This book is about the theoretical and practical aspects of the statistics of Extreme Events in Nature. Most importantly, this is the first text in which Copulas are introduced and used in Geophysics. Several topics are fully original, and show how standard models and calculations can be improved by exploiting the opportunities offered by Copulas. In addition, new quantities useful for design and risk assessment are introduced.
This book offers an in-depth investigation into the complexities of long-term structural health monitoring (SHM) in civil structures, specifically focusing on the challenges posed by small data and environmental and operational changes (EOCs). Traditional contact-based sensor networks in SHM produce large amounts of data, complicating big data management. In contrast, synthetic aperture radar (SAR)-aided SHM often faces challenges with small datasets and limited displacement data. Additionally, EOCs can mimic the structural damage, resulting in false errors that can critically affect economic and safety issues. Addressing these challenges, this book introduces seven advanced unsupervised learning methods for SHM, combining AI, data sampling, and statistical analysis. These include techniques for managing datasets and addressing EOCs. Methods range from nearest neighbor searching and Hamiltonian Monte Carlo sampling to innovative offline and online learning frameworks, focusing on data augmentation and normalization. Key approaches involve deep autoencoders for data processing and novel algorithms for damage detection. Validated using simulated data from the I-40 Bridge, USA, and real-world data from the Tadcaster Bridge, UK, these methods show promise in addressing SAR-aided SHM challenges, offering practical tools for real-world applications. The book, thereby, presents a comprehensive suite of innovative strategies to advance the field of SHM.
This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.
Carlo Testa demonstrates that while pairings of famed directors and writers are commonplace in modern Italian cinema, the study of the interrelation between Italian cinema and European literature has been almost completely neglected in film scholarship.
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