Theory and Algorithms Commons^™

Formal Models Of The Extension Activity Of Dna Polymerase Enzymes, Srujan Kumar Enaganti

Electronic Thesis and Dissertation Repository

The study of formal language operations inspired by enzymatic actions on DNA is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion-deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping concatenation, conditional concatenation, contextual intra- and intermolecular recombinations, as well as template-guided recombination.

First, a formal language operation is proposed and investigated, inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA polymerase enzyme. Given two DNA strings u and v, where the shorter …

A Study Of Pseudo-Periodic And Pseudo-Bordered Words For Functions Beyond Identity And Involution, Manasi Kulkarni

Electronic Thesis and Dissertation Repository

Periodicity, primitivity and borderedness are some of the fundamental notions in combinatorics on words. Motivated by the Watson-Crick complementarity of DNA strands wherein a word (strand) over the DNA alphabet \{A, G, C, T\} and its Watson-Crick complement are informationally ``identical", these notions have been extended to consider pseudo-periodicity and pseudo-borderedness obtained by replacing the ``identity" function with ``pseudo-identity" functions (antimorphic involution in case of Watson-Crick complementarity). For a given alphabet $\Sigma$, an antimorphic involution $\theta$ is an antimorphism, i.e., $\theta(uv)=\theta(v) \theta(u)$ for all $u,v \in \Sigma^{*}$ and an involution, i.e., $\theta(\theta(u))=u$ for all $u \in \Sigma^{*}$. In this thesis, …

Algorithms For Peptide Identification From Mixture Tandem Mass Spectra, Yi Liu

Electronic Thesis and Dissertation Repository

The large amount of data collected in an mass spectrometry experiment requires effective computational approaches for the automated analysis of those data. Though extensive research has been conducted for such purpose by the proteomics community, there are still remaining challenges, among which, one particular challenge is that the identification rate of the MS/MS spectra collected is rather low. One significant reason that contributes to this situation is the frequently observed mixture spectra, which result from the concurrent fragmentation of multiple precursors in a single MS/MS spectrum. However, nearly all the mainstream computational methods still take the assumption that the acquired …

Algorithms To Compute Characteristic Classes, Martin Helmer

Electronic Thesis and Dissertation Repository

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …