In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic – and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training – all you need is the discipline to follow logical arguments and a pen in your hand.

In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic – and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training – all you need is the discipline to follow logical arguments and a pen in your hand.

This book constitutes the refereed proceedings of the Second International Bioinformatics, WABI 2002, held in Rome, Italy, in September 2002.The 39 revised full papers presented together with an full invited paper were carefully reviewed and selected from 83 submissions. Among the topics addressed are exact and approximate algorithms for genomics, genetics, sequence analysis, gene and signal recognition, alignment, molecular evolution, phylogenetics, structure determination and prediction, gene expression and gene networks, proteomics, functional genomics, and drug design.

This volume presents the proceedings of the Fifth Annual Symposium on Combinatorial Pattern Matching, held at Asilomar, California, in June 1994. The 26 selected papers in this volume are organized in chapters on Alignments, Various Matchings, Combinatorial Aspects, and Bio-Informatics. Combinatorial Pattern Matching addresses issues of searching and matching of strings and more complicated patterns, as for example trees. The goal is to derive non-trivial combinatorial properties for such structures and then to exploit these properties in order to achieve superior performance for the corresponding computational problems. In recent years, combinatorial pattern matching has developed into a full-fledged area of algorithmics and is expected to grow even further during the next years.

Traditionally an area of study in computer science, string algorithms have, in recent years, become an increasingly important part of biology, particularly genetics. This volume is a comprehensive look at computer algorithms for string processing. In addition to pure computer science, Gusfield adds extensive discussions on biological problems that are cast as string problems and on methods developed to solve them. This text emphasizes 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.

Integer linear programming (ILP) is a versatile modeling and optimization technique that is increasingly used in non-traditional ways in biology, with the potential to transform biological computation. However, few biologists know about it. This how-to and why-do text introduces ILP through the lens of computational and systems biology. It uses in-depth examples from genomics, phylogenetics, RNA, protein folding, network analysis, cancer, ecology, co-evolution, DNA sequencing, sequence analysis, pedigree and sibling inference, haplotyping, and more, to establish the power of ILP. This book aims to teach the logic of modeling and solving problems with ILP, and to teach the practical 'work flow' involved in using ILP in biology. Written for a wide audience, with no biological or computational prerequisites, this book is appropriate for entry-level and advanced courses aimed at biological and computational students, and as a source for specialists. Numerous exercises and accompanying software (in Python and Perl) demonstrate the concepts.