Mathematical Principles In Bioinformatics
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Mathematical Principles In Bioinformatics
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Author : Stephen S.-T. Yau
language : en
Publisher: Springer Nature
Release Date : 2024-01-11
Mathematical Principles In Bioinformatics written by Stephen S.-T. Yau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-11 with Science categories.
This textbook introduces bioinformatics to students in mathematics with no biology background assumed and it provides solid mathematical tools for biology students along with an understanding of how to implement them in bioinformatics problems. In addition to the basics, the text offers new approaches to understanding biological sequences. The concise presentation distinguishes itself from others on the subject, discussing and providing principles that relate to current open problems in bioinformatics as well as considering a variety of models. The convex hull principle is highlighted, opening a new interdisciplinary research area at the intersection of biology, mathematics, and computer science. Prerequisites include first courses in linear algebra, probability and statistics, and mathematical analysis. Researchers in mathematics, biology, and math-biology, will also find aspects of this text useful. This textbook is written based on the authors' research works that have been published in various journals along with the lecture notes used when teaching bioinformatics courses at the University of Illinois at Chicago and at Tsinghua University. The content may be divided into two parts. The first part includes three chapters, introducing some basic concepts. Chapter 1 provides biological background in molecular biology for mathematicians. Chapter 2 describes biological databases that are commonly used. Chapter 3 is concerned with alignment methods including global/local alignment, heuristic alignment, and multiple alignment. The second part consisting of five chapters, describes several bioinformatics principles using a rigorous mathematical formulation. Chapter 4 introduces the time-frequency spectral principle and its applications in bioinformatics. In Chapters 5 and 6, two strategies are used, the graphical representation and the natural vector method, to represent biological sequences, and conduct sequence comparison and phylogenetic analysis without alignment. Chapter 7 presents the convex hull principle and shows how it can be used to mathematically determine whether a certain amino acid sequence can be a protein. The last chapter summarizes additional mathematical ideas relating to sequence comparisons, such as new feature vectors and metrics. This part focuses on the governing principle in biology and provides plenty of alignment-free methods, which cannot be found in any other book.
Mathematics Of Bioinformatics
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Author : Matthew He
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-16
Mathematics Of Bioinformatics written by Matthew He and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-16 with Computers categories.
Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.
Computational Genome Analysis
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Author : Richard C. Deonier
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-27
Computational Genome Analysis written by Richard C. Deonier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-27 with Computers categories.
This book presents the foundations of key problems in computational molecular biology and bioinformatics. It focuses on computational and statistical principles applied to genomes, and introduces the mathematics and statistics that are crucial for understanding these applications. The book features a free download of the R software statistics package and the text provides great crossover material that is interesting and accessible to students in biology, mathematics, statistics and computer science. More than 100 illustrations and diagrams reinforce concepts and present key results from the primary literature. Exercises are given at the end of chapters.
Theory And Mathematical Methods In Bioinformatics
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Author : Shiyi Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-26
Theory And Mathematical Methods In Bioinformatics written by Shiyi Shen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-26 with Science categories.
This monograph addresses, in a systematic and pedagogical manner, the mathematical methods and the algorithms required to deal with the molecularly based problems of bioinformatics. Prominent attention is given to pair-wise and multiple sequence alignment algorithms, stochastic models of mutations, modulus structure theory and protein configuration analysis. Strong links to the molecular structures of proteins, DNA and other biomolecules and their analyses are developed.
Mathematical Grammar Of Biology
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Author : Michel Eduardo Beleza Yamagishi
language : en
Publisher: Springer
Release Date : 2017-08-31
Mathematical Grammar Of Biology written by Michel Eduardo Beleza Yamagishi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Mathematics categories.
This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.
Mathematical Modeling Of Biological Systems Volume Ii
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Author : Andreas Deutsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12
Mathematical Modeling Of Biological Systems Volume Ii written by Andreas Deutsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-12 with Mathematics categories.
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Infogenomics
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Author : Vincenzo Manca
language : en
Publisher: Springer Nature
Release Date : 2023-11-16
Infogenomics written by Vincenzo Manca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Technology & Engineering categories.
The book presents a conceptual and methodological basis for the mathematical and computational analysis of genomes. Genomes are containers of biological information, which direct the cell functions and the evolution of organisms. Combinatorial, probabilistic, and informational aspects are fundamental ingredients of any mathematical investigation of genomes aimed at providing mathematical principles for extracting the information that they contain. The topics presented in the book include research themes developed by authors in the last 15 years, and in many aspects, the book continues a preceding volume (Vincenzo Manca, Infobiotics: Information in biotic systems, Springer, 2013). The main inspiring idea of the book is an informational perspective to Genomics. Information is the most recent, among the fundamental mathematical and physical concepts developed in the last two centuries. It has revolutionized the whole science and continues, in this direction, to dominate the trends of the contemporary science. In fact, any discipline collects data from observations, by providing theories able to explain, predict, and dominate natural phenomena. But data are containers of information, whence information is essential in any scientific elaboration. Many open problems in deciphering genomes will be addressed, by showing an informational approach to the discovery of “genome languages”, according to which genomic texts are written. Life strategies, at many levels of organization, are encoded in these texts, and randomness has a crucial role in the birth and in the development of biological information, where the interplay of casualty and computation is probably the most secret key of life intelligence.
Infobiotics
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Author : Vincenzo Manca
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12
Infobiotics written by Vincenzo Manca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Technology & Engineering categories.
The book presents topics in discrete biomathematics. Mathematics has been widely used in modeling biological phenomena. However, the molecular and discrete nature of basic life processes suggests that their logic follow principles that are intrinsically based on discrete and informational mechanisms. The ultimate reason of polymers, as key element of life, is directly based on the computational power of strings, and the intrinsic necessity of metabolism is related to the mathematical notion of multiset. The switch of the two roots of bioinformatics suggests a change of perspective. In bioinformatics, the biologists ask computer scientists to assist them in processing biological data. Conversely, in infobiotics mathematicians and computer scientists investigate principles and theories yielding new interpretation keys of biological phenomena. Life is too important to be investigated by biologists alone, and though computers are essential to process data from biological laboratories, many fundamental questions about life can be appropriately answered by a perspicacious intervention of mathematicians, computer scientists, and physicists, who will complement the work of chemists, biochemists, biologists, and medical investigators. The volume is organized in seven chapters. The first part is devoted to research topics (Discrete information and life, Strings and genomes, Algorithms and Biorhythms, Life Strategies), the second one to mathematical backgrounds (Numbers and Measures, Languages and Grammars, Combinations and Chances).
An Introduction To Systems Biology
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Author : Uri Alon
language : en
Publisher: CRC Press
Release Date : 2019-07-12
An Introduction To Systems Biology written by Uri Alon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Mathematics categories.
Praise for the first edition: ... superb, beautifully written and organized work that takes an engineering approach to systems biology. Alon provides nicely written appendices to explain the basic mathematical and biological concepts clearly and succinctly without interfering with the main text. He starts with a mathematical description of transcriptional activation and then describes some basic transcription-network motifs (patterns) that can be combined to form larger networks. – Nature [This text deserves] serious attention from any quantitative scientist who hopes to learn about modern biology ... It assumes no prior knowledge of or even interest in biology ... One final aspect that must be mentioned is the wonderful set of exercises that accompany each chapter. ... Alon’s book should become a standard part of the training of graduate students. – Physics Today Written for students and researchers, the second edition of this best-selling textbook continues to offer a clear presentation of design principles that govern the structure and behavior of biological systems. It highlights simple, recurring circuit elements that make up the regulation of cells and tissues. Rigorously classroom-tested, this edition includes new chapters on exciting advances made in the last decade. Features: Includes seven new chapters The new edition has 189 exercises, the previous edition had 66 Offers new examples relevant to human physiology and disease The book website including course videos can be found here: https://www.weizmann.ac.il/mcb/UriAlon/introduction-systems-biology-design-principles-biological-circuits.
Statistical Methods In Bioinformatics
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Author : Warren J. Ewens
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-18
Statistical Methods In Bioinformatics written by Warren J. Ewens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-18 with Science categories.
Advances in computers and biotechnology have had a profound impact on biomedical research, and as a result complex data sets can now be generated to address extremely complex biological questions. Correspondingly, advances in the statistical methods necessary to analyze such data are following closely behind the advances in data generation methods. The statistical methods required by bioinformatics present many new and difficult problems for the research community. This book provides an introduction to some of these new methods. The main biological topics treated include sequence analysis, BLAST, microarray analysis, gene finding, and the analysis of evolutionary processes. The main statistical techniques covered include hypothesis testing and estimation, Poisson processes, Markov models and Hidden Markov models, and multiple testing methods. The second edition features new chapters on microarray analysis and on statistical inference, including a discussion of ANOVA, and discussions of the statistical theory of motifs and methods based on the hypergeometric distribution. Much material has been clarified and reorganized. The book is written so as to appeal to biologists and computer scientists who wish to know more about the statistical methods of the field, as well as to trained statisticians who wish to become involved with bioinformatics. The earlier chapters introduce the concepts of probability and statistics at an elementary level, but with an emphasis on material relevant to later chapters and often not covered in standard introductory texts. Later chapters should be immediately accessible to the trained statistician. Sufficient mathematical background consists of introductory courses in calculus and linear algebra. The basic biological concepts that are used are explained, or can be understood from the context, and standard mathematical concepts are summarized in an Appendix. Problems are provided at the end of each chapter allowing the reader to develop aspects of the theory outlined in the main text. Warren J. Ewens holds the Christopher H. Brown Distinguished Professorship at the University of Pennsylvania. He is the author of two books, Population Genetics and Mathematical Population Genetics. He is a senior editor of Annals of Human Genetics and has served on the editorial boards of Theoretical Population Biology, GENETICS, Proceedings of the Royal Society B and SIAM Journal in Mathematical Biology. He is a fellow of the Royal Society and the Australian Academy of Science. Gregory R. Grant is a senior bioinformatics researcher in the University of Pennsylvania Computational Biology and Informatics Laboratory. He obtained his Ph.D. in number theory from the University of Maryland in 1995 and his Masters in Computer Science from the University of Pennsylvania in 1999. Comments on the first edition: "This book would be an ideal text for a postgraduate course...[and] is equally well suited to individual study.... I would recommend the book highly." (Biometrics) "Ewens and Grant have given us a very welcome introduction to what is behind those pretty [graphical user] interfaces." (Naturwissenschaften) "The authors do an excellent job of presenting the essence of the material without getting bogged down in mathematical details." (Journal American Statistical Association) "The authors have restructured classical material to a great extent and the new organization of the different topics is one of the outstanding services of the book." (Metrika)