In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions, that can be solved by using a non trivial brute-force approach. Given a metabolic network, each individual story should explain how some interesting metabolites are derived from some others through a chain of reactions, by keeping all alternative pathways between sources and targets. Enumerating cycles or paths in an undirected graph, such as a protein-protein interaction undirected network, is an example of an enumeration problem in which all the solutions can be listed through an optimal algorithm, i.e. the time required to list all the solutions is dominated by the time to read the graph plus the time required to print all of them. By extending this result to directed graphs, it would be possible to deal more efficiently with feedback loops and signed paths analysis in signed or interaction directed graphs, such as gene regulatory networks. Finally, enumerating mouths or bubbles with a source s in a directed graph, that is enumerating all the two vertex-disjoint directed paths between the source s and all the possible targets, is an example of an enumeration problem in which all the solutions can be listed through a linear delay algorithm, meaning that the delay between any two consecutive solutions is linear, by turning the problem into a constrained cycle enumeration problem. Such patterns, in a de Bruijn graph representation of the reads obtained by sequencing, are related to polymorphisms in DNA- or RNA-seq data.

For well over a century, academic disciplines have studied human behavior using quantitative information. Until recently, however, the humanities have remained largely immune to the use of data—or vigorously resisted it. Thanks to new developments in computer science and natural language processing, literary scholars have embraced the quantitative study of literary works and have helped make Digital Humanities a rapidly growing field. But these developments raise a fundamental, and as yet unanswered question: what is the meaning of literary quantity? In Enumerations, Andrew Piper answers that question across a variety of domains fundamental to the study of literature. He focuses on the elementary particles of literature, from the role of punctuation in poetry, the matter of plot in novels, the study of topoi, and the behavior of characters, to the nature of fictional language and the shape of a poet’s career. How does quantity affect our understanding of these categories? What happens when we look at 3,388,230 punctuation marks, 1.4 billion words, or 650,000 fictional characters? Does this change how we think about poetry, the novel, fictionality, character, the commonplace, or the writer’s career? In the course of answering such questions, Piper introduces readers to the analytical building blocks of computational text analysis and brings them to bear on fundamental concerns of literary scholarship. This book will be essential reading for anyone interested in Digital Humanities and the future of literary study.

Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools. Two major themes run in parallel through the book, generating functions and group theory. The former theme takes enumerative sequences and then uses analytic tools to discover how they are made up. Group theory provides a concise introduction to groups and illustrates how the theory can be used to count the number of symmetries a particular object has. These enrich and extend basic group ideas and techniques. The authors present their material through examples that are carefully chosen to establish key results in a natural setting. The aim is to progressively build fundamental theorems and techniques. This development is interspersed with exercises that consolidate ideas and build confidence. Some exercises are linked to particular sections while others range across a complete chapter. Throughout, there is an attempt to present key enumerative ideas in a graphic way, using diagrams to make them immediately accessible. The development assumes some basic group theory, a familiarity with analytic functions and their power series expansion along with some basic linear algebra.

Penetration Tester's Open Source Toolkit, Third Edition, discusses the open source tools available to penetration testers, the ways to use them, and the situations in which they apply. Great commercial penetration testing tools can be very expensive and sometimes hard to use or of questionable accuracy. This book helps solve both of these problems. The open source, no-cost penetration testing tools presented do a great job and can be modified by the student for each situation. This edition offers instruction on how and in which situations the penetration tester can best use them. Real-life scenarios support and expand upon explanations throughout. It also presents core technologies for each type of testing and the best tools for the job. The book consists of 10 chapters that covers a wide range of topics such as reconnaissance; scanning and enumeration; client-side attacks and human weaknesses; hacking database services; Web server and Web application testing; enterprise application testing; wireless penetrating testing; and building penetration test labs. The chapters also include case studies where the tools that are discussed are applied. New to this edition: enterprise application testing, client-side attacks and updates on Metasploit and Backtrack. This book is for people who are interested in penetration testing or professionals engaged in penetration testing. Those working in the areas of database, network, system, or application administration, as well as architects, can gain insights into how penetration testers perform testing in their specific areas of expertise and learn what to expect from a penetration test. This book can also serve as a reference for security or audit professionals. - Details current open source penetration testing tools - Presents core technologies for each type of testing and the best tools for the job - New to this edition: Enterprise application testing, client-side attacks and updates on Metasploit and Backtrack

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

The Cambridge Descartes Lexicon is the definitive reference source on René Descartes, 'the father of modern philosophy' and arguably among the most important philosophers of all time. Examining the full range of Descartes' achievements and legacy, it includes 256 in-depth entries that explain key concepts relating to his thought. Cumulatively they uncover interpretative disputes, trace his influences, and explain how his work was received by critics and developed by followers. There are entries on topics such as certainty, cogito ergo sum, doubt, dualism, free will, God, geometry, happiness, human being, knowledge, Meditations on First Philosophy, mind, passion, physics, and virtue, which are written by the largest and most distinguished team of Cartesian scholars ever assembled for a collaborative research project - 92 contributors from ten countries.

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.