Understanding ion channel gating has been a goal of researchers since Hodgkin and Huxley's classic publication in 1952, but the gating mechanism has remained elusive. In this book it is shown how electrons can control gating. Introducing the electron as a gating agent requires amplification, but until now there has been no appropriate mechanism for amplification.

John Roemer points out that there are two views of equality of opportunity that are widely held today. The first, which he calls the nondiscrimination principle, states that in the competition for positions in society, individuals should be judged only on attributes relevant to the performance of the duties of the position in question. Attributes such as race or sex should not be taken into account. The second states that society should do what it can to level the playing field among persons who compete for positions, especially during their formative years, so that all those who have the relevant potential attributes can be considered.

Common to both positions is that at some point the principle of equal opportunity holds individuals accountable for achievements of particular objectives, whether they be education, employment, health, or income. Roemer argues that there is consequently a "before" and an "after" in the notion of equality of opportunity: before the competition starts, opportunities must be equalized, by social intervention if need be; but after it begins, individuals are on their own. The different views of equal opportunity should be judged according to where they place the starting gate which separates "before" from "after." Roemer works out in a precise way how to determine the location of the starting gate in the different views.

These three elegant essays develop principles central to the understanding of the diverse ways in which imperfect information affects the distribution of resources, incentives, and the evaluation of economic policy. The first concerns the special role that information plays in the allocation process when it is possible to improve accuracy through private investment. The common practice of hiring “experts” whose information is presumably much better than their clients' is analyzed. Issues of cooperative behavior when potential group members possess diverse pieces of information are addressed. Emphasis is placed on the adaptation of the “core” concept from game theory to the resource allocation model with differential information.

The second essay deals with the extent to which agents can influence the random events they face. This is known as moral hazard, and in its presence there is a potential inefficiency in the economic system. Two special models are studied: the role of moral hazard in a monetary economy, and the role of an outside adjudicatory agency that has the power to enforce fines and compensation.

The final essay discusses the problem of certainty equivalence in economic policy. Conditions under which a full stochastic optimization can be calculated by solving a related, much simpler “certainty equivalence” problem are developed. The reduction in the complexity of calculation involved is very great compared with the potential loss of efficiency.

Essential Demographic Methods brings to readers the full range of ideas and skills of demographic analysis that lie at the core of social sciences and public health. Classroom tested over many years, filled with fresh data and examples, this approachable text is tailored to the needs of beginners, advanced students, and researchers alike. An award-winning teacher and eminent demographer, Kenneth Wachter uses themes from the individual lifecourse, history, and global change to convey the meaning of concepts such as exponential growth, cohorts and periods, lifetables, population projection, proportional hazards, parity, marity, migration flows, and stable populations. The presentation is carefully paced and accessible to readers with knowledge of high-school algebra. Each chapter contains original problem sets and worked examples.

From the most basic concepts and measures to developments in spatial demography and hazard modeling at the research frontier, Essential Demographic Methods brings out the wider appeal of demography in its connections across the sciences and humanities. It is a lively, compact guide for understanding quantitative population analysis in the social and biological world.

At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations. Evolutionary Dynamics is concerned with these equations of life. In this book, Martin A. Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem.

Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner’s Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system—and everything that arises as a consequence of living systems—in terms of evolutionary dynamics.

This book is a companion volume to Dynamic Macroeconomic Theory by Thomas J. Sargent. It provides scrimmages in dynamic macroeconomic theory--precisely the kind of drills that people will need in order to learn the techniques of dynamic programming and its applications to economics. By doing these exercises, the reader can acquire the ability to put the theory to work in a variety of new situations, build technical skill, gain experience in fruitful ways of setting up problems, and learn to distinguish cases in which problems are well posed from cases in which they are not.The basic framework provided by variants of a dynamic general equilibrium model is used to analyze problems in macroeconomics and monetary economics. An equilibrium model provides a mapping from parameters of preferences, technologies, endowments, and "rules of the game" to a probability model for time series. The rigor of the logical connections between theory and observations that the mapping provides is an attractive feature of dynamic equilibrium, or "rational expectations," models. This book gives repeated and varied practice in constructing and interpreting this mapping.