Mathematical Principles In Bioinformatics

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Mathematical Principles in Bioinformatics

Stephen S.-T. Yau,Xin Zhao,Kun Tian,Hongyu Yu
Mathematical Principles in Bioinformatics Book PDF

Author : Stephen S.-T. Yau,Xin Zhao,Kun Tian,Hongyu Yu
Publisher : Springer Nature
Page : 177 pages
File Size : 55,8 Mb
Release : 2024-01-11
Category : Science
ISBN : 9783031482953

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Mathematical Principles in Bioinformatics by Stephen S.-T. Yau,Xin Zhao,Kun Tian,Hongyu Yu Pdf

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

Matthew He,Sergey Petoukhov
Mathematics of Bioinformatics Book PDF

Author : Matthew He,Sergey Petoukhov
Publisher : John Wiley & Sons
Page : 231 pages
File Size : 46,6 Mb
Release : 2011-03-16
Category : Computers
ISBN : 9781118099520

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Mathematics of Bioinformatics by Matthew He,Sergey Petoukhov Pdf

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.

Theory and Mathematical Methods in Bioinformatics

Shiyi Shen
Theory and Mathematical Methods in Bioinformatics Book PDF

Author : Shiyi Shen
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 45,8 Mb
Release : 2008-01-26
Category : Science
ISBN : 9783540748915

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Theory and Mathematical Methods in Bioinformatics by Shiyi Shen Pdf

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.

Statistical Methods in Bioinformatics

Warren J. Ewens,Gregory R. Grant
Statistical Methods in Bioinformatics Book PDF

Author : Warren J. Ewens,Gregory R. Grant
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 48,9 Mb
Release : 2006-03-30
Category : Science
ISBN : 9780387266480

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Statistical Methods in Bioinformatics by Warren J. Ewens,Gregory R. Grant Pdf

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)

Computational Genome Analysis

Richard C. Deonier,Simon Tavaré,Michael S. Waterman
Computational Genome Analysis Book PDF

Author : Richard C. Deonier,Simon Tavaré,Michael S. Waterman
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 44,7 Mb
Release : 2005-12-27
Category : Computers
ISBN : 9780387288079

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Computational Genome Analysis by Richard C. Deonier,Simon Tavaré,Michael S. Waterman Pdf

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.

Introduction to Mathematical Methods in Bioinformatics

Alexander Isaev
Introduction to Mathematical Methods in Bioinformatics Book PDF

Author : Alexander Isaev
Publisher : Springer
Page : 294 pages
File Size : 53,9 Mb
Release : 2006-10-04
Category : Science
ISBN : 9783540484264

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Introduction to Mathematical Methods in Bioinformatics by Alexander Isaev Pdf

This book looks at the mathematical foundations of the models currently in use. All existing books on bioinformatics are software-orientated and they concentrate on computer implementations of mathematical models of biology. This book is unique in the sense that it looks at the mathematical foundations of the models, which are crucial for correct interpretation of the outputs of the models.

Theory And Mathematical Methods For Bioinformatics, 1/e

Shen,Jack A Tuszynski,Shiyi
Theory And Mathematical Methods For Bioinformatics 1 e Book PDF

Author : Shen,Jack A Tuszynski,Shiyi
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2010-12-01
Category : Electronic
ISBN : 8184896255

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Theory And Mathematical Methods For Bioinformatics, 1/e by Shen,Jack A Tuszynski,Shiyi Pdf

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. The book will be useful to students, research scientists and practitioners of bioinformatics and related fields, especially those who are interested in the underlying mathematical methods and theory. Among the methods presented in the book, 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. In particular, for proteins an in-depth exposition of secondary structure prediction methods should be a valuable tool in both molecular biology and in applications to rational drug design. The book can also be used as a textbook and for this reason most of the chapters include exercises and problems at the level of a graduate program in bioinformatics.

Mathematical Modeling of Biological Systems, Volume II

Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz
Mathematical Modeling of Biological Systems Volume II Book PDF

Author : Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 48,7 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 9780817645564

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Mathematical Modeling of Biological Systems, Volume II by Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz Pdf

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.

Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications

Petoukhov, Sergey,He, Matthew
Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics Advanced Patterns and Applications Book PDF

Author : Petoukhov, Sergey,He, Matthew
Publisher : IGI Global
Page : 290 pages
File Size : 41,6 Mb
Release : 2009-10-31
Category : Computers
ISBN : 9781605661254

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Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications by Petoukhov, Sergey,He, Matthew Pdf

"This book compiles studies that demonstrate effective approaches to the structural analysis of genetic systems and bioinformatics"--Provided by publisher.

Infobiotics

Vincenzo Manca
Infobiotics Book PDF

Author : Vincenzo Manca
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 46,7 Mb
Release : 2013-03-12
Category : Technology & Engineering
ISBN : 9783642362231

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Infobiotics by Vincenzo Manca Pdf

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).

Infogenomics

Vincenzo Manca,Vincenzo Bonnici
Infogenomics Book PDF

Author : Vincenzo Manca,Vincenzo Bonnici
Publisher : Springer Nature
Page : 295 pages
File Size : 47,5 Mb
Release : 2023-11-16
Category : Technology & Engineering
ISBN : 9783031445019

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Infogenomics by Vincenzo Manca,Vincenzo Bonnici Pdf

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.

Proving Darwin

Gregory J. Chaitin
Proving Darwin Book PDF

Author : Gregory J. Chaitin
Publisher : Pantheon
Page : 146 pages
File Size : 40,7 Mb
Release : 2012
Category : Bioinformatics
ISBN : 9780375423147

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Proving Darwin by Gregory J. Chaitin Pdf

Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world.

Towards a Mathematical Theory of Complex Biological Systems

C Bianca,N Bellomo
Towards a Mathematical Theory of Complex Biological Systems Book PDF

Author : C Bianca,N Bellomo
Publisher : World Scientific
Page : 228 pages
File Size : 48,9 Mb
Release : 2011-01-12
Category : Mathematics
ISBN : 9789814460972

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Towards a Mathematical Theory of Complex Biological Systems by C Bianca,N Bellomo Pdf

This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling. Contents:Looking for a Mathematical Theory of Biological SystemsOn the Complexity of Biological SystemsImmune System, Wound Healing Process, and System Biology:The Immune System: A Phenomenological OverviewWound Healing Process and Organ RepairFrom Levels of Biological Organization to System BiologyMathematical Tools:Mathematical Tools and StructuresMultiscale Modeling: Linking Molecular, Cellular, and Tissues ScalesApplications and Research Perspectives:A Model for the Malign Keloid Formation and Immune System CompetitionMacroscopic Models of Chemotaxis by KTAP Asymptotic MethodsLooking Ahead Readership: Researchers in mathematical modeling and biological systems. Keywords:Mathematical Theory;Biological Systems;SubsystemKey Features:Provides a new conceptual background to applied mathematicians involved in the challenging research field of living systems, and specifically biology systemsGives more accurate ODE, cellular-automata, and continuum models from the biological point of view

Mathematical Grammar of Biology

Michel Eduardo Beleza Yamagishi
Mathematical Grammar of Biology Book PDF

Author : Michel Eduardo Beleza Yamagishi
Publisher : Springer
Page : 82 pages
File Size : 51,7 Mb
Release : 2017-08-31
Category : Mathematics
ISBN : 9783319626895

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Mathematical Grammar of Biology by Michel Eduardo Beleza Yamagishi Pdf

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.

Bioinformatics

Andrzej Polanski,Marek Kimmel
Bioinformatics Book PDF

Author : Andrzej Polanski,Marek Kimmel
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 49,6 Mb
Release : 2007-04-19
Category : Computers
ISBN : 9783540241669

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Bioinformatics by Andrzej Polanski,Marek Kimmel Pdf

This textbook presents mathematical models in bioinformatics and describes biological problems that inspire the computer science tools used to manage the enormous data sets involved. The first part of the book covers mathematical and computational methods, with practical applications presented in the second part. The mathematical presentation avoids unnecessary formalism, while remaining clear and precise. The book closes with a thorough bibliography, reaching from classic research results to very recent findings. This volume is suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on mathematical and computer science background.