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Algebraic and Combinatorial Computational Biology

Algebraic and Combinatorial Computational Biology
  • Author : Raina Robeva,Matthew Macauley
  • Publisher :Unknown
  • Release Date :2018-10-08
  • Total pages :434
  • ISBN : 9780128140697
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Summary : Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. Integrates a comprehensive selection of tools from computational biology into educational or research programs Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations Contains scalable material for use in undergraduate and graduate-level classes and research projects Introduces the reader to freely-available professional software Supported by illustrative datasets and adaptable computer code

Algebraic Statistics for Computational Biology

Algebraic Statistics for Computational Biology
  • Author : L. Pachter,B. Sturmfels
  • Publisher :Unknown
  • Release Date :2005-08-22
  • Total pages :420
  • ISBN : 0521857007
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Summary : This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Algebraic Combinatorics for Computational Biology

Algebraic Combinatorics for Computational Biology
  • Author : Nicholas Karl Eriksson
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :250
  • ISBN : 0542824094
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Summary : Algebraic statistics is the study of the algebraic varieties that correspond to discrete statistical models. Such statistical models are used throughout computational biology, for example to describe the evolution of DNA sequences. This perspective on statistics allows us to bring mathematical techniques to bear and also provides a source of new problems in mathematics.

Patterns in Permutations and Words

Patterns in Permutations and Words
  • Author : Sergey Kitaev
  • Publisher :Unknown
  • Release Date :2011-08-30
  • Total pages :494
  • ISBN : 9783642173332
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Summary : There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

Exam Prep for: Algebraic and Combinatorial Computational ...

Exam Prep for: Algebraic and Combinatorial Computational ...
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2021
  • Total pages :229
  • ISBN : 1230987654XX
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Summary :

Algebraic and Discrete Mathematical Methods for Modern Biology

Algebraic and Discrete Mathematical Methods for Modern Biology
  • Author : Raina Robeva
  • Publisher :Unknown
  • Release Date :2015-05-09
  • Total pages :382
  • ISBN : 9780128012710
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Summary : Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. Examines significant questions in modern biology and their mathematical treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Combinatorial Computational Biology of RNA

Combinatorial Computational Biology of RNA
  • Author : Christian Reidys
  • Publisher :Unknown
  • Release Date :2010-10-29
  • Total pages :258
  • ISBN : 0387767312
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Summary : In this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology. It begins with an introductory chapter, which motivates and sets the background of this research. In the following chapter, all the concepts are systematically developed. The reader will find * integration of more than forty research papers covering topics like, RSK-algorithm, reflection principle, singularity analysis and random graph theory * systematic presentation of the theory of pseudo-knotted RNA structures including their generating function, uniform generation as well as central and discrete limit theorems * computational biology of pseudo-knotted RNA structures, including dynamic programming paradigms and a new folding algorithm * analysis of neutral networks of pseudo knotted RNA structures and their random graph theory, including neutral paths, giant components and connectivity All algorithms presented are freely available through springer.com and implemented in C. A proofs section at the end contains the necessary technicalities. This book will serve graduate students and researchers in the fields of discrete mathematics, mathematical and computational biology. It is suitable as a textbook for a graduate course in mathematical and computational biology.

Algebraic and Discrete Mathematical Methods for Modern Biology

Algebraic and Discrete Mathematical Methods for Modern Biology
  • Author : Raina Robeva
  • Publisher :Unknown
  • Release Date :2015-05-09
  • Total pages :382
  • ISBN : 9780128012710
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Summary : Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. Examines significant questions in modern biology and their mathematical treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Computational Discrete Mathematics

Computational Discrete Mathematics
  • Author : Sriram Pemmaraju,Steven Skiena
  • Publisher :Unknown
  • Release Date :2009-10-15
  • Total pages :229
  • ISBN : 9781107268715
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Summary : This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

A Project-Based Guide to Undergraduate Research in Mathematics

A Project-Based Guide to Undergraduate Research in Mathematics
  • Author : Pamela E. Harris,Erik Insko,Aaron Wootton
  • Publisher :Unknown
  • Release Date :2020-04-17
  • Total pages :324
  • ISBN : 9783030378530
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Summary : This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

Analytic Combinatorics

Analytic Combinatorics
  • Author : Philippe Flajolet,Robert Sedgewick
  • Publisher :Unknown
  • Release Date :2009-01-15
  • Total pages :229
  • ISBN : 9781139477161
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Summary : Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Computational Algebraic Geometry

Computational Algebraic Geometry
  • Author : HENRY SCHENCK,Hal Schenck
  • Publisher :Unknown
  • Release Date :2003-10-06
  • Total pages :193
  • ISBN : 0521536502
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Summary : Table of contents

Basic Phylogenetic Combinatorics

Basic Phylogenetic Combinatorics
  • Author : Andreas Dress,Katharina T. Huber,Jacobus Koolen
  • Publisher :Unknown
  • Release Date :2012
  • Total pages :264
  • ISBN : 9780521768320
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Summary : Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problems arising in evolutionary biology.

Combinatorial and Computational Geometry

Combinatorial and Computational Geometry
  • Author : Jacob E. Goodman,Janos Pach,Pach János,Emo Welzl
  • Publisher :Unknown
  • Release Date :2005-08-08
  • Total pages :616
  • ISBN : 0521848628
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Summary : This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Mathematical Concepts and Methods in Modern Biology

Mathematical Concepts and Methods in Modern Biology
  • Author : Raina Robeva,Terrell Hodge
  • Publisher :Unknown
  • Release Date :2013-02-26
  • Total pages :372
  • ISBN : 9780124157934
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Summary : Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology

Combinatorics

Combinatorics
  • Author : Theodore G. Faticoni
  • Publisher :Unknown
  • Release Date :2014-08-21
  • Total pages :328
  • ISBN : 9781118407486
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Summary : Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examining presented ideas and seeing proofs before reaching conclusions Elementary applications that do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations Combinatorics: An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

Combinatorial Commutative Algebra

Combinatorial Commutative Algebra
  • Author : Ezra Miller,Bernd Sturmfels
  • Publisher :Unknown
  • Release Date :2006-03-30
  • Total pages :420
  • ISBN : 9780387271033
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Summary : Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Analytic Combinatorics in Several Variables

Analytic Combinatorics in Several Variables
  • Author : Robin Pemantle,Mark C. Wilson
  • Publisher :Unknown
  • Release Date :2013-05-31
  • Total pages :380
  • ISBN : 9781107031579
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Summary : This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.

Handbook of Discrete and Computational Geometry, Third Edition

Handbook of Discrete and Computational Geometry, Third Edition
  • Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
  • Publisher :Unknown
  • Release Date :2017-11-22
  • Total pages :1928
  • ISBN : 9781351645911
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Summary : The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Algorithms on Strings, Trees and Sequences

Algorithms on Strings, Trees and Sequences
  • Author : Dan Gusfield
  • Publisher :Unknown
  • Release Date :1997-05-28
  • Total pages :229
  • ISBN : 9781139811002
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Summary : String algorithms are a traditional area of study in computer science. In recent years their importance has grown dramatically with the huge increase of electronically stored text and of molecular sequence data (DNA or protein sequences) produced by various genome projects. This 1997 book is a general text on computer algorithms for string processing. In addition to pure computer science, the book contains extensive discussions on biological problems that are cast as string problems, and on methods developed to solve them. It emphasises the fundamental ideas and techniques central to today's applications. New approaches to this complex material simplify methods that up to now have been for the specialist alone. With over 400 exercises to reinforce the material and develop additional topics, the book is suitable as a text for graduate or advanced undergraduate students in computer science, computational biology, or bio-informatics. Its discussion of current algorithms and techniques also makes it a reference for professionals.

Comparative Genomics

Comparative Genomics
  • Author : D. Sankoff,J.H. Nadeau
  • Publisher :Unknown
  • Release Date :2000-09-30
  • Total pages :557
  • ISBN : 0792365844
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Summary : A comprehensive account of genomic rearrangement, focusing on the mechanisms of inversion, translocation, gene and genome duplication and gene transfer and on the patterns that result from them in comparative maps. Includes analyses of genomic sequences in organelles, prokaryotes and eukaryotes as well as comparative maps of the nuclear genomes in higher plants and animals. The book showcases a variety of algorithmic and statistical approaches to rearrangement and map data.