students and faculty members from our department, and outside
our department, to learn about what we've been doing all semester. In
addition, there will be a few in-class quizzes and (reasonable)
homework assignments, because at this point in our careers, we all
understand that it is simply not possible to truly learn mathematics
by just watching and not doing.
This course is suitable for students who have a basic foundation at
the undergraduate level in abstract algebra, complex analysis,
differential equations, and probability theory (though a deficiency in
one of these is not a problem). After successfully completing this
course, a student will have knowledge of how discrete mathematical
techniques have been applied to the field of biology, the challenges
that still exist, and areas of active research. Students are
encouraged to pursue any research problems they find interesting as an
ongoing project after the semester ends.
Resources
People involved in combinatorics of DNA/RNA
PhD listed iff it is not in mathematics, applied math,
or mathematical sciences.
- Peter
Clote, Boston College (Biology, CS. Formerly Math/CS.)
- Jennifer R. Galovich
, St. John's U. and College of St. Benedict
(Math). Phylogenetics, combinatorics of RNA.
- Daniela
Genova, U. North Florida (Math). Formal languages and DNA
sequences.
- Christine Heitsch, Georgia Tech (Math)
- Debra
Knisley, Eastern Tennessee State (Math/stats)
- Asamoah Nkwanta, Morgan State (Math. Sci. / CS)
- Svetlana Poznanovik, Clemson (Math. Sci.)
- Christian Reidys, U. Southern Denmark
(Math/CS)
- Peter Stadler, U. Leipzig (Bioinformatics)
- Michael Waterman, U. Southern California (Bio Sci,
Math, CS. PhD Stats)
-
Michael Zuker, Rensselaer Polytechnic Institute (Math)
Literature on the combinatorics of RNA
People who work on new & novel aspects of discrete
mathematical biology
PhD listed iff it is not in mathematics, applied math,
or mathematical sciences.
- Réka
Albert, Penn State (Physics). Biological physics and
network modeling.
- Edward Allen
, Wake Forest (Math). Combinatorics. Biological signaling
networks from omics data.
- Elizabeth S. Allman, U. Alaska, Fairbanks
(Math/stats). Algebraic statistics, phylogenetics.
- David
Anderson, Wisconsin (Math). Biochemical
reaction networks.
- Peter Clote, Boston College (Biology,
CS. Formerly Math/CS). Combinatorics of RNA.
- Margaret Cozzens, Rutgers (DIMACS). Graph theory
and biology.
- Elena
Dimitrova, Clemson (Math. Sci.). Algebraic and systems
biology.
- Mathias Drton, U. Washington (Statistics. PhD
Stats). Algebraic statistics.
- Jo Ellis-Monaghan, Saint Michael's College
(Math). Graph theory and biology.
- Andrew Francis, U. Western Sidney
(Math). Algebraic biology, evolutionary processes.
- Jennifer R. Galovich
, St. John's U. and College of St. Benedict
(Math). Phylogenetics, combinatorics of RNA.
- Luis
Garcia-Puente, Sam Houston State U. (Math/stats). Algebraic and
computational biology.
- Daniela
Genova, U. North Florida (Math). Formal languages and DNA
sequences.
- David Haws, IBM Genomics Lab.
Phylogenetics and algebraic statistics.
- Monika Heiner, Brandenburg Technical U.,
Cottbus (CS. PhD CS). Petri nets
- Christine Heitsch, Georgia Tech (Math.)
- Franziska Hinkelmann, Ohio State (Mathematics
Biosciences Institute) Algebraic and systems
biology.
- Terrell Hodge, Western
Michigan (Math). Phylogenetics, metabolic pathways
- Valerie
Hower, U. Miami (Math). Computational biology.
- Abdul
Jarrah, American University of Sharjah (Math). Algebraic
and computational biology.
- Natasha Jonoska, U. South Florida
(Math/stats). Biomolecular computations.
- John Jungck, U. Delaware (Interdisciplinary Science
Instruction, PhD biology). Mathematical molecular evolution.
- Winfried
Just, Ohio U. (Math). Systems biology, dynamical
systems, neuronal networks.
- Debra
Knisley, Eastern Tennessee State
(Math/stats). Combinatorics of RNA.
- Jeff
Knisley, Eastern Tennessee State
(Math/stats). Computational biology.
- Reinhard Laubenbacher, University of Connecticut (Center for Quantitative Medicine). Algebraic biology, cancer systems
biology.
- Matthew Macauley, Clemson
(Math. Sci.). Discrete dynamical systems, Boolean
networks.
- Henning S. Mortveit, Virginia Tech (Virginia
Bioinformatics Institute). Discrete dynamical
systems.
- Asamoah Nkwanta, Morgan State (Math. Sci. /
CS). Combinatorics of RNA.
- Megan
Owen, Waterloo. Phylogenetic trees and
networks.
- Lior
Pachter, Berkeley (Math, Molecular Biology, EE&CE.). Algebraic
statistics, computational biology.
- Sonja
Petrovic, Illinois Instutute of Technology (Applied mathematics). Algebraic
statistics.
- Svetlana Poznanovik, Clemson
(Math. Sci.). Combinatorics of RNA.
- Christian Reidys, U. Southern Denmark
(Math/CS). Combinatorics of RNA.
- John
Rhodes, U. Alaska, Fairbanks (Math/stats). Algebraic statistics,
phylogenetics.
- Manda
Riehl, U. Wisconsin, Eau Claire (Math). Combinatorics of genome
mutations.
- Raina Robeva, Sweet Briar College. Systems
biology.
- Joseph Rusinko, Winthrop (Math). Algebraic
geometry and phylogenetics.
- Anne
Shiu, Texas A & M (Math). Biochemical reaction networks,
genomics, algebraic statistics.
- Ilya Shmulevich, U. Washington. (Institute for Systems
Biology. PhD EE). Boolean networks.
- Peter Stadler, U. Leipzig
(Bioinformatics). Combinatorics of RNA.
- Brandilyn Stigler, SMU (Math). Algebraic and
computational biology.
- Bernd
Sturmfels, Berkeley (Math, Statistics, CS). Algebraic statistics,
computational biology.
- Seth
Sullivant, NC State (Math). Algebraic statistics.
- Jeremy Sumner, U. Tasmania (Math). Group
theory and phylogenetics.
- Glenn Tesler, UCSD (Math). Bioinformatics, genome assembly.
- Alan Veliz-Cuba, Houston (Biochemistry and
Cell Biology).
Algebraic and systems biology.
- Michael Waterman, U. Southern California (Bio Sci,
Math, CS. PhD Stats). Combinatorics of RNA.
- Ruriko Yoshida,
U. Kentucky (Statistics). Algebraic statistics, phylogenetics.
- Mingfu Zhu, Duke (Center for Human Genome
Variation). Computational genomics.
- Michael Zuker, Rensselaer Polytechnic Institute
(Math). Combinatorics of RNA.
Places