A large deviations approach to limit theory for heavy-tailed time series (Q328780)

This book is organized as follows: The book is divided into 13 chapters : Chapter 1: Dynamic Mode Decomposition : An introduction Consists of DMD; Formulating the DMD architecture; The DMD algorithm; Example code and decomposition; Limitation of the DMD method; Broader context of equation-free methods; and Interdisciplinary connection of DMD. Chapter 2: Fluid dynamics: Consists of Model decomposition in fluids; Application of DMD in fluids; and Example Re=100 flow around a cylindrical wake. Chapter 3: Koopman analysis: Consists of Spectral theory and eigenfunction expansions; The Koopman operator; Connections with DMD; and Example dynamical systems. Chapter 4: Video processing: Consists of background/foreground video separation; RPCA and DMD; DMD for background subtraction; Simple example and algorithm; and DMD for video surveillance. Chapter 5: Multiresolution DMD: Consists of Time frequency analysis and the Gabor transform; Wavelets and MRA; Formulating mrDMD; The mrDMD algorithm; and Example code and decomposition. Chapter 6: DMD with control: Consists of Formulating DMDc; the DMDc algorithm; Examples; Connection to system identification methods; and Connections to Koopman operator theory Chapter 7: Delay Coordinates , ERA, and Hidden Markov models: Consists of Delay coordinates and shift stacking data; Connections to ERA and Hankel matrices; and HMMs. Chapter 8: Noise and power: Consists of Power spectrum; truncating data and singular value thresholding; and Compensating for noise in the DMD spectrum. Chapter 9: Sparsity and DMD: Consists of Compressed sensing; Sparsity-promoting DMD; Sub-Nyquist sampled DMD; Compressed DMD; and Code for Compressed DMD. Chapter 10: DMD for Nonlinear observables: Consists of Koopman observables; Nonlinear observables for partial differential equations; Extended and kernel DMD; and Implementing extended and kernel DMD. Chapter 11: Epidemiology: Consists of Modeling infectious disease spread; Infectious disease data; DMD for Infectious disease data; Examples; and The epidemiological interpretation of DMD modes. Chapter 12: Neuroscience: Consists of Experimental techniques to measure neural activity; Modal decomposition in neuroscience; and DMD on neural recordings. Chapter 13: Financial Trading: Consists of Financial investment and algorithmic trading; Financial time series data and DMD; Trading algorithms and training; and Trading performance. In addition it contains Glossary/ Bibliography. The book is well organized and presents the most important Data-Driven Modeling of Complex systems with DMD. Suitable for senior undergraduate and undergraduate students as well as practical engineers, scientist and researchers interested Data-Driven Modeling of Complex systems.