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Algebraic and Combinatorial Computational Biology

Algebraic and Combinatorial Computational Biology
A Book

by Raina Robeva,Matthew Macauley

  • Publisher : Academic Press
  • Release : 2018-10-08
  • Pages : 434
  • ISBN : 0128140690
  • Language : En, Es, Fr & De
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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
A Book

by L. Pachter,B. Sturmfels

  • Publisher : Cambridge University Press
  • Release : 2005-08-22
  • Pages : 420
  • ISBN : 9780521857000
  • Language : En, Es, Fr & De
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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
A Book

by Nicholas Karl Eriksson

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 250
  • ISBN : 9780542824098
  • Language : En, Es, Fr & De
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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
A Book

by Sergey Kitaev

  • Publisher : Springer Science & Business Media
  • Release : 2011-08-30
  • Pages : 494
  • ISBN : 3642173330
  • Language : En, Es, Fr & De
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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 ...
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Combinatorial Computational Biology of RNA

Combinatorial Computational Biology of RNA
Pseudoknots and Neutral Networks

by Christian Reidys

  • Publisher : Springer Science & Business Media
  • Release : 2010-10-29
  • Pages : 258
  • ISBN : 9780387767314
  • Language : En, Es, Fr & De
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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
A Book

by Raina Robeva

  • Publisher : Academic Press
  • Release : 2015-05-09
  • Pages : 382
  • ISBN : 0128012714
  • Language : En, Es, Fr & De
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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

A Project-Based Guide to Undergraduate Research in Mathematics

A Project-Based Guide to Undergraduate Research in Mathematics
Starting and Sustaining Accessible Undergraduate Research

by Pamela E. Harris,Erik Insko,Aaron Wootton

  • Publisher : Springer Nature
  • Release : 2020-04-17
  • Pages : 324
  • ISBN : 3030378535
  • Language : En, Es, Fr & De
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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.

Connections Between Algebra, Combinatorics, and Geometry

Connections Between Algebra, Combinatorics, and Geometry
A Book

by Susan M. Cooper,Sean Sather-Wagstaff

  • Publisher : Springer
  • Release : 2014-05-16
  • Pages : 317
  • ISBN : 1493906267
  • Language : En, Es, Fr & De
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Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Lectures on Algebraic Statistics

Lectures on Algebraic Statistics
A Book

by Mathias Drton,Bernd Sturmfels,Seth Sullivant

  • Publisher : Springer Science & Business Media
  • Release : 2009-04-25
  • Pages : 172
  • ISBN : 3764389052
  • Language : En, Es, Fr & De
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How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

Computational Algebraic Geometry

Computational Algebraic Geometry
A Book

by HENRY SCHENCK,Hal Schenck

  • Publisher : Cambridge University Press
  • Release : 2003-10-06
  • Pages : 193
  • ISBN : 9780521536509
  • Language : En, Es, Fr & De
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Table of contents

Computational Discrete Mathematics

Computational Discrete Mathematics
Combinatorics and Graph Theory with Mathematica ®

by Sriram Pemmaraju,Steven Skiena

  • Publisher : Cambridge University Press
  • Release : 2009-10-15
  • Pages : 329
  • ISBN : 1107268710
  • Language : En, Es, Fr & De
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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.

Mathematical Concepts and Methods in Modern Biology

Mathematical Concepts and Methods in Modern Biology
Using Modern Discrete Models

by Raina Robeva,Terrell Hodge

  • Publisher : Academic Press
  • Release : 2013-02-26
  • Pages : 372
  • ISBN : 0124157939
  • Language : En, Es, Fr & De
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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

Advances in Bioinformatics and Computational Biology

Advances in Bioinformatics and Computational Biology
7th Brazilian Symposium on Bioinformatics, BSB 2012, Campo Grande, Brazil, August 15-17, 2012, Proceedings

by Marcilio C.P. de Souto,Maricel G. Kann

  • Publisher : Springer
  • Release : 2012-08-10
  • Pages : 204
  • ISBN : 3642319270
  • Language : En, Es, Fr & De
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This book constitutes the refereed proceedings of the 7th Brazilian Symposium on Bioinformatics, BSB 2012, held in Campo Grande, Brazil, in August 2012. The 16 regular papers presented were carefully reviewed and selected for inclusion in this book. It also contains a joint paper from two of the guest speakers. The Brazilian Symposium on Bioinformatics covers all aspects of bioinformatics and computational biology, including sequence analysis; motifs, and pattern matching; biological databases, data management, data integration, and data mining; biomedical text mining; structural, comparative, and functional genomics; personal genomics; protein structure, modeling, and simulation; gene identification, regulation and expression analysis; gene and protein interaction and networks; molecular docking; molecular evolution and phylogenetics; computational systems biology; computational proteomics; statistical analysis of molecular sequences; algorithms for problems in computational biology; applications in molecular biology, biochemistry, genetics, medicine, microbiology and associated subjects.

Algebraic Biology

Algebraic Biology
Second International Conference, AB 2007, Castle of Hagenberg, Austria, July 2-4, 2007, Proceedings

by Hirokazu Anai,Katsuhisa Horimoto

  • Publisher : Springer Science & Business Media
  • Release : 2007-06-22
  • Pages : 377
  • ISBN : 3540734325
  • Language : En, Es, Fr & De
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This book constitutes the refereed proceedings of the Second International Conference on Algebraic Biology, AB 2007, held at the Castle of Hagenberg, Austria in July 2007 as part of the RISC Summer 2007, organized by the Research Institute for Symbolic Computation. The 19 revised full papers presented together with 3 invited papers and 4 tutorials were carefully reviewed and selected from 40 submissions. The conference is the interdisciplinary forum for the presentation of research on all aspects of applications of symbolic computation (computer algebra, computational logic, and related methods) in biology as well as other problems in biology being approached with symbolic methods.

Analytic Combinatorics in Several Variables

Analytic Combinatorics in Several Variables
A Book

by Robin Pemantle,Mark C. Wilson

  • Publisher : Cambridge University Press
  • Release : 2013-05-31
  • Pages : 380
  • ISBN : 1107031575
  • Language : En, Es, Fr & De
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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.

Basic Phylogenetic Combinatorics

Basic Phylogenetic Combinatorics
A Book

by Andreas Dress,Katharina T. Huber,Jacobus Koolen

  • Publisher : Cambridge University Press
  • Release : 2012
  • Pages : 264
  • ISBN : 0521768322
  • Language : En, Es, Fr & De
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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.

Applications of Combinatorics and Graph Theory to the Biological and Social Sciences

Applications of Combinatorics and Graph Theory to the Biological and Social Sciences
A Book

by Fred Roberts

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 345
  • ISBN : 1468463810
  • Language : En, Es, Fr & De
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This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned.

Handbook of Finite Fields

Handbook of Finite Fields
A Book

by Gary L. Mullen,Daniel Panario

  • Publisher : CRC Press
  • Release : 2013-06-17
  • Pages : 1068
  • ISBN : 1439873828
  • Language : En, Es, Fr & De
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Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Combinatorial Commutative Algebra

Combinatorial Commutative Algebra
A Book

by Ezra Miller,Bernd Sturmfels

  • Publisher : Springer Science & Business Media
  • Release : 2006-03-30
  • Pages : 420
  • ISBN : 0387271031
  • Language : En, Es, Fr & De
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Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs