This book provides a comprehensive introduction to the techniques, tools and methods for inverse problems and data assimilation. Inverse problems are widespread today in science and technology, and this book is written at the interface between mathematics and applications, designed for students, researchers and developers in mathematics, physics, engineering, acoustics, electromagnetics, meteorology, biology, environmental and other applied sciences.

Basic analytic questions and tools are introduced, as well as a wide variety of concepts, methods and approaches to formulate and solve inverse problems, among others classical regularization and iterative methods, but also more recent approaches like sampling and probe methods, field reconstruction techniques in acoustics and electromagnetics and source reconstruction. In the framework of data assimilation, stochastic and deterministic methods are becoming more and more intertwined both variational and ensemble data assimilation methods are introduced, as well as stochastic and deterministic viewpoints and analysis. Applications range from neural kernel reconstruction to inverse acoustic and electromagnetic scattering and thermography, from magnetic tomography for fuel cells or in a medical environment to weather forecasting and earth science. OCTAVE /MATLAB codes are included, which serve as a first step towards simulations and more sophisticated inversion or data assimilation algorithms.

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Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth.

In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener-Hopf algebras and graph C*-algebras.]]>

Intelligent systems often depend on data provided by information agents, for example, sensor data or crowdsourced human computation. Providing accurate and relevant data requires costly effort that agents may not always be willing to provide. Thus, it becomes important not only to verify the correctness of data, but also to provide incentives so that agents that provide high-quality data are rewarded while those that do not are discouraged by low rewards.

We cover different settings and the assumptions they admit, including sensing, human computation, peer grading, reviews, and predictions. We survey different incentive mechanisms, including proper scoring rules, prediction markets and peer prediction, Bayesian Truth Serum, Peer Truth Serum, Correlated Agreement, and the settings where each of them would be suitable. As an alternative, we also consider reputation mechanisms. We complement the game-theoretic analysis with practical examples of applications in prediction platforms, community sensing, and peer grading.

]]>The first part of this volume gathers the lecture notes of the courses of the "XVII Escuela Hispano-Francesa", held in Gij#65533;n, Spain, in June 2016. Each chapter is devoted to an advanced topic and presents state-of-the-art research in a didactic and self-contained way. Young researchers will find a complete guide to beginning advanced work in fields such as High Performance Computing, Numerical Linear Algebra, Optimal Control of Partial Differential Equations and Quantum Mechanics Simulation, while experts in these areas will find a comprehensive reference guide, including some previously unpublished results, and teachers may find these chapters useful as textbooks in graduate courses.

The second part features the extended abstracts of selected research work presented by the students during the School. It highlights new results and applications in Computational Algebra, Fluid Mechanics, Chemical Kinetics and Biomedicine, among others, offering interested researchers a convenient reference guide to these latest advances.]]>