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Item type:Publication, Access status: with files , Graph-based Methods for the Design of DNA ComputationsThe reliability of results in DNA based computations strongly depends on the DNA sequences representing the units of information. The task of finding appropriate sequences is currently handled by means of conventional computing. The most accurate criterium for this purpose is the free energy of hybridization complexes built by two DNA single strands. This thesis addresses two issues in this area. First, finding of a secondary structure of DNA/DNA complexes having minimal free energy. For this, a novel graph-based representation of DNA/DNA complexes is introduced and two advanced methods calculating the free energy based on dynamic programming are proposed. Second, the validation of a given set of DNA words to encode a particular assignment of a mathematical problem. For this, a method is developed based on free energy assessment. It is suitable for DNA computing models that are based on an interdependent encoding of DNA words, which represent two different types of entities in the mathematical problem. Another accomplishment of the thesis is an optimization of the Floyd-Warshall algorithm for finding shortest paths in a weighted graph. A memory reduction method for the particular case of bipartite graphs is established.Publicationtype: Doctoral Thesis476 1795 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Coding theory via Groebner basesCoding theory plays an important role in efficient transmission of data over noisy channels.In this thesis efficient encoding procedure for linear codes is developed using an algebraic approach. Description of linear codes as ideals in a residue class ring are given in terms of Groebner basis. While investigating primitive Reed Muller codes, a special family of linear codes with designed Hamming distance is obtained. A result proves their superiority over existing primitive Reed Muller codes. Furthermore, codes associated to a particular binomial ideal, defined as a sum of toric ideal and a prime ideal, are explored through minimal generators and Groebner basis. For these non-toric binomial ideals universal Groebner bases, Graver bases and circuits are also found. It is shown that each such binomial ideal has a natural reduced Groebner basis which provides a very compact encoding procedure. Finally, the binomial ideal of a linear code is presented in terms of its syzygy modules and the corresponding finite free resolution is also given.Publicationtype: Doctoral Thesis561 1118