Markov Chains and Molecular Evolution
My dissertation: Substitution Markov chains with applications to molecular evolution.
Working SeminarInformation regarding the working seminar "Molecular Evolution" that I hosted during the Spring semester, 2011 can be found at this website.
Research InterestsMy research interests are twofold, I am interested in:
1. Symbolic dynamics in general and substitution dynamical systems in particular.
2. Applying tools from symbolic dynamics to study molecular evolution, particularly alignment-free analysis of DNA sequences.
Preprints and Papers
- Topological Entropy of DNA Sequences. This is a preprint version of the paper that was published in Bioinformatics on February 4, 2011. doi:10.1093/bioinformatics/btr077
Romanian translation of the abstract (by Alexander Ovsov Web Geek Science)
- Random Substitution-Insertion-Deletion (RSID) Model of Molecular Evolution with Alignment-free Parameter Estimation. This is a preprint explaining one of the applications of my thesis.
- Topological Pressure and Coding Sequence Density Estimation in the Human Genome. This paper generalizes topological entropy via topological pressure and elucidates many applications to genome analysis. Namely, topological pressure can be used to estimate coding sequence density, differentiate between synonymous codons, and (via equilibrium measures) distinguish between shorts reads of coding and non-coding DNA.
Talks and Posters
Here are a few talks that I have given and posters I have presented
- Random Substitutions poster presented at the International Conference on Random Dynamical Systems at the Chern Institute of Mathematics, Nankai University, Tianjin, China, June 8-12, 2009.
- The Poster advertising the Summer School on Dynamical Systems, Mathematisches Institut, Georg-August-Universität Göttingen, July 12-26, 2009 at which I led a problem session and gave a talk entitled "Randomizations of Deterministic Substitutions."
- The presentation I gave at Penn State on February 9, 2010 in fulfillment of my Ph.D comprehensive examination. (linked to after I submit my thesis)
- Random Substitutions and Martin Boundaries Part 1, part one of a series of talks given at the Penn State seminar on probability and its applications, March 26, 2010.
- Random Substitutions and Martin Boundaries Part 2: Applications to Molecular Evolution, part two of a series of talks given at the Penn State seminar on probability and its applications, April 2, 2010.
- Topological Entropy slides to a seminar I gave on January 21, 2011. Note that this is a PDF version and so does not include the transitions (and some images overlap).
- Topological Pressure slides to a seminar I gave in Summer, 2011. Note that this is a PDF version and so does not include the transitions (and some images overlap).