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Uncertainty Principle For Time Series
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Book Synopsis Time Series Analysis and Inverse Theory for Geophysicists by : David Gubbins
Download or read book Time Series Analysis and Inverse Theory for Geophysicists written by David Gubbins and published by Cambridge University Press. This book was released on 2004-03-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data. These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets. Solutions to the exercises are available on a website at http://publishing.cambridge.org/resources/0521819652
Author :Hans G. Feichtinger Publisher :Springer Science & Business Media ISBN 13 :9780817642396 Total Pages :384 pages Book Rating :4.6/5 (423 download)
Book Synopsis Advances in Gabor Analysis by : Hans G. Feichtinger
Download or read book Advances in Gabor Analysis written by Hans G. Feichtinger and published by Springer Science & Business Media. This book was released on 2003 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an overview of recent developments in Gabor analysis. Scientists in various disciplines related to the subject treat a range of topics from covering theory to numerics, as well as applications of Gabor analysis.
Book Synopsis The Uncertainty Principle in Harmonic Analysis by : Victor Havin
Download or read book The Uncertainty Principle in Harmonic Analysis written by Victor Havin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
Download or read book Data Science written by Ivo D. Dinov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.
Book Synopsis Time-Series Analysis and Cyclostratigraphy by : Graham P. Weedon
Download or read book Time-Series Analysis and Cyclostratigraphy written by Graham P. Weedon and published by Cambridge University Press. This book was released on 2005-09-15 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and tidal cycles. It is suitable for senior undergraduate and graduate courses in environmental science, palaeoceanography and geology.
Book Synopsis A Certain Uncertainty by : Mark P. Silverman
Download or read book A Certain Uncertainty written by Mark P. Silverman and published by Cambridge University Press. This book was released on 2014-07-10 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging introduction to statistical reasoning will teach you how to apply powerful statistical tools in a technical context.
Book Synopsis Topics in Nonlinear Time Series Analysis by : Andreas Galka
Download or read book Topics in Nonlinear Time Series Analysis written by Andreas Galka and published by World Scientific. This book was released on 2000 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented ? algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.
Book Synopsis The Physical Principles of the Quantum Theory by : Werner Heisenberg
Download or read book The Physical Principles of the Quantum Theory written by Werner Heisenberg and published by Courier Corporation. This book was released on 2013-04-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nobel Laureate discusses quantum theory, uncertainty, wave mechanics, work of Dirac, Schroedinger, Compton, Einstein, others. "An authoritative statement of Heisenberg's views on this aspect of the quantum theory." — Nature.
Book Synopsis Machine Learning Techniques for Time Series Classification by : Michael Botsch
Download or read book Machine Learning Techniques for Time Series Classification written by Michael Botsch and published by Cuvillier Verlag. This book was released on 2023-06-23 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classification of time series is an important task in various fields, e.g., medicine, finance, and industrial applications. This work discusses strong temporal classification using machine learning techniques. Here, two problems must be solved: the detection of those time instances when the class labels change and the correct assignment of the labels. For this purpose the scenario-based random forest algorithm and a segment and label approach are introduced. The latter is realized with either the augmented dynamic time warping similarity measure or with interpretable generalized radial basis function classifiers. The main application presented in this work is the detection and categorization of car crashes using machine learning. Depending on the crash severity different safety systems, e.g., belt tensioners or airbags must be deployed at time instances when the best-possible protection of passengers is assured.
Book Synopsis Time in Quantum Mechanics by : Gonzalo Muga
Download or read book Time in Quantum Mechanics written by Gonzalo Muga and published by Springer. This book was released on 2007-11-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the quantum theory. This multi-authored book, written as an introductory guide for newcomers to the subject, as well as a useful source of information for the expert, covers many of the open questions. The book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory.
Book Synopsis The Mathematics Of Natural Catastrophes by : Gordon Woo
Download or read book The Mathematics Of Natural Catastrophes written by Gordon Woo and published by World Scientific. This book was released on 1999-10-15 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book about natural catastrophes, focusing on the mathematical aspects of these phenomena. Although academic in style and didactic in purpose, it is practical in the treatment of the diverse issues covered, which range from hazard warning and forecasting to engineering design criteria and insurance loss estimation. Addressing as it does many mathematical topics not found together in a single volume, the book should be of value to all those with a quantitative educational interest in or professional concern for natural catastrophes.
Book Synopsis Foundations of Time-Frequency Analysis by : Karlheinz Gröchenig
Download or read book Foundations of Time-Frequency Analysis written by Karlheinz Gröchenig and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Book Synopsis Fundamental Principles of Modern Theoretical Physics by : R. H. Furth
Download or read book Fundamental Principles of Modern Theoretical Physics written by R. H. Furth and published by Elsevier. This book was released on 2013-10-22 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental Principles of Modern Theoretical Physics
Book Synopsis The Analysis of Change by : John Mordechai Gottman
Download or read book The Analysis of Change written by John Mordechai Gottman and published by Psychology Press. This book was released on 2013-02-01 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuity and change have been major concerns of the social and behavioral sciences -- in the study of human development and in the study of processes that unfold in various ways across time. There has been a veritable explosion of techniques for studying change over time which have fundamentally changed how we need to think of and study change. Unfortunately, many of the old precepts and beliefs are still among us. The field of methodology for the study of change is itself ready to change. Recently, there have been many analytic and conceptual developments questioning our cherished beliefs about the study of change. As such, how are individuals to think about issues and correctly analyze change? The chapters in this volume address these issues. Divided into two sections, this book deals with designs that analyze change in multiple subjects, and with change in single subjects and an interacting system. Papers presented in this volume are accessible to scientists who are not methodologists. The character of the papers are more like primers than basic treatises on methodology, written for other methodologists. It is time that people stop thinking in rigid ways about how to study change and be introduced to a range of many possibilities. Change, stability, order and chaos are elusive concepts. The pursuit of the laws of change must be approached in as flexible and creative a fashion as possible. This book should help to lead the way.
Download or read book Calculating Catastrophe written by G. Woo and published by World Scientific. This book was released on 2011 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Natural hazards. 1.1. Causation and association. 1.2. Extra-terrestrial hazards. 1.3. Meteorological hazards. 1.4. Geological hazards. 1.5. Geomorphic hazards. 1.6. Hydrological hazards -- 2. Societal hazards. 2.1. Political violence. 2.2. Infectious disease pandemics. 2.3. Industrial and transportation accidents. 2.4. Fraud catastrophe -- 3. A sense of scale. 3.1. Size scales of natural hazards. 3.2. Hazard spatial scales. 3.3. The human disaster toll. 3.4. Models of a fractal world -- 4. A measure of uncertainty. 4.1. The concept of probability. 4.2. The meaning of uncertainty. 4.3. Aleatory and epistemic uncertainty. 4.4. Probability ambiguity. 4.5. The weighing of evidence -- 5. A matter of time. 5.1. Temporal models of hazards. 5.2. Long-term data records. 5.3. Statistics of extremes -- 6. Catastrophe complexity. 6.1. Emergent catastrophes. 6.2. Financial crashes. 6.3. Ancillary hazards -- 7. Terrorism. 7.1. A thinking man's game. 7.2. Defeating terrorist networks. 7.3. Counter-radicalization -- 8. Forecasting. 8.1. Earthquake forecasting. 8.2. Verification. 8.3. River flows and sea waves. 8.4. Accelerating approach to criticality. 8.5. Evidence-based diagnosis -- 9. Disaster warning. 9.1. Decision in the balance. 9.2. Evacuation. 9.3. The wisdom of experts -- 10. Disaster scenarios. 10.1. Scenario simulation. 10.2. Footprints and vulnerability. 10.3. Fermi problems -- 11. Catastrophe cover. 11.1. Probable maximum loss. 11.2. Coherent risk measures. 11.3. The Samaritan's dilemma -- 12. Catastrophe risk securitization. 12.1. Catastrophe bonds. 12.2. The price of innovation -- 13. Risk horizons. 13.1. Ecological catastrophe. 13.2. Climate change. 13.3. War and conflict resolution
Book Synopsis Principles of Neural Coding by : Rodrigo Quian Quiroga
Download or read book Principles of Neural Coding written by Rodrigo Quian Quiroga and published by CRC Press. This book was released on 2013-05-06 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding how populations of neurons encode information is the challenge faced by researchers in the field of neural coding. Focusing on the many mysteries and marvels of the mind has prompted a prominent team of experts in the field to put their heads together and fire up a book on the subject. Simply titled Principles of Neural Coding, this book covers the complexities of this discipline. It centers on some of the major developments in this area and presents a complete assessment of how neurons in the brain encode information. The book collaborators contribute various chapters that describe results in different systems (visual, auditory, somatosensory perception, etc.) and different species (monkeys, rats, humans, etc). Concentrating on the recording and analysis of the firing of single and multiple neurons, and the analysis and recording of other integrative measures of network activity and network states—such as local field potentials or current source densities—is the basis of the introductory chapters. Provides a comprehensive and interdisciplinary approach Describes topics of interest to a wide range of researchers The book then moves forward with the description of the principles of neural coding for different functions and in different species and concludes with theoretical and modeling works describing how information processing functions are implemented. The text not only contains the most important experimental findings, but gives an overview of the main methodological aspects for studying neural coding. In addition, the book describes alternative approaches based on simulations with neural networks and in silico modeling in this highly interdisciplinary topic. It can serve as an important reference to students and professionals.
Book Synopsis Toeplitz Approach to Problems of the Uncertainty Principle by : Alexei Poltoratski
Download or read book Toeplitz Approach to Problems of the Uncertainty Principle written by Alexei Poltoratski and published by American Mathematical Soc.. This book was released on 2015-03-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems. These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Pólya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts. A co-publication of the AMS and CBMS.
