Their son, mostly for fun, writes this collection of vignettes about two prominent scientists. The forward includes a description of the two, summarizing their character and their careers. The summary contains an explanation of the title, Entropy Squared. The forward ends with remarks about the accuracy of the vignettes. Some vignettes include a representation of the impact on the son and some have historical significance. The first two sections concern Gttingen, Germany, from where that American, Joe, as a fellow student put it, acquired his wife. The first section of Gttingen vignettes is from the time of meeting and from visits until World War II. The second is from after the War. Marias career at Sarah Lawrence College separates sections of their supporting the World War II war effort, Joe at the Ballistics Research Laboratory of Aberdeen Proving Grounds and Maria with the Manhattan, nuclear bomb, Project. The Sarah Lawrence College section goes beyond memories because biographers have said little about Marias time at Sarah Lawrence. Sections concerning each are followed by a section on Maria receiving of the Nobel Prize. The conclusion is a memorial to Joe.

The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly dispara

A compilation of sixty biographical sketches of influential female scientists, discussing topics like the state of the modern female scientist and the underrepresentation of women at the higher levels of academia.

"This work strikes a balance between the pure functional aspects of F# and the object-oriented and imperative features that make it so useful in practice, enable .NET integration, and make large-scale data processing possible." —Thore Graepel, PhD, Researcher, Microsoft Research Ltd. Over the next five years, F# is expected to become one of the world's most popular functional programming languages for scientists of all disciplines working on the Windows platform. F# is free and, unlike MATLAB® and other software with numerical/scientific origins, is a full-fledged programming language. Developed in consultation with Don Syme of Microsoft Research Ltd.—who wrote the language—F# for Scientists explains and demonstrates the powerful features of this important new programming language. The book assumes no prior experience and guides the reader from the basics of computer programming to the implementation of state-of-the-art algorithms. F# for Scientists begins with coverage of introductory material in the areas of functional programming, .NET, and scientific computing, and goes on to explore: Program structure Optimization Data structures Libraries Numerical analysis Databases Input and output Interoperability Visualization Screenshots of development using Visual Studio are used to illustrate compilation, debugging, and interactive use, while complete examples of a few whole programs are included to give readers a complete view of F#'s capabilities. Written in a clear and concise style, F# for Scientists is well suited for researchers, scientists, and developers who want to program under the Windows platform. It also serves as an ideal supplemental text for advanced undergraduate and graduate students with a background in science or engineering.

A modern, comprehensive treatment of latent class and latent transition analysis for categorical data On a daily basis, researchers in the social, behavioral, and health sciences collect information and fit statistical models to the gathered empirical data with the goal of making significant advances in these fields. In many cases, it can be useful to identify latent, or unobserved, subgroups in a population, where individuals' subgroup membership is inferred from their responses on a set of observed variables. Latent Class and Latent Transition Analysis provides a comprehensive and unified introduction to this topic through one-of-a-kind, step-by-step presentations and coverage of theoretical, technical, and practical issues in categorical latent variable modeling for both cross-sectional and longitudinal data. The book begins with an introduction to latent class and latent transition analysis for categorical data. Subsequent chapters delve into more in-depth material, featuring: A complete treatment of longitudinal latent class models Focused coverage of the conceptual underpinnings of interpretation and evaluationof a latent class solution Use of parameter restrictions and detection of identification problems Advanced topics such as multi-group analysis and the modeling and interpretation of interactions between covariates The authors present the topic in a style that is accessible yet rigorous. Each method is presented with both a theoretical background and the practical information that is useful for any data analyst. Empirical examples showcase the real-world applications of the discussed concepts and models, and each chapter concludes with a "Points to Remember" section that contains a brief summary of key ideas. All of the analyses in the book are performed using Proc LCA and Proc LTA, the authors' own software packages that can be run within the SAS® environment. A related Web site houses information on these freely available programs and the book's data sets, encouraging readers to reproduce the analyses and also try their own variations. Latent Class and Latent Transition Analysis is an excellent book for courses on categorical data analysis and latent variable models at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the social, behavioral, and health sciences who conduct latent class and latent transition analysis in their everyday work.

Bistatic radar consists of a radar system which comprises a transmitter and receiver which are separated by a distance comparable to the expected target distance. This book provides a general theoretical description of such bistatic technology in the context of synthetic aperture, inverse synthetic aperture and forward scattering radars from the point of view of analytical geometrical and signal formation as well as processing theory. Signal formation and image reconstruction algorithms are developed with the application of high informative linear frequency and phase code modulating techniques, and numerical experiments that confirm theoretical models are carried out. The authors suggest the program implementation of developed algorithms. A theoretical summary of the latest results in the field of bistatic radars is provided, before applying an analytical geometrical description of scenarios of bistatic synthetic aperture, inverse synthetic aperture and forward scattering radars with cooperative and non-cooperative transmitters. Signal models with linear frequency and phase code modulation are developed, and special phase modulations with C/A (coarse acquisition) and P (precision) of GPS satellite transmitters are considered. The authors suggest Matlab implementations of all geometrical models and signal formation and processing algorithms. Contents 1. Bistatic Synthetic Aperture Radar (BSAR) Survey. 2. BSAR Geometry. 3. BSAR Waveforms and Signal Models. 4. BSAR Image Reconstruction Algorithms. 5. Analytical Geometrical Determination of BSAR Resolution. 6. BSAR Experimental Results. 7. BSAR Matlab Implementation. A general theoretical description of bistatic technology within the scope of synthetic aperture, inverse synthetic aperture and forward scattering radars from the point of view of analytical geometrical and signal formation and processing theory. Signal formation and image reconstruction algorithms are developed in this title, with application of high informative linear frequency and phase code modulating techniques. Numerical experiments that confirm theoretical models are carried out and the authors suggest program implementation for the algorithms developed.

Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network design, river flow forecasting, floods and droughts, river network analysis, infiltration, soil moisture, sediment transport, surface water and groundwater quality modeling, ecosystems modeling, water distribution networks, environmental and water resources management, and parameter estimation. Such applications have used several different entropy formulations, such as Shannon, Tsallis, Rényi, Burg, Kolmogorov, Kapur, configurational, and relative entropies, which can be derived in time, space, or frequency domains. More recently, entropy-based concepts have been coupled with other theories, including copula and wavelets, to study various issues associated with environmental and water resources systems. Recent studies indicate the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering, including establishing and explaining physical connections between theory and reality. The objective of this Special Issue is to provide a platform for compiling important recent and current research on the applications of entropy theory in environmental and water engineering. The contributions to this Special Issue have addressed many aspects associated with entropy theory applications and have shown the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering.

This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.

"A work of scientific substance and critical wisdom, developed in the urbane idiom of a French scholar." -- J. T. Fraser, founder, International Society for the Study of Time "This is the book for those of us who couldn't wade completely through Hawking's A Brief History of Time and now have it collecting dust on our bookshelves. Well written, thought-provoking, and, most important, understandable." -- Michael Epstein, analytical spectroscopist/chemist, National Institute of Standards and Technology What is time? Does it really pass? These and other fascinating questions about the nature of time animate a continuing philosophical and scientific debate. In this popular French book, now available for the first time in English; my Lestienne moves to make the bewildering concepts of time accessible--and interesting. He uses Galileo, Newton, Einstein, and others to demonstrate how the concepts of causality and entropy became so pervasive that they eventually were substituted for time itself. He also shows how recent advances in astronomy, particle physics, developmental life sciences, and the neurosciences are helping to shape a new philosophical vision of time.

Integrates fundamental concepts with experimental data and practical applications, including worked examples and end-of-chapter problems.