Table of Contents:
Chapter 1: Introduction
1.1 Background of the Study
1.2 Research Problem
1.3 Research Questions
1.4 Objectives of the Study
1.5 Significance of the Study
1.6 Scope of Study
1.7 Limitations of Study

Chapter 2: Literature Review
2.1 Introduction to Topological Data Analysis
2.2 Machine Learning in Biomedical Research
2.3 Computational Biology in Applied Topology
2.4 Previous Studies and Research in the Field

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Justification of Research Methodology

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Interpretation of Data
4.3 Comparison with Previous Studies
4.4 Implications of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Contributions to the Field
5.4 Recommendations for Future Research

Brief Overview:
Topological data analysis (TDA) and machine learning have gained significant attention in recent years, especially in the field of biomedical research. This thesis focuses on the application of TDA and machine learning in computational biology, specifically in the realm of applied topology. The integration of topological methods with machine learning algorithms has shown promising results in identifying complex patterns and structures in biological data, leading to advancements in understanding various biological processes. This research aims to explore the potential of TDA and machine learning in biomedical research, providing insights into the synergistic relationship between these two methodologies. Through a comprehensive literature review, research methodology, and discussion of findings, this thesis seeks to contribute to the growing body of knowledge in the intersection of computational biology, topology, and machine learning.

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