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Step into the World of Mathematics
Modern life is increasingly relying on digital technology, which in turn runs on mathematics. However, this underlying math is hidden from us. That is mostly a good thing since we do not want to be solving equations and calculating fractions just to get things done in our everyday business. But the mathematical details do matter for anyone who wants to understand how stuff works, or wishes to create something new in the jungle of apps and algorithms. This book takes a look at the mathematical models behind weather forecasting, climate change prediction, artificial intelligence, medical imaging and computer graphics. The reader is expected to have only a curious mind; technical math skills are not needed for enjoying this text.
Inverse Problems and Applications
This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.
Linear and Nonlinear Inverse Problems with Practical Applications
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Intelligent Diagnosis of Lung Cancer and Respiratory Diseases
Intelligent Diagnosis of Lung Cancer and Respiratory Diseases presents information about diseases of the respiratory system and the relevant diagnostic imaging techniques. The book focuses on intelligent diagnostic imaging systems. The first section of the book deals with the physiological underpinnings of 3 major diseases that affect the respiratory system: tuberculosis, lung cancer and COVID-19. This section also explains the basic principles of artificial Intelligence that support the diagnosis of these diseases. The next section presents applications of intelligent systems to support the imaging diagnosis of COVID-19 and lung cancer, with emphasis on digital health and telemedicine approaches. Each chapter is organized into a readable format, and is accompanied with detailed bibliographical information for further reading. This book is a reference for everyone seeking to understand how artificial intelligence can provide solutions for diagnostic support systems by processing and analyzing radiological images to improve early diagnosis and, consequently, lung disease prognosis.
Digital Mammography
This book constitutes the refereed proceedings of the 8th International Workshop on Digital Mammography, IWDM 2006, held in Manchester, UK, June 2006. The book presents 52 revised full papers and 34 revised poster papers, organized in topical sections on breast density, CAD, clinical practice, tomosynthesis, registration and multiple view mammmography, physics models, wavelet methods, full-field digital mammography, and segmentation.
Radon Transforms and Tomography
One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major t...
Nonlinear Wave Equations
This volume contains the proceedings of the AMS Special Session on Nonlinear Waves and Integrable Systems, held on April 13-14, 2013, at the University of Colorado, Boulder, Colorado. The field of nonlinear waves is an exciting area of modern mathematical research that also plays a major role in many application areas from physics and fluids. The articles in this volume present a diverse cross section of topics from this field including work on the Inverse Scattering Transform, scattering theory, inverse problems, numerical methods for dispersive wave equations, and analytic and computational methods for free boundary problems. Significant attention to applications is also given throughout the articles with an extensive presentation on new results in the free surface problem in fluids. This volume will be useful to students and researchers interested in learning current techniques in studying nonlinear dispersive systems from both the integrable systems and computational points of view.
Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis
This book comprehensively covers the topic of COVID-19 and other pandemics and epidemics data analytics using computational modelling. Biomedical and Health Informatics is an emerging field of research at the intersection of information science, computer science, and health care. The new era of pandemics and epidemics bring tremendous opportunities and challenges due to the plentiful and easily available medical data allowing for further analysis. The aim of pandemics and epidemics research is to ensure high-quality, efficient healthcare, better treatment and quality of life by efficiently analyzing the abundant medical, and healthcare data including patient’s data, electronic health recor...
Mathematical Methods And Models In Composites (Second Edition)
Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinfor...
Partial Differential Equation Methods for Image Inpainting
This book introduces the mathematical concept of partial differential equations (PDE) for virtual image restoration. It provides insight in mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation and numerical analysis. It is addressed towards generally informed mathematicians and graduate students in mathematics with an interest in image processing and mathematical analysis.
