Mathematics

Phylogenetic Comparative Methods in R

Liam J. Revell & Luke J. Harmon

Graph Theory in America: The First Hundred Years

Robin Wilson, John J. Watkins & David J. Parks

An authoritative introduction to the latest comparative methods in evolutionary biology

Phylogenetic comparative methods are a suite of statistical approaches that enable biologists to analyze and better understand the evolutionary tree of life, and shed vital new light on patterns of divergence and common ancestry among all species on Earth. This textbook shows how to carry out phylogenetic comparative analyses in the R statistical computing environment. Liam Revell and Luke Harmon provide an incisive conceptual overview of each method along with worked examples using real data and challenge problems that encourage students to learn by doing.

• Covers every major method of modern phylogenetic comparative analysis in R • Explains the basics of R and discusses topics such as trait evolution, diversification, trait-dependent diversification, biogeography, and visualization • Features a wealth of exercises and challenge problems • Serves as an invaluable resource for students and researchers, with applications in ecology, evolution, anthropology, disease transmission, conservation biology, and a host of other areas • Written by two of today’s leading developers of phylogenetic comparative methods

Liam J. Revell is associate professor of biology at the University of Massachusetts, Boston, and an adjunct researcher at the Universidad Católica de la Santísima Concepción in Chile. Luke J. Harmon is professor of biological sciences at the University of Idaho and the author of Phylogenetic Comparative Methods: Learning from Trees. How a new mathematical field grew and matured in America

Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois.

Following graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included.

Robin Wilson is emeritus professor of mathematics at the Open University. His many books include Four Colors Suffice (Princeton). John J. Watkins is professor emeritus of mathematics at Colorado College. David J. Parks received a PhD in mathematics at the Open University. His doctoral thesis forms the basis of this book.

September 9780691219035 Paperback $50.00 | £40.00 9780691219028 Hardback $165.00 | £128.00 January 9780691194028 Hardback $35.00 | £28.00

320 pages. 147 b/w illus. 156 × 235 mm. ebook 9780691240657 Mathematics

Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts

Matthew Emerton & Toby Gee

PDE Control of String-Actuated Motion

Ji Wang & Miroslav Krstic

A foundational account of a new construction in the p-adic Langlands correspondence

Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur’s formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale (ϕ, Γ)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil–Mézard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.

Matthew Emerton is professor of mathematics at the University of Chicago. Toby Gee is professor of mathematics at Imperial College London. New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevators

Control applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states. In PDE Control of String-Actuated Motion, Ji Wang and Miroslav Krstic develop control algorithms for these complex PDE-ODE systems evolving on time-varying domains.

Motivated by physical systems, the book’s algorithms are designed to operate, with rigorous mathematical guarantees, in the presence of real-world challenges, such as unknown parameters, unmeasured distributed states, environmental disturbances, delays, and event-triggered implementations. The book leverages the power of the PDE backstepping approach and expands its scope in many directions.

Ji Wang is associate professor in the Department of Automation at Xiamen University, China, and a former postdoctoral scholar at the University of California, San Diego. Miroslav Krstic is Distinguished Professor at the University of California, San Diego, where he also serves as senior associate vice chancellor for research. He is a recipient of the Bellman, Reid, and Oldenburger awards, and is the coauthor of many books, including Delay-Adaptive Linear Control and Adaptive Control of Parabolic PDEs (both Princeton).

Annals of Mathematics Studies

January 9780691241357 Paperback $85.00 | £66.00 9780691241340 Hardback $180.00 | £140.00 Princeton Series in Applied Mathematics

November 9780691233499 Paperback $70.00 | £54.00 9780691233482 Hardback $165.00 | £128.00