# Algebraic And Combinatorial Computational Biology

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## Algebraic and Combinatorial Computational Biology

Author | : Raina Robeva,Matthew Macauley |

Publsiher | : Academic Press |

Total Pages | : 434 |

Release | : 2018-10-08 |

ISBN | : 0128140690 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Algebraic and Combinatorial Computational Biology Book Excerpt:**

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

## Patterns in Permutations and Words

Author | : Sergey Kitaev |

Publsiher | : Springer Science & Business Media |

Total Pages | : 494 |

Release | : 2011-08-30 |

ISBN | : 3642173330 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Patterns in Permutations and Words Book Excerpt:**

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.

## Combinatorial Computational Biology of RNA

Author | : Christian Reidys |

Publsiher | : Springer Science & Business Media |

Total Pages | : 258 |

Release | : 2010-10-29 |

ISBN | : 9780387767314 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Combinatorial Computational Biology of RNA Book Excerpt:**

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 Statistics for Computational Biology

Author | : L. Pachter,B. Sturmfels |

Publsiher | : Cambridge University Press |

Total Pages | : 420 |

Release | : 2005-08-22 |

ISBN | : 9780521857000 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Algebraic Statistics for Computational Biology Book Excerpt:**

This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

## Algebraic and Discrete Mathematical Methods for Modern Biology

Author | : Raina Robeva |

Publsiher | : Academic Press |

Total Pages | : 382 |

Release | : 2015-05-09 |

ISBN | : 0128012714 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Algebraic and Discrete Mathematical Methods for Modern Biology Book Excerpt:**

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

## The Real Object Hypothesis of Language The ROAL Model

Author | : Noury Bakrim |

Publsiher | : BoD - Books on Demand |

Total Pages | : 66 |

Release | : 2021-08-18 |

ISBN | : 2322403407 |

Category | : Language Arts & Disciplines |

Language | : EN, FR, DE, ES & NL |

**The Real Object Hypothesis of Language The ROAL Model Book Excerpt:**

In addition of proposing a model of language based on a bio-mathematical reduction within a synthesis between deduction, induction it suggests a much more important role of learning symmetry (especially iconicity) parallel to Universal Grammar. Without any theoretical megalomania, the model you will be discovering, reading and hopefully discussing hypothesizes two propositional principles with an important role of thermodynamic information : the shift from the bio-semiotic to the semiotic order along with the neural/dynamic mapping is embedded in the shift from thermodynamic laws without proposition (methodologically defined by hypothetic-probabilistic states of the ''internal observer'', Boltzmann-Bernoulli proposals and quantization) to biological and cultural consciousness (selection, combination, self-reference and symmetry etc etc)

## Models of the Mind

Author | : Grace Lindsay |

Publsiher | : Bloomsbury Publishing |

Total Pages | : 320 |

Release | : 2021-03-04 |

ISBN | : 1472966457 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Models of the Mind Book Excerpt:**

The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.

## Phenotypic Switching

Author | : Herbert Levine,Mohit Kumar Jolly,Prakash Kulkarni,Vidyanand Nanjundiah |

Publsiher | : Academic Press |

Total Pages | : 762 |

Release | : 2020-06-10 |

ISBN | : 012817997X |

Category | : Medical |

Language | : EN, FR, DE, ES & NL |

**Phenotypic Switching Book Excerpt:**

Phenotypic Switching: Implications in Biology and Medicine provides a comprehensive examination of phenotypic switching across biological systems, including underlying mechanisms, evolutionary significance, and its role in biomedical science. Contributions from international leaders discuss conceptual and theoretical aspects of phenotypic plasticity, its influence over biological development, differentiation, biodiversity, and potential applications in cancer therapy, regenerative medicine and stem cell therapy, among other treatments. Chapters discuss fundamental mechanisms of phenotypic switching, including transition states, cell fate decisions, epigenetic factors, stochasticity, protein-based inheritance, specific areas of human development and disease relevance, phenotypic plasticity in melanoma, prostate cancer, breast cancer, non-genetic heterogeneity in cancer, hepatitis C, and more. This book is essential for active researchers, basic and translational scientists, clinicians, postgraduates and students in genetics, human genomics, pathology, bioinformatics, developmental biology, evolutionary biology and adaptive opportunities in yeast. Thoroughly addresses the conceptual, experimental and translational aspects that underlie phenotypic plasticity Emphasizes quantitative approaches, nonlinear dynamics, mechanistic insights and key methodologies to advance phenotypic plasticity studies Features a diverse range of chapter contributions from international leaders in the field

## A Project Based Guide to Undergraduate Research in Mathematics

Author | : Pamela E. Harris,Erik Insko,Aaron Wootton |

Publsiher | : Springer Nature |

Total Pages | : 324 |

Release | : 2020-04-17 |

ISBN | : 3030378535 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**A Project Based Guide to Undergraduate Research in Mathematics Book Excerpt:**

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.

## Discrete and Topological Models in Molecular Biology

Author | : Nataša Jonoska,Masahico Saito |

Publsiher | : Springer Science & Business Media |

Total Pages | : 524 |

Release | : 2013-12-23 |

ISBN | : 3642401937 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Discrete and Topological Models in Molecular Biology Book Excerpt:**

Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

## Algebraic and Numeric Biology

Author | : Katsuhisa Horimoto,Masahiko Nakatsui,Nikolaj Popov |

Publsiher | : Springer |

Total Pages | : 185 |

Release | : 2012-01-13 |

ISBN | : 3642280676 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Algebraic and Numeric Biology Book Excerpt:**

This book constitutes the refereed proceedings of the 4th International Conference on Algebraic Biology, ANB 2010, held at the Castle of Hagenberg, Austria in July/August 2010. The conference is a follow up of the AB Conference. The 10 papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on mathematical modeling, system analysis and design, genomics, molecular structure analysis, automata theory, artificial intelligence, sequence analysis, automated reasoning, formal language and hybrid symbolic numerical methods.

## Using the Mathematics Literature

Author | : Kristine K. Fowler |

Publsiher | : CRC Press |

Total Pages | : 475 |

Release | : 2004-05-25 |

ISBN | : 9780824750350 |

Category | : Language Arts & Disciplines |

Language | : EN, FR, DE, ES & NL |

**Using the Mathematics Literature Book Excerpt:**

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

## Discrete Mathematics Days 2022

Author | : Luis Felipe Tabera Alonso |

Publsiher | : Ed. Universidad de Cantabria |

Total Pages | : 323 |

Release | : 2022-07-03 |

ISBN | : 8419024023 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Discrete Mathematics Days 2022 Book Excerpt:**

El congreso Discrete Mathematics Days (DMD20/22) tendrá lugar del 4 al 6 de julio de 2022, en la Facultad de Ciencias de la Universidad de Cantabria (Santander, España). Este congreso internacional se centra en avances dentro del campo de la Matemática discreta, incluyendo, de manera no exhaustiva: · Algoritmos y Complejidad · Combinatoria · Teoría de Códigos · Criptografía · Geometría Discreta y Computacional · Optimización Discreta · Teoría de Grafos · Problemas de localización discreta y temas relacionados Las ediciones anteriores de este evento se celebraros en Sevilla (2018) y Barcelona (2016), estos congresos heredan la tradición de las Jornadas de Matemática Discreta y Algorítmica (JMDA), el encuentro bienal en España en Matemática Discreta (desde 1998). Durante la celebración del congreso tendrán lugar cuatro conferencias plenarias, cuarenta y dos presentaciones orales y una sesión de once pósteres. Abstract The Discrete Mathematics Days (DMD20/22) will be held on July 4-6, 2022, at Facultad de Ciencias of the Universidad de Cantabria (Santander, Spain). The main focus of this international conference is on current topics in Discrete Mathematics, including (but not limited to): Algorithms and Complexity Combinatorics Coding Theory Cryptography Discrete and Computational Geometry Discrete Optimization Graph Theory Location and Related Problems The previous editions were held in Sevilla in 2018 and in Barcelona in 2016, inheriting the tradition of the Jornadas de Matemática Discreta y Algorítmica (JMDA), the Spanish biennial meeting (since 1998) on Discrete Mathematics. The program consists on four plenary talks, 42 contributed talks and a poster session with 11 contributions.

## Mathematical Concepts and Methods in Modern Biology

Author | : Raina Robeva,Terrell Hodge |

Publsiher | : Academic Press |

Total Pages | : 372 |

Release | : 2013-02-26 |

ISBN | : 0124157939 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Mathematical Concepts and Methods in Modern Biology Book Excerpt:**

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

## Algebraic Statistics

Author | : Seth Sullivant |

Publsiher | : American Mathematical Soc. |

Total Pages | : 490 |

Release | : 2018-11-19 |

ISBN | : 1470435179 |

Category | : Geometry, Algebraic |

Language | : EN, FR, DE, ES & NL |

**Algebraic Statistics Book Excerpt:**

Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

## Markov Bases in Algebraic Statistics

Author | : Satoshi Aoki,Hisayuki Hara,Akimichi Takemura |

Publsiher | : Springer Science & Business Media |

Total Pages | : 300 |

Release | : 2012-07-25 |

ISBN | : 1461437199 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Markov Bases in Algebraic Statistics Book Excerpt:**

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.

## Essentials of Tropical Combinatorics

Author | : Michael Joswig |

Publsiher | : American Mathematical Society |

Total Pages | : 398 |

Release | : 2021-12-08 |

ISBN | : 1470466538 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Essentials of Tropical Combinatorics Book Excerpt:**

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

## Foundations of Computational Mathematics Hong Kong 2008

Author | : Felipe Cucker,Allan Pinkus,Michael J. Todd |

Publsiher | : Cambridge University Press |

Total Pages | : 276 |

Release | : 2009-07-02 |

ISBN | : 0521739705 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Foundations of Computational Mathematics Hong Kong 2008 Book Excerpt:**

Surveys and summaries of the latest research in numerical analysis, optimization, computer algebra and scientific computing.

## Introduction to Computational Biology

Author | : Michael S. Waterman |

Publsiher | : CRC Press |

Total Pages | : 448 |

Release | : 1995-06-01 |

ISBN | : 9780412993916 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Introduction to Computational Biology Book Excerpt:**

Biology is in the midst of a era yielding many significant discoveries and promising many more. Unique to this era is the exponential growth in the size of information-packed databases. Inspired by a pressing need to analyze that data, Introduction to Computational Biology explores a new area of expertise that emerged from this fertile field- the combination of biological and information sciences. This introduction describes the mathematical structure of biological data, especially from sequences and chromosomes. After a brief survey of molecular biology, it studies restriction maps of DNA, rough landmark maps of the underlying sequences, and clones and clone maps. It examines problems associated with reading DNA sequences and comparing sequences to finding common patterns. The author then considers that statistics of pattern counts in sequences, RNA secondary structure, and the inference of evolutionary history of related sequences. Introduction to Computational Biology exposes the reader to the fascinating structure of biological data and explains how to treat related combinatorial and statistical problems. Written to describe mathematical formulation and development, this book helps set the stage for even more, truly interdisciplinary work in biology.

## Lectures on Algebraic Statistics

Author | : Mathias Drton,Bernd Sturmfels,Seth Sullivant |

Publsiher | : Springer Science & Business Media |

Total Pages | : 172 |

Release | : 2009-04-25 |

ISBN | : 3764389052 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Lectures on Algebraic Statistics Book Excerpt:**

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.