Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.

A preeminent physicist unveils a field-defining theory of the origins and purpose of life. Why are we alive? Most things in the universe aren't. And everything that is alive traces back to things that, puzzlingly, weren't. For centuries, the scientific question of life's origins has confounded us. But in Every Life Is on Fire, physicist Jeremy England argues that the answer has been under our noses the whole time, deep within the laws of thermodynamics. England explains how, counterintuitively, the very same forces that tend to tear things apart assembled the first living systems. But how life began isn't just a scientific question. We ask it because we want to know what it really means to be alive. So England, an ordained rabbi, uses his theory to examine how, if at all, science helps us find purpose in a vast and mysterious universe. In the tradition of Viktor Frankl's Man's Search for Meaning, Every Life Is on Fire is a profound testament to how something can come from nothing.

Life on earth is characterized by three striking phenomena that demand explanation: adaptation—the marvelous fit between organism and environment; diversity—the great variety of organisms; and complexity—the enormous intricacy of their internal structure. Natural selection explains adaptation. But what explains diversity and complexity? Daniel W. McShea and Robert N. Brandon argue that there exists in evolution a spontaneous tendency toward increased diversity and complexity, one that acts whether natural selection is present or not. They call this tendency a biological law—the Zero-Force Evolutionary Law, or ZFEL. This law unifies the principles and data of biology under a single framework and invites a reconceptualization of the field of the same sort that Newton’s First Law brought to physics. Biology’s First Law shows how the ZFEL can be applied to the study of diversity and complexity and examines its wider implications for biology. Intended for evolutionary biologists, paleontologists, and other scientists studying complex systems, and written in a concise and engaging format that speaks to students and interdisciplinary practitioners alike, this book will also find an appreciative audience in the philosophy of science.

This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.

This open access book features essays written by philosophers, biologists, ecologists and conservation scientists facing the current biodiversity crisis. Despite increasing communication, accelerating policy and management responses, and notwithstanding improving ecosystem assessment and endangered species knowledge, conserving biodiversity continues to be more a concern than an accomplished task. Why is it so?The overexploitation of natural resources by our species is a frequently recognised factor, while the short-term economic interests of governments and stakeholders typically clash with the burdens that implementing conservation actions imply. But this is not the whole story. This book develops a different perspective on the problem by exploring the conceptual challenges and practical defiance posed by conserving biodiversity, namely: on the one hand, the difficulties in defining what biodiversity is and characterizing that “thing” to which the word ‘biodiversity’ refers to; on the other hand, the reasons why assessing biodiversity and putting in place effective conservation actions is arduous.

This book provides an introduction to the role of diversity in complex adaptive systems. A complex system--such as an economy or a tropical ecosystem--consists of interacting adaptive entities that produce dynamic patterns and structures. Diversity plays a different role in a complex system than it does in an equilibrium system, where it often merely produces variation around the mean for performance measures. In complex adaptive systems, diversity makes fundamental contributions to system performance. Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system. Provides a concise and accessible introduction Shows how diversity underpins robustness and fuels tipping points Covers all types of diversity The essential primer on diversity in complex adaptive systems

Gaining access to high-quality data is a vital necessity in knowledge-based decision making. But data in its raw form often contains sensitive information about individuals. Providing solutions to this problem, the methods and tools of privacy-preserving data publishing enable the publication of useful information while protecting data privacy. Introduction to Privacy-Preserving Data Publishing: Concepts and Techniques presents state-of-the-art information sharing and data integration methods that take into account privacy and data mining requirements. The first part of the book discusses the fundamentals of the field. In the second part, the authors present anonymization methods for preserving information utility for specific data mining tasks. The third part examines the privacy issues, privacy models, and anonymization methods for realistic and challenging data publishing scenarios. While the first three parts focus on anonymizing relational data, the last part studies the privacy threats, privacy models, and anonymization methods for complex data, including transaction, trajectory, social network, and textual data. This book not only explores privacy and information utility issues but also efficiency and scalability challenges. In many chapters, the authors highlight efficient and scalable methods and provide an analytical discussion to compare the strengths and weaknesses of different solutions.