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. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the
degree of Doctor of Philosophy. / Fall Semester 2017. / October 30, 2017. / Functional Data Analysis, Genomics, Neuroscience, Next Generation Sequencing, Shape Analysis, Statistics / Includes bibliographical references. / 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.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_605031 |
| Contributors | Wesolowski, Sergiusz (author), Wu, Wei (professor co-directing dissertation), Bertram, R. (Richard) (professor co-directing dissertation), Srivastava, Anuj, 1968- (university representative), Beerli, Peter (committee member), Mio, Washington (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (95 pages), computer, application/pdf |
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