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.
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
Probabilistic models are becoming increasingly important in analysing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analysing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it aims to be accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time present the state-of-the-art in this new and highly important field.
Interdisciplinary perspectives on the evolutionary and biological roots of syntax, describing current research on syntax in fields ranging from linguistics to neurology. Syntax is arguably the most human-specific aspect of language. Despite the proto-linguistic capacities of some animals, syntax appears to be the last major evolutionary transition in humans that has some genetic basis. Yet what are the elements to a scenario that can explain such a transition? In this book, experts from linguistics, neurology and neurobiology, cognitive psychology, ecology and evolutionary biology, and computer modeling address this question. Unlike most previous work on the evolution of language, Biological Foundations and Origin of Syntax follows through on a growing consensus among researchers that language can be profitably separated into a number of related and interacting but largely autonomous functions, each of which may have a distinguishable evolutionary history and neurological base. The contributors argue that syntax is such a function.The book describes the current state of research on syntax in different fields, with special emphasis on areas in which the findings of particular disciplines might shed light on problems faced by other disciplines. It defines areas where consensus has been established with regard to the nature, infrastructure, and evolution of the syntax of natural languages; summarizes and evaluates contrasting approaches in areas that remain controversial; and suggests lines for future research to resolve at least some of these disputed issues. Contributors Andrea Baronchelli, Derek Bickerton, Dorothy V. M. Bishop, Denis Bouchard, Robert Boyd, Jens Brauer, Ted Briscoe, David Caplan, Nick Chater, Morten H. Christiansen, Terrence W.Deacon, Francesco d'Errico, Anna Fedor, Julia Fischer, Angela D. Friederici, Tom Givón, Thomas Griffiths, Balázs Gulyás, Peter Hagoort, Austin Hilliard, James R. Hurford, Péter Ittzés, Gerhard Jäger, Herbert Jäger, Edith Kaan, Simon Kirby, Natalia L. Komarova, Tatjana Nazir, Frederick Newmeyer, Kazuo Okanoya, Csaba Plèh, Peter J. Richerson, Luigi Rizzi, Wolf Singer, Mark Steedman, Luc Steels, Szabolcs Számadó, Eörs Szathmáry, Maggie Tallerman, Jochen Triesch, Stephanie Ann White
"Few of us really appreciate the full power of math--the extent to which its influence is not only in every office and every home, but also in every courtroom and hospital ward. In this ... book, Kit Yates explores the true stories of life-changing events in which the application--or misapplication--of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupted by faulty algorithms; innocent victims of miscarriages of justice; and the unwitting victims of software glitches"--Publisher marketing.
This volume features highlights from the DIMACS Special Year on "Mathematical Support for Molecular Biology". Top researchers presented both new research results and comprehensive overviews on the use of mathematics (especially discrete mathematics) and theoretical computer science in molecular biology. The book provides a unique "snapshot" of this growing area of study. It will be of interest to both experts and novices seeking information on the state of the research.
To formalize the dynamics of living things is to search for invariants in a system that contains an irreducible aspect of “fuzziness”, because biological processes are characterized by their large statistical variability, and strong dependence on temporal and environmental factors. What is essential is the identification of what remains stable in a “living being” that is highly fluctuating. The use of mathematics is not limited to the use of calculating tools to simulate and predict results. It also allows us to adopt a way of thinking that is founded on concepts and hypotheses, leading to their discussion and validation. Instruments of mathematical intelligibility and coherence have gradually “fashioned” the view we now have of biological systems. Teaching and research, fundamental or applied, are now dependent on this new order known as Integrative Biology or Systems Biology.
Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.
