### Counting labeled transitions in continuous-time Markov models of evolution

- J. Math. Biol
, 2008

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### Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution

- Annals of Applied Statistics
, 2009

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### Exonic remnants of whole-genome duplication reveal cis-regulatory function

, 2009

"... of coding exons ..."

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### Summary statistics for endpoint-conditioned continuous-time Markov chains

- Journal of Applied Probability
, 2011

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### *) Corresponding author:

"... 2.5), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. ..."

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2.5), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### COMPUTATIONAL MODELS OF FUNCTION AND EVOLUTION OF CIS-REGULATORY SEQUENCES BY

"... Gene expression is controlled by regulatory DNA sequences, often called cis-regulatory modules or CRMs in higher organisms. Even though complete genomes are available in many species, a catalog of CRMs is far from complete. Meanwhile, how basic building blocks of CRMs, called transcription factor bi ..."

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Gene expression is controlled by regulatory DNA sequences, often called cis-regulatory modules or CRMs in higher organisms. Even though complete genomes are available in many species, a catalog of CRMs is far from complete. Meanwhile, how basic building blocks of CRMs, called transcription factor binding sites (TFBSs), coordinate to drive gene expression is unclear. My thesis is focused on predicting the location of CRMs in genomes and understanding their function and evolution through computational methods. The first part of my thesis developed a comparative genomic method of CRM prediction. This method is based on a probabilistic model of CRM evolution, capturing the constraint as well as turnover of TFBSs during evolution. Through a statistical approach that marginal-izes hidden variables, the method is able to deal with the uncertainty of sequence alignment and prediction of individual TFBSs, two primary technical hurdles of existing methods. In a related work, I collaborated with a graduate colleague to study the empirical evolutionary pattern of TFBSs, taking advantage of the recently available 12 Drosophila genomes. We found, among other things, that the evolution of binding sites is constrained by the affinities

### DOI 10.1007/s00285-007-0120-8 Mathematical Biology Counting labeled transitions in continuous-time Markov models of evolution

, 2007

"... Abstract Counting processes that keep track of labeled changes to discrete evolutionary traits play critical roles in evolutionary hypothesis testing. If we assume that trait evolution can be described by a continuous-time Markov chain, then it suffices to study the process that counts labeled trans ..."

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Abstract Counting processes that keep track of labeled changes to discrete evolutionary traits play critical roles in evolutionary hypothesis testing. If we assume that trait evolution can be described by a continuous-time Markov chain, then it suffices to study the process that counts labeled transitions of the chain. For a binary trait, we demonstrate that it is possible to obtain closed-form analytic solutions for the probability mass and probability generating functions of this evolutionary counting process. In the general, multi-state case we show how to compute moments of the counting process using an eigen decomposition of the infinitesimal generator, provided the latter is a diagonalizable matrix. We conclude with two examples that demonstrate the utility of our results.

### Article

, 2007

"... Analyses of deep mammalian sequence alignments and constraint predictions for 1 % of the human genome ..."

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Analyses of deep mammalian sequence alignments and constraint predictions for 1 % of the human genome