Models For Life

An overview of current models of biological systems, reflecting the major advances that have been made over the past decade.

In this candid and witty autobiography, Nobel laureate Herbert A. Simon looks at his distinguished and varied career, continually asking himself whether (and how) what he learned as a scientist helps to explain other aspects of his life. A brilliant polymath in an age of increasing specialization, Simon is one of those rare scholars whose work defines fields of inquiry. Crossing disciplinary lines in half a dozen fields, Simon's story encompasses an explosion in the information sciences, the transformation of psychology by the information-processing paradigm, and the use of computer simulation for modeling the behavior of highly complex systems. Simon's theory of bounded rationality led to a Nobel Prize in economics, and his work on building machines that think—based on the notion that human intelligence is the rule-governed manipulation of symbols—laid conceptual foundations for the new cognitive science. Subsequently, contrasting metaphors of the maze (Simon's view) and of the mind (neural nets) have dominated the artificial intelligence debate. There is also a warm account of his successful marriage and of an unconsummated love affair, letters to his children, columns, a short story, and political and personal intrigue in academe.

The authors of this monograph have developed a large and important class of survival analysis models that generalize most of the existing models. In a unified, systematic presentation, this monograph fully details those models and explores areas of accelerated life testing usually only touched upon in the literature. Accelerated Life Models:

David Michaels, a solitary widower, is a returning college student who models nude for art classes part time. He gets more than he bargained for when he shares the platform with another model, the sometimes wild and always vivacious Lydia Nelson.

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Now in paperback, “a compelling, accessible, and provocative piece of work that forces us to question many of our assumptions” (Gillian Tett, author of Fool’s Gold). Quants, physicists working on Wall Street as quantitative analysts, have been widely blamed for triggering financial crises with their complex mathematical models. Their formulas were meant to allow Wall Street to prosper without risk. But in this penetrating insider’s look at the recent economic collapse, Emanuel Derman—former head quant at Goldman Sachs—explains the collision between mathematical modeling and economics and what makes financial models so dangerous. Though such models imitate the style of physics and employ the language of mathematics, theories in physics aim for a description of reality—but in finance, models can shoot only for a very limited approximation of reality. Derman uses his firsthand experience in financial theory and practice to explain the complicated tangles that have paralyzed the economy. Models.Behaving.Badly. exposes Wall Street’s love affair with models, and shows us why nobody will ever be able to write a model that can encapsulate human behavior.

A fascinating consideration of the work of life models and the models’ own perspectives on their craft.

The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.