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Wesolowski, S. (2017). Developing SRSF Shape Analysis Techniques for Applications in Neuroscience and Genomics. Retrieved from http://purl.flvc.org/fsu/fd/FSU_FALL2017_Wesolowski_fsu_0071E_14177
Dissertation focuses on exploring the capabilities of the SRSF statistical shape analysis framework through various applications. Each application gives rise to a specific mathematical shape analysis model. The theoretical investigation of the models, driven by real data problems, give rise to new tools and theorems necessary to conduct a sound inference in the space of shapes. From theoretical standpoint the robustness results are provided for the model parameters estimation and an ANOVA-like statistical testing procedure is discussed. The projects were a result of the collaboration between theoretical and application-focused research groups: the Shape Analysis Group at the Department of Statistics at Florida State University, the Center of Genomics and Personalized Medicine at FSU and the FSU's Department of Neuroscience. As a consequence each of the projects consists of two aspects—the theoretical investigation of the mathematical model and the application driven by a real life problem. The applications components, are similar from the data modeling standpoint. In each case the problem is set in an infinite dimensional space, elements of which are experimental data points that can be viewed as shapes. The three projects are: ``A new framework for Euclidean summary statistics in the neural spike train space''. The project provides a statistical framework for analyzing the spike train data and a new noise removal procedure for neural spike trains. The framework adapts the SRSF elastic metric in the space of point patterns to provides a new notion of the distance. ``SRSF shape analysis for sequencing data reveal new differentiating patterns''. This project uses the shape interpretation of the Next Generation Sequencing data to provide a new point of view of the exon level gene activity. The novel approach reveals a new differential gene behavior, that can't be captured by the state-of-the art techniques. Code is available online on github repository. ``How changes in shape of nucleosomal DNA near TSS influence changes of gene expression''. The result of this work is the novel shape analysis model explaining the relation between the change of the DNA arrangement on nucleosomes and the change in the differential gene expression.
Functional Data Analysis, Genomics, Neuroscience, Next Generation Sequencing, Shape Analysis, Statistics
Date of Defense
October 30, 2017.
Submitted Note
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Bibliography Note
Includes bibliographical references.
Advisory Committee
Wei Wu, Professor Co-Directing Dissertation; Richard Bertram, Professor Co-Directing Dissertation; Anuj Srivastava, University Representative; Peter Beerli, Committee Member; Washington Mio, Committee Member; Giray Ökten, Committee Member.
Publisher
Florida State University
Identifier
FSU_FALL2017_Wesolowski_fsu_0071E_14177
Wesolowski, S. (2017). Developing SRSF Shape Analysis Techniques for Applications in Neuroscience and Genomics. Retrieved from http://purl.flvc.org/fsu/fd/FSU_FALL2017_Wesolowski_fsu_0071E_14177