Dan Graur

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part I: Theoretical basis

This paper develops a theoretical framework for calculating sequence alignment probabilities under a general continuous-time Markov model of insertions and deletions using perturbation theory.

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part III: Algorithm for first approximation

The paper develops an algorithm to approximate the probability of local multiple sequence alignments using a perturbative formulation of a continuous-time Markov model of indels, showing it works well for moderate gap and branch lengths.

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part II: Perturbation analyses

This paper applies an ab initio perturbative formulation to calculate alignment probabilities under indel models, showing that fewest-indel terms can accurately approximate local alignment probabilities under modest conditions.

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part IV: Incorporation of substitutions and other mutations

This paper extends a perturbative formulation of a continuous-time Markov model of sequence evolution to include substitutions and other mutations like genomic rearrangements.