Thesis (M. S.)--Biomedical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Lee, Robert; Committee Member: Kemp, Melissa; Committee Member: Prinz, Astrid; Committee Member: Ting, Lena; Committee Member: Wiesenfeld, Kurt.

Thesis (M.S.)--Montana State University--Bozeman, 2006. / Typescript. Chairperson, Graduate Committee: Brendan Mumey. Includes bibliographical references (leaves 31-32).

No description available.

Thesis (Ph.D.) - University of Glasgow, 2007. / Ph.D. thesis submitted to the Information and Mathematical Sciences Faculty, Department of Computing Science, University of Glasgow, 2007. Includes bibliographical references. Print version also available.

Coding theory has several applications in Genetics and Bioengineering. This thesis concentrates on a specific application from Computational Biology. This concerns the construction of new DNA codes which satisfy certain combinatorial constraints, using an alphabet of four symbols. The interest in these codes arises because it is possible to synthesise short single strands of DNA known as oligonucleotides. The codes can be useful in the design of these oligonucleotides. For example, the codes are used in DNA computing, as bar codes in molecular libraries and in microarray technologies. The computer algebra system Magma, which deals successfully with coding theory computation, is applied initially to the construction of DNA codes sat- isfying a GC-content constraint and a minimum Hamming distance constraint. The constraints are specified to avoid unwanted hybridizations and to ensure uniform melting temperatures. Additionally, another constraint, known as a reverse-complement constraint, is added to further prevent unwanted hybridiza- tions. This additional constraint is studied using involutions in a permutation group. Codes constructed in this thesis are derived from linear codes over GF(4) and Z4 and additive codes over GF(4). Previous approaches to the construction of these codes are extended in several ways. Longer codes are constructed, the examination of cyclic and extended cyclic codes is more comprehensive, and cosets of codes are considered. In addition, attention is paid to the mapping from field or ring elements to the DNA nucleotides; different mappings can give different lower bounds. Further improvements have been made after the tech- niques of shortening and puncturing are applied to the table of best codes, and also by searching for codes in the tables that have an all-ones vector in their dual. The use of a database of best known linear codes is also considered. In many cases codes are obtained which are larger than the best codes currently known. In the case of codes of length greater than twenty, linear DNA codes have not been constructed previously and so all codes obtained are the best known re- sults. Generator polynomials are given for the codes constructed. Coset leaders are also given in cases where cosets of linear codes are used. Thus it is possible for the reader to construct the codes without repeating the work presented in the thesis. Additionally, files of codewords are available online when the codes constructed are the best known codes and have fewer than 50000 codewords.

We investigate reaction-diffusion models for populations whose members undergo two specific processes: dispersal and settling. Systems of this type occur throughout biological science, in contexts ranging from ecology to cell biology.Here we consider three distinct applications, namely: / • animal translocation, / • the invasion of a domain by precursor and differentiated cells, and / • the development of tissue-engineered cartilage. / Mathematical modelling of these systems provides an understanding of the population-level patterns that emerge from the behaviour of individuals. / A multi-species reaction-diffusion model is developed and analysed for each of the three applications. We present numerical results, which are illuminated through analytical results derived for simplified or limiting cases. For these special cases, results are obtained using analytical techniques including perturbation analysis, travelling wave analysis and phase plane methods. These analytic results provide a more complete understanding of system behaviour than numerical results alone. Emphasis is placed on connecting modelling results with experimental observations. / The first application considered is animal translocations. Translocations are widely used to reintroduce threatened species to areas where they have disappeared. A variety of different dispersal and settling mechanisms are considered, and results compared. The model is applied to a case study of a double translocation of the Maud Island frog, Leiopelma pakeka. Results suggest that settling occurs at a constant rate, with repulsion playing a significantrole in dispersal. This research demonstrates that mathematical modelling of translocations is useful in suggesting design and monitoring strategies for future translocations, and as an aid in understanding observed behaviour. / The second application we investigate is the invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric (intestinal) nervous system, but is presented in general terms and is of broader applicability. Regions of the parameter space are characterised according to existence, shape and speed of travelling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, these results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells. / As a third application, we propose a model for the development of cartilage around a single chondrocyte. The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components. Our observations could explain differences observed experimentally between various scaffold media. Modelling results are also used to predict the minimum chondrocyte seeding density required to produce functional cartilage. / In summary, we develop reaction-diffusion models for dispersing and settling populations for three biological applications. Numerical and analytical results provide an understanding of population-level behaviour. This thesis demonstrates that mathematical modelling of biological systems can further understanding of biological systems and help to answer questions posed by experimental research.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 117-122).

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Mathematics." Includes bibliographical references (p. 147-153).

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 101-109). Also available in print.

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