Morningside Lectures in Mathematics Volume 5
Published: 2 February 2018
Publisher: International Press of Boston, Inc.
Paperback
342 pages
(ISBN 9781571463579)
The notes collected here originated in seminars on analysis in partial differential equations, given during the academic year of 2014 to 2015 at the Morningside Center of Mathematics, Chinese Academy of Sciences (CAS), and at the Center of Harmonic Analysis and Its Application, Academy of Mathematics and Systems Science, CAS.
Included are: Hajer Bahouri, on critical Sobolev embeddings in Orlicz spaces and applications to PDEs with exponential nonlinearity; Hongjie Dong, on nonstandard Schauder estimates for parabolic equations; Frederic Herau, on hypocoercive methods and applications for simple linear inhomogeneous kinetic models; Nicolas Lerner, on Carleman inequalities; Jean-Pierre Puel, on controllability of Navier-Stokes equations; and Jiahong Wu, on 2D magnetohydrodynamic equations with partial or fractional dissipation.
ISBN: 978-1-119-25824-7
Mar 2018
464 pages
Delivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis
Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets.
Discrete Fourier Analysis and Wavelets introduces a new chapter on frames?a new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sophisticated signal analysis. The new coverage also expands upon the discussion on spectrograms using a frames approach. In addition, the book includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets. These new chapters also include appropriate exercises and MATLABR projects for further experimentation and practice.
Series:
Theoretical and Applied Mathematics
Binding: Softcover
Pub. Date: 2018 - 2nd quarter
ISBN: 978-1-53613-374-5
In this book, the authors report the results obtained by the application of wavelet analysis to two physics experiments: the motion of variable mass pendulum and the motion of variable length pendulum. These two motions, which furnish non stationary signals for their motions, are analyzed by means of a comparative Fourier Transform and Wavelet Transform. Afterwards, interval arithmetic extensions for the standard algorithms for the decimated and undecimated unidimensional Haar wavelet transform, as well as the standard and non-standard formulations for the two-dimensional HWT, are presented. In one paper, wavelet analysis and other statistical tools are employed in order to analyse different aspects of Sicily temperature data. Sicily represents one of the hot spots for studying climate change in the Mediterranean area because of its vulnerability to desertification processes. The authors aim to highlight how wavelet transform can be employed to extract information from experimental results obtained by spectroscopic techniques, such as InfraRed, light and neutron scattering spectroscopies. In particular, this book shows how it is possible to characterize the registered spectral profiles by means of Wavelet Cross Correlation to evaluate spectra and the degree of similarity between images. Later, an iterative a trous coarsening algorithm combined with a wavelet extrapolation procedure is presented and analyzed to filter and identify the mean trend of simulated 1D data with non trivial boundary conditions. Results show that the wavelet extrapolation based algorithm considered for the data-driven analysis is robust and reliable, allowing for an increased confidence region of the wavelet transform. In the concluding chapter, the authors aim to show that the wavelet transform has several advantages and benefits over classical methods of spectral analysis and other approches. (Nova)
Preface
Chapter 1. Wavelet Approach in Physics Education
(S. Magazu and M.T. Caccamo, Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universita di Messina, Viale Ferdinando Stagno D'Alcontres, Messina, Italy, and others)
Chapter 2. Int-HWT: Interval Extensions and Optimizations to Increase Performance and Accuracy of Haar Wavelet Transforms
(Vinicius R. dos Santos, Renata H. S. Reiser, Mauri?cio Pilla, and Alice J. Kozakevicius, Centre for Technological Development (CDTec), Federal University of Pelotas-UFPEL, Pelotas, RS, Brazil, and others)
Chapter 3. Wavelet Analysis as a Tool for Characterizing Trends in Climatic Data
(F. Colombo, S. Magazu, and M.T. Caccamo, Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universita di Messina, Viale Ferdinando Stagno D'Alcontres, Messina, Italy, and others)
Chapter 4. Applications of Wavelet Analyses on Spectroscopic Experiments
(M.T. Caccamo and S. Magazu, Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universita di messina, Viale Ferdinando Stagno D'Alcontres, Messina, Italy, and others)
Chapter 5. The "a Trous" Transform with Wavelet Extrapolated Boundary Extensions for Data Analysis
(Alice J. Kozakevicius and Alex A. Schmidt, Department of Mathematics, Universidade Federal de Santa Maria-UFSM, Santa Maria, RS, Brazil)
Chapter 6. Wavelets in Processing of Neurophysiological Data Related to Ambiguous Images Perception
(A. N. Pisarchik, A. N. Pavlov, A. E. Hramov, V. A. Maksimenko, A. E. Runnova, and M. O. Zhuravlev, Yuri Gagarin State Technical University of Saratov, Russia)
Index
Published: 12 July 2018 (Estimated)
240 Pages
234x156mm
ISBN: 9780198821656
This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortacgil instead questions the foundations of the subject, and proposes a new direction.
Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.
Fundemental concepts
1: Parallelizable manifolds
2: The nonlinear curvature
3: Local Lie Groups (LLG.s)
4: The centralizer
5: s-invariance
6: The linear curvature
7: The structure object
Some Consequences
8: The nonlinear Spencer sequence
9: Deformations
10: The de Rham cohomology of a LLG
11: The linear Spencer sequence
12: The secondary characteristic classes
13: The homogeneous flow
14: The Van Est Theorem
15: The symmetry group
How to Generalize
16: Klein geometries
17: The universal jet groupoids
18: Embeddings of Klein geometries into universal jet groupoids
19: The de.nition of a prehomogeneous geometry (PHG)
20: Curvature and generalized PHG.s
Due 2018-03-22
1st ed. 2018, XLII, 640 p. 37 illus.
Hardcover
ISBN 978-3-319-65303-7
Springer Series in Statistics
Provides essential data analysis tools for answering complex big data
questions based on real world data
Contains machine learning estimators that provide inference within data
science
Offers applications that demonstrate 1) the translation of the real world
application into a statistical estimation problem and 2) the targeted
statistical learning methodology to answer scientific questions of interest
based on real data
This textbook for graduate students in statistics, data science, and public health deals with the
practical challenges that come with big, complex, and dynamic data. It presents a scientific
roadmap to translate real-world data science applications into formal statistical estimation
problems by using the general template of targeted maximum likelihood estimators. These
targeted machine learning algorithms estimate quantities of interest while still providing valid
inference. Targeted learning methods within data science area critical component for solving
scientific problems in the modern age. The techniques can answer complex questions including
optimal rules for assigning treatment based on longitudinal data with time-dependent
confounding, as well as other estimands in dependent data structures, such as networks.
Included in Targeted Learning in Data Science are demonstrations with soft ware packages
and real data sets that present a case that targeted learning is crucial for the next generation
of statisticians and data scientists. Th is book is a sequel to the first textbook on machine
learning for causal inference, Targeted Learning, published in 2011. Mark van der Laan, PhD, is
Jiann-Ping Hsu/Karl E. Peace Professor of Biostatistics and Statistics at UC Berkeley. His
research interests include statistical methods in genomics, survival analysis, censored data,
machine learning, semiparametric models, causal inference, and targeted learning. Dr. van der
Laan received the 2004 Mortimer Spiegelman Award, the 2005 Van Dantzig Award, the 2005
COPSS Snedecor Award, the 2005 COPSS Presidential Award, and has graduated over 40 PhD
students in biostatistics and statistics.
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