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- All Subjects: Mappings (Mathematics)
- Creators: Khan, M Nadeem Shafi
- Creators: Lacroix, Zoé
Description
Genomic and proteomic sequences, which are in the form of deoxyribonucleic acid (DNA) and amino acids respectively, play a vital role in the structure, function and diversity of every living cell. As a result, various genomic and proteomic sequence processing methods have been proposed from diverse disciplines, including biology, chemistry, physics, computer science and electrical engineering. In particular, signal processing techniques were applied to the problems of sequence querying and alignment, that compare and classify regions of similarity in the sequences based on their composition. However, although current approaches obtain results that can be attributed to key biological properties, they require pre-processing and lack robustness to sequence repetitions. In addition, these approaches do not provide much support for efficiently querying sub-sequences, a process that is essential for tracking localized database matches. In this work, a query-based alignment method for biological sequences that maps sequences to time-domain waveforms before processing the waveforms for alignment in the time-frequency plane is first proposed. The mapping uses waveforms, such as time-domain Gaussian functions, with unique sequence representations in the time-frequency plane. The proposed alignment method employs a robust querying algorithm that utilizes a time-frequency signal expansion whose basis function is matched to the basic waveform in the mapped sequences. The resulting WAVEQuery approach is demonstrated for both DNA and protein sequences using the matching pursuit decomposition as the signal basis expansion. The alignment localization of WAVEQuery is specifically evaluated over repetitive database segments, and operable in real-time without pre-processing. It is demonstrated that WAVEQuery significantly outperforms the biological sequence alignment method BLAST for queries with repetitive segments for DNA sequences. A generalized version of the WAVEQuery approach with the metaplectic transform is also described for protein sequence structure prediction. For protein alignment, it is often necessary to not only compare the one-dimensional (1-D) primary sequence structure but also the secondary and tertiary three-dimensional (3-D) space structures. This is done after considering the conformations in the 3-D space due to the degrees of freedom of these structures. As a result, a novel directionality based 3-D waveform mapping for the 3-D protein structures is also proposed and it is used to compare protein structures using a matched filter approach. By incorporating a 3-D time axis, a highly-localized Gaussian-windowed chirp waveform is defined, and the amino acid information is mapped to the chirp parameters that are then directly used to obtain directionality in the 3-D space. This mapping is unique in that additional characteristic protein information such as hydrophobicity, that relates the sequence with the structure, can be added as another representation parameter. The additional parameter helps tracking similarities over local segments of the structure, this enabling classification of distantly related proteins which have partial structural similarities. This approach is successfully tested for pairwise alignments over full length structures, alignments over multiple structures to form a phylogenetic trees, and also alignments over local segments. Also, basic classification over protein structural classes using directional descriptors for the protein structure is performed.
ContributorsRavichandran, Lakshminarayan (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Spanias, Andreas S (Thesis advisor) / Chakrabarti, Chaitali (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Lacroix, Zoé (Committee member) / Arizona State University (Publisher)
Created2011
Description
Mostly, manufacturing tolerance charts are used these days for manufacturing tolerance transfer but these have the limitation of being one dimensional only. Some research has been undertaken for the three dimensional geometric tolerances but it is too theoretical and yet to be ready for operator level usage. In this research, a new three dimensional model for tolerance transfer in manufacturing process planning is presented that is user friendly in the sense that it is built upon the Coordinate Measuring Machine (CMM) readings that are readily available in any decent manufacturing facility. This model can take care of datum reference change between non orthogonal datums (squeezed datums), non-linearly oriented datums (twisted datums) etc. Graph theoretic approach based upon ACIS, C++ and MFC is laid out to facilitate its implementation for automation of the model. A totally new approach to determining dimensions and tolerances for the manufacturing process plan is also presented. Secondly, a new statistical model for the statistical tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables is presented. 4-D probability Maps have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Points inside the part map represent the pass percentage for parts manufactured. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size tolerance only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the part map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Map generated by using Minkowski Sum techniques on the individual part maps is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assembleability percentages for the assembly.
ContributorsKhan, M Nadeem Shafi (Author) / Phelan, Patrick E (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Farin, Gerald (Committee member) / Roberts, Chell (Committee member) / Henderson, Mark (Committee member) / Arizona State University (Publisher)
Created2011