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Inverse Problems and Data Assimilation
A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.
Inverse Problems and Data Assimilation
This concise introduction provides an entry point to the world of inverse problems and data assimilation for advanced undergraduates and beginning graduate students in the mathematical sciences. It will also appeal to researchers in science and engineering who are interested in the systematic underpinnings of methodologies widely used in their disciplines. The authors examine inverse problems and data assimilation in turn, before exploring the use of data assimilation methods to solve generic inverse problems by introducing an artificial algorithmic time. Topics covered include maximum a posteriori estimation, (stochastic) gradient descent, variational Bayes, Monte Carlo, importance sampling and Markov chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended and ensemble Kalman filters, and particle filters for data assimilation. The book contains a wealth of examples and exercises, and can be used to accompany courses as well as for self-study.
An Introduction to Sequential Monte Carlo
This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general...
Data Assimilation
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organize...
Künneth Geometry
An elegant introduction to symplectic geometry and Lagrangian foliations, including a systematic study of bi-Lagrangian geometry.
Annual Report
None
Automated Planning and Acting
This book presents the most recent and advanced techniques for creating autonomous AI systems capable of planning and acting effectively.
Ethnopharmacology
Ethnopharmacology is one of the world’s fastest-growing scientific disciplines encompassing a diverse range of subjects. It links natural sciences research on medicinal, aromatic and toxic plants with socio-cultural studies and has often been associated with the development of new drugs. The Editors of Ethnopharmacology have assembled an international team of renowned contributors to provide a critical synthesis of the substantial body of new knowledge and evidence on the subject that has emerged over the past decade. Divided into three parts, the book begins with an overview of the subject including a brief history, ethnopharmacological methods, the role of intellectual property protectio...
