ALGEBRA & DISCRETE
MATHEMATICS SEMINAR
4:00 PM, Thursday, February 2, 2012, Martin M-102
Refreshments 3:30 PM, Martin O-112
Combinatorics of matchings: from RNA to
permutations
Svetlana Poznanovikj
Georgia Tech
This talk will illustrate how understanding the combinatorics of matchings
can help us gain insight into different questions in mathematics and computational biology. The first part of the talk will address the important problem of
RNA folding. We will explain how matchings can be used to model RNA folding and analyze a recent RNA secondary structure prediction method based on
a stochastic context-free grammar. Using combinatorial analysis of this model
together with some analytic tools, we show that the distribution of many biologically significant features of RNA secondary structures is asymptotically Gaussian and we derive explicit formulas for their expectations. In the second part of
the talk, we will discuss properties of matchings that are related to the number
of inversions and cycles in permutations. The analysis of their distribution on
matchings of fixed type helps us derive refined results for permutations.
For further information, contact Matthew Macauley, macaule@clemson.edu, 656-1838, Martin O-325.
Online: http://www.math.clemson.edu/~macaule/adm-seminar/