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研究生：	盧提文 Lu, Ti-Wen
論文名稱：	以多基因體學尺度分析冠狀病毒之基因重組拓樸結構：人類SARS-CoV及-CoV-2和動物SARS相關冠狀病毒 Multi-genomics scale analysis on the topology of viral recombination among coronaviruses: human SARS-CoV, and SARS-CoV-2, and animal SARS-CoV-related coronaviruses
指導教授：	江孟蓉 Chiang, River
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系應用數學碩博士班 Department of Mathematics
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	45
中文關鍵詞：	拓樸數據分析、持續同調、新冠病毒、序列重組
外文關鍵詞：	Topological Data Analysis, Persistent Homology, SARS-CoV-2, Gene Recombination
相關次數：	點閱：154 下載：12
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論文中，我們將簡介持續同調（persistent homology)，一種應用在有限度量空間的同調理論。持續同調能夠作為數據分析方法協助我們判斷數據中被提取的資訊為雜訊或具備代表性。以代數拓樸為基礎，持續同調是拓樸數據分析中常用的工具且尤其適合探討高維度的數據。
為了說明持續同調在應用上的有效性，我們在不同基因體學的層次以該方法分析來自不同動物宿主且與 SARS-CoV-2 和 SARS-CoV 相關的病毒序列之可能重組事件。SARS-CoV-2 自從流行病 COVID-19 爆發以來備受關注。此研究方法受到 Chan, Carlsson 和 Rabadan 三位教授關於病毒演化的研究啟發。藉由辨認持續同調的生成元，我們能夠呈現可能的病毒序列重組事件。

In this thesis, we give a brief review on persistent homology as a homology theory adapted to finite metric spaces. It is therefore well-suited in data analysis to characterize and extract representative information distinguished from noise. Coming from algebraic topology, it is one of the tools in topological data analysis and is especially suitable to study datasets of high dimensions.
To illustrate its effectiveness in applications, we use persistent homology to analyze putative recombination events among a variety of SARS-CoV-2 and SARS-CoV related viruses from different animal hosts and at different genomics levels. SARS-CoV-2 has been of high concern since the outbreak of the pandemic COVID-19. This approach is inspired by the work of Chan, Carlsson, and Rabadan. By identifying generators of the persistent homology, we are able to present possible recombination events.

Introduction 1 
1  Motivation 1 
2  Prior Works 2 
2.1 Computation of Persistent Homology 2 
2.2 Application on Virus Evolution 2
3 Our Works 2 
Background 4 
1 Basic Algebraic Topology 4 
1.1 Simplicial Complexes 4 
1.2 Homology Groups of Simplicial Complexes 4 
2  Persistent Homology 5 
2.1 The Structure Theorem 7 
2.2 Barcodes and Persistence Diagram 8 
2.3 A Practice Example 9 
3  Basic Ideas of Genomics 12 
3.1 Sequence Alignment 12 
3.2 Phylogeny, Phylogenetic Tree, and Phylogenetic Network 13 
4 Basic Virology of SARS-CoV-2 14 
4.1 Emergence and the Outbreak 14 
4.2 Virion Structure 14 
4.3 Genomics and Phylogeny 15
4.4 Animal Hosts 17 
Statement: Trees Have Trivial Persistent Homology 18 
1 Definition 18
2 Propositions 19 
3 Theorem 21 
Materials and Methods 24 
1  Materials 24 
2  Methods 25 
2.1  Multiple sequence alignment 25 
2.2  Computation of pairwise hamming distance matrix 27 
2.3  Computation of persistent homology with the pairwise distance matrix as input data 27 
2.4  Finding possible generators and the visualization 27 
Results 28 
1  Similarity patterns among the coronaviruses at different genomics levels 28 
2  Persistent homology of the viral genomes at different genomics levels 31 
2.1 Trivial first persistent homology at whole genome level 31 
2.2 First persistent homology at gene level 31 
3  Identification of the basis for the only H1 barcode 34 
4  Analysis after adding Guangdong pangolin SARS-CoV-2 related coronavirus 35 
Discussion 38 
1  Biological interpretations for homologous cycles of the generators 38 
2  A comparison between methods detecting recombination events 38 
3  Applicable to organisms other than viruses? 42 
Bibliography 43
                                    

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校內：2024-02-01公開
校外：2024-02-01公開

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