Topological Data Analysis For Genomics And Evolution

Biology has entered the age of Big Data. The technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. Topological data analysis is a rapidly-developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology alongside mathematicians interested in applied topology.

Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

This timely text introduces topological data analysis from scratch, with detailed case studies.

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Darwin's theory of evolution by natural selection fails to explain the forms of organisms because it focuses on inheritance and survival, not on how organisms are generated. The first part of this 2007 book (by Gerry Webster) looks critically of the conceptual structure of Darwinism and describes the limitation of the theory of evolution as a comprehensive biological theory, arguing that a theory of biological form is needed to understand the structure of organisms and their transformations as revealed in taxonomy. The second part of the book (by Brian Goodwin) explores such a theory in terms of organisms as developing and transforming dynamic systems, within which gene action is to be understood. A number of specific examples, including tetrapod limb formation and Drosophila development, are used to illustrate how these hierarchically-organized dynamic fields undergo robust symmetry-breaking cascades to produce generic forms.

The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.

Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.

System Biology encompasses the knowledge from diverse fields such as Molecular Biology, Immunology, Genetics, Computational Biology, Mathematical Biology, etc. not only to address key questions that are not answerable by individual fields alone, but also to help in our understanding of the complexities of biological systems. Whole genome expression studies have provided us the means of studying the expression of thousands of genes under a particular condition and this technique had been widely used to find out the role of key macromolecules that are involved in biological signaling pathways. However, making sense of the underlying complexity is only possible if we interconnect various signaling pathways into human and computer readable network maps. These maps can then be used to classify and study individual components involved in a particular phenomenon. Apart from transcriptomics, several individual gene studies have resulted in adding to our knowledge of key components that are involved in a signaling pathway. It therefore becomes imperative to take into account of these studies also, while constructing our network maps to highlight the interconnectedness of the entire signaling pathways and the role of that particular individual protein in the pathway. This collection of articles will contain a collection of pioneering work done by scientists working in regulatory signaling networks and the use of large scale gene expression and omics data. The distinctive features of this book would be: Act a single source of information to understand the various components of different signaling network (roadmap of biochemical pathways, the nature of a molecule of interest in a particular pathway, etc.), Serve as a platform to highlight the key findings in this highly volatile and evolving field, and Provide answers to various techniques both related to microarray and cell signaling to the readers.

This book constitutes the refereed proceedings of the 20th International Conference on Distributed Computing and Intelligent Technology, ICDCIT 2024, which was held in Bhubaneswar, India, during January 17–20, 2024. The 24 full papers presented in this volume were carefully reviewed and selected from 116 submissions. The papers are organized in the following topical sections: Distributed Computing (DC) and Intelligent Technology (IT). The DC track solicits original research papers contributing to the foundations and applications of distributed computing, whereas the IT track solicits original research papers contributing to the foundations and applications of Intelligent Technology.

Since the identification of the first cases of the coronavirus in December 2019, there has been a significant amount of confusion regarding the origin and spread of the so-called 'coronavirus', SARS-CoV-2, and the cause of the disease COVID-19. Conflicting messages from the media and officials across different countries and organizations, the abundance of disparate sources of information, unfounded conspiracy theories on the origins of the virus, unproven therapies, and inconsistent public health measures, have all served to increase anxiety in the population. Where did the virus come from? How is it transmitted? How does it cause disease? Is it like flu? What is a pandemic? In this concise and accessible introduction, a leading expert provides answers to these commonly asked questions. This revised and updated edition now also covers how the virus mutates, how important these mutations are, how vaccines work, and what we can expect in the near and long-term future.