Fourier Methods in Imaging

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9

This book presents current theories of diffraction, imaging, and related topics based on Fourier analysis and synthesis techniques, which are essential for understanding, analyzing, and synthesizing modern imaging, optical communications and networking, as well as micro/nano systems. Applications covered include tomography; magnetic resonance imaging; synthetic aperture radar (SAR) and interferometric SAR; optical communications and networking devices; computer-generated holograms and analog holograms; and wireless systems using EM waves.

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical point of view. Some aspects, linear prediction for example, are explained here thoroughly for the first time.

The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.

As rapid advances in biotechnology occur, there is a need for a pedagogical tool to aid current students and laboratory professionals in biotechnological methods; Methods in Biotechnology is an invaluable resource for those students and professionals. Methods in Biotechnology engages the reader by implementing an active learning approach, provided advanced study questions, as well as pre- and post-lab questions for each lab protocol. These self-directed study sections encourage the reader to not just perform experiments but to engage with the material on a higher level, utilizing critical thinking and troubleshooting skills. This text is broken into three sections based on level – Methods in Biotechnology, Advanced Methods in Biotechnology I, and Advanced Methods in Biotechnology II. Each section contains 14-22 lab exercises, with instructor notes in appendices as well as an answer guide as a part of the book companion site. This text will be an excellent resource for both students and laboratory professionals in the biotechnology field.

Imaging in Endocrinology will provide endocrinologists and radiologists of all levels with an outstanding diagnostic imaging atlas to aid them in the diagnosis and management of all the major endocrine diseases they are likely to encounter. In full colour throughout, the 300 high-quality images consist of CT scans, MRI, NMR and histopathology slides, and are arranged by each specific endocrine condition, resulting in a visually outstanding and easily accessible tool that guides the user through exactly what to look out for and provides a practical and extremely useful aid in helping them formulate a diagnosis. Every major endocrine condition is covered in a specific section, including diseases of the thyroid, pituitary, reproductive and adrenal glands, the pancreas, bone metabolism problems, and the various forms of endocrine cancers. Each disease covered will offer a comparison of the normal findings so as to further assist in diagnosis. An accompanying website contains an online slide-atlas of all the figures in the book, to allow users to download all figures for use in presentations. Led by Paolo Pozzilli, an internationally-recognised expert in this field, the authors have assembled a wonderful collection of images that will be greatly valued by endocrinologists and radiologists alike, ensuring this is the perfect tool to consult when assessing patients with endocrine disease.

An introduction to classical biostatistical methods in epidemiology Biostatistical Methods in Epidemiology provides an introduction to a wide range of methods used to analyze epidemiologic data, with a focus on nonregression techniques. The text includes an extensive discussion of measurement issues in epidemiology, especially confounding. Maximum likelihood, Mantel-Haenszel, and weighted least squares methods are presented for the analysis of closed cohort and case-control data. Kaplan-Meier and Poisson methods are described for the analysis of censored survival data. A justification for using odds ratio methods in case-control studies is provided. Standardization of rates is discussed and the construction of ordinary, multiple decrement and cause-deleted life tables is outlined. Sample size formulas are given for a range of epidemiologic study designs. The text ends with a brief overview of logistic and Cox regression. Other highlights include: Many worked examples based on actual data Discussion of exact methods Recommendations for preferred methods Extensive appendices and references Biostatistical Methods in Epidemiology provides an excellent introduction to the subject for students, while also serving as a comprehensive reference for epidemiologists and other health professionals. For more information, visit www.wiley.com/mathematics

Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models: Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book.

A thorough, practical reference on the social patterns behind health outcomes Methods in Social Epidemiology provides students and professionals with a comprehensive reference for studying the social distribution and social determinants of health. Covering the theory, models, and methods used to measure and analyze these phenomena, this book serves as both an introduction to the field and a practical manual for data collection and analysis. This new second edition has been updated to reflect the field's tremendous growth in recent years, including advancements in statistical modeling and study designs. New chapters delve into genetic methods, structural cofounding, selection bias, network methods, and more, including new discussion on qualitative data collection with disadvantaged populations. Social epidemiology studies the way society's innumerable social interactions, both past and present, yields different exposures and health outcomes between individuals within populations. This book provides a thorough, detailed overview of the field, with expert guidance toward the real-world methods that fuel the latest advances. Identify, measure, and track health patterns in the population Discover how poverty, race, and socioeconomic factors become risk factors for disease Learn qualitative data collection techniques and methods of statistical analysis Examine up-to-date models, theory, and frameworks in the social epidemiology sphere As the field continues to evolve, researchers continue to identify new disease-specific risk factors and learn more about how the social system promotes and maintains well-known exposure disparities. New technology in data science and genomics allows for more rigorous investigation and analysis, while the general thinking in the field has become more targeted and attentive to causal inference and core assumptions behind effect identification. It's an exciting time to be a part of the field, and Methods in Social Epidemiology provides a solid reference for any student, researcher, or faculty in public health.

Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.