Format: Paperback / softback, 196 pages, height x width: 234x156 mm,
weight: 380 g, 1 Tables, black and white; 17 Illustrations, color; 36 Illustrations, black and white
Pub. Date: 13-Apr-2025
ISBN-13: 9781032418865
Deep learning is an important element of artificial intelligence, especially in applications such as image classification in which various architectures of neural network, e.g., convolutional neural networks, have yielded reliable results. This book introduces deep learning for time series analysis, particularly for cyclic time series. It elaborates on the methods employed for time series analysis at the deep level of their architectures. Cyclic time series usually have special traits that can be employed for better classification performance. These are addressed in the book. Processing cyclic time series is also covered herein.
An important factor in classifying stochastic time series is the structural risk associated with the architecture of classification methods. The book addresses and formulates structural risk, and the learning capacity defined for a classification method. These formulations and the mathematical derivations will help the researchers in understanding the methods and even express their methodologies in an objective mathematical way. The book has been designed as a self-learning textbook for the readers with different backgrounds and understanding levels of machine learning, including students, engineers, researchers, and scientists of this domain. The numerous informative illustrations presented by the book will lead the readers to a deep level of understanding about the deep learning methods for time series analysis.
The concept of deep machine learning is easier to understand by paying attention to the cyclic stochastic time series and a time series whose content is non-stationary not only within the cycles, but also over the cycles as the cycle-to-cycle variations
PREFACE. I-FUNDAMENTALS OF LEARNING. Introduction to Learning. Learning
Theory. Pre-processing and Visualisation. II ESSENTIALS OF TIME SERIES
ANALYSIS. Basics of Time Series. Multi-Layer Perceptron (MLP) Neural Networks
for Time Series Classification. Dynamic Models for Sequential Data Analysis.
III DEEP LEARNING APPROACHES TO TIME SERIES CLASSIFICATION. Clustering for
Learning at Deep Level. Deep Time Growing Neural Network. Deep Learning of
Cyclic Time Series. Hybrid Method for Cyclic Time Series. Recurrent Neural
Networks (RNN). Convolutional Neural Networks. Bibliography.
Format: Hardback, 449 pages, height x width: 240x168 mm, XVI, 449 p., 1 Hardback
Series: Classic Texts in the Sciences
Pub. Date: 01-Jul-2025
ISBN-13: 9783031854736
This book presents a historical account of Felix Klein's "Comparative Reflections on Recent Research in Geometry" (1872), better known as his "Erlangen Program.” Originally conceived and written when Klein was collaborating with Sophus Lie, this bold essay initially made little impression on contemporary researchers. Decades later, however, it eventually became a famous classic. Eminent mathematicians hailed Klein’s main message ? the role of invariants of transformation groups in geometry ? as presaging major developments in mathematics and physics.
The first part of this book focuses on the prehistory surrounding Klein’s “Erlangen Program,” stressing the motivations that led Klein to write it. The core of the book (Part II) then presents a new translation of Klein's original text, followed by detailed textual analysis aimed at guiding the reader through its rather terse and opaque prose. Part III deals with its complicated reception history, treated in four periods spanning the years from 1872 to 1930. This culminated during Klein’s lifetime with his efforts to promote the "Erlangen Program” as a framework for interpreting Einstein’s theory of relativity. After his death in 1925, the viability of this framework became a contentious issue among leading differential geometers. Part IV looks back on the transformations in mathematics that led to a modernized interpretation of Klein’s message. The book also explores in depth how the growing fame of the “Erlangen Program” undermined Klein’s friendship with Sophus Lie, leading to a dramatic public break between them in 1893.
Beyond the "Erlangen Program” itself, this book deals with many of Felix Klein’s other works. As an introduction to a largely forgotten world of ideas, this study will appeal not only to experts but also to graduate students and all those with a serious interest in the history of modern mathematics.
Preface.- Introduction.- Part I. Prehistory of the Erlangen Program.-
1 Klein as a Young Geometer.-
2. Klein Encounters Sophus Lie.-
3. Klein on
Cayleys Projective Metric.- Part II. Kleins Erlangen Program with
Commentary.-
4. Kleins Erlangen Program.-
5. Textual Analysis of Kleins
Erlangen Program.- Part III. Four Phases of Reception and Transformation.-
6. First Phase of Reception, 18731889.-
7. Second Phase of Reception,
18901899.-
8. Third Phase of Reception, 19001916.-
9. Fourth Phase of
Reception, 19171930.- Part IV. Reconsiderations.- 10 Historical
Reflections.- Bibliography.- Name Index.
Format: Hardback, 173 pages, height x width: 235x155 mm, IX, 173 p., 1 Hardback
Series: Springer Biographies
Pub. Date: 02-Jul-2025
ISBN-13: 9789819624027
This book is not only about the history of mathematics, but also by telling the story of some of the most distinctive personalities in the history of mathematics, it goes on to reveal the various strange treasures, bright flowers and hidden passions of the mathematical kingdom. Some of these mathematicians were thinkers, writers, poets, musicians, painters, politicians, judges, soldiers, clerks, young men of society or even prisoners. The mathematical world constructed by these geniuses is exquisite, and a walk in such a world not only expands our mathematical horizons and imagination, but also raises our humanistic cultivation to a higher level.
Written for general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. The readers will also enjoy reading the beautiful and simple language of all the articles and interviews.
Chapter 1. Thales of Miletus, First of The Seven Sages.
Chapter 2. Archimedes: The God of Mathematics.
Chapter 3. The World of Omar Khayyam.-
Chapter 4. Qin Jiushao, Daogu Bridge, and the Mathematical Treatise in Nine Sections.
Chapter 5. The Reclusive FrenchmenDescartes and Pascal .
Chapter 6. Leibniz: Unattainable Heights.
Chapter 7. John von Neumann, Who Made the World a Better Place.
Chapter 8. Paul Erds: A Narrowly Missed Opportunity.-
Chapter 9. Mathematicians and Poets.
Chapter 10. Mathematicians and Political Leaders.
Chapter 11. Hua Luogeng and Shiing-Shen Chern Two Contemporary Chinese Masters.
Chapter 12. "My life can be said to form a circle." An interview with Nobel laureate Professor Chen-Ning Yang.
Format: Paperback / softback, 153 pages, height x width: 235x155 mm,
22 Illustrations, color; 8 Illustrations, black and white; XII, 153 p. 30 illus., 22 illus. in color.,
Series: SpringerBriefs in Mathematics
Pub. Date: 08-Jul-2025
ISBN-13: 9783031875991
This book provides an introduction to the theory of connection matrices in the context of combinatorial multivector fields. The theory of connection matrices was proposed by Conley and Franzosa for classical continuous-time dynamical systems as a tool for studying connecting orbits between isolated invariant sets. It generalizes the Morse complex in Morse theory, and has found numerous applications in dynamics. Connection matrices have been and still are a challenging topic to study, as there are no complete introductory texts, and both their intricate definition and properties are scattered over numerous research papers.
In recent years, dynamical concepts have found their way into a combinatorial context. Starting with combinatorial vector fields, introduced by Forman to generalize classical Morse theory, it has been realized that this transfer of ideas can lead to important applications. Similarly, Conley's theory of isolated invariant sets has been transferred to the combinatorial setting. This, when combined with the concept of multivector fields, opens the door to a complete combinatorial dynamical theory.
In this book, we take Conley's theory one step further, by presenting a complete discussion of connection matrices for combinatorial multivector fields. While some of the results in this book are based on known approaches, we show in a detailed way how they can be carried over to the case of multivector fields on general Lefschetz complexes. Along the way, we introduce notions which are new even in the classical setting, such as a formal approach to addressing the nonuniqueness of connection matrices, as well as mechanisms for comparing connection matrices even under poset changes. Finally, we show that specifically for the case of Forman's gradient combinatorial vector fields connection matrices are necessarily unique, and can be determined explicitly in a straightforward way.
Focusing on the combinatorial theory of connection matrices has a number of advantages. On the one hand, many of the technical difficulties of the classical continuous-time dynamics situation are not present in the discrete combinatorial context. This allows us to provide a complete and informal introduction to the theory in the second section of the book. This in turn will enable the readers to construct and analyze their own examples easily. On the other hand, the complete theory, including the existence of connecting orbits in the combinatorial setting can be presented in detail, based on an explicit distinction between the algebraic and topological parts of the theory. In this way, it is our hope that this book will be an impetus for further knowledge transfer between dynamics and combinatorics, and even topological data analysis.
This text is aimed at researchers in the fields of dynamics and topological data analysis, and it is suitable for advanced graduate students interested in applying connection matrix methods to their own studies.
Preface.- Introduction.- Main Results.- Preliminaries.- Poset Filtered
Chain Complexes.- Algebraic Connection Matrices.- Connection Matrices in
Lefschetz Complexes.- Dynamics of Combinatorial Multivector Fields.-
Connection Matrices for Forman's Gradient Vector Fields.- Future Work and
Open Problems.- References.
Format: Hardback, 223 pages, height x width: 235x155 mm, 3 Illustrations,
color; 4 Illustrations, black and white; VIII, 223 p. 7 illus., 3 illus. in color.,
Series: Springer INdAM Series 63
Pub. Date: 06-Jul-2025
ISBN-13: 9789819661817
This book originates from the INdAM Workshop “Analysis and Numerics of Design, Control, and Inverse Problems”and explores a broad spectrum of cutting-edge topics in Applied Mathematics, including Control of Partial Differential Equations (PDEs), Shape Optimization, Inverse Problems and Numerical Analysis.
At the heart of many real-world applications lies the challenge of steering a system toward a desired configuration?often in the most efficient way possible. Whether it involves optimizing the shape of a structure, controlling the behavior of a physical system, or designing high-precision numerical methods, these challenges share a common mathematical framework.
This book brings together powerful techniques from functional analysis, PDEs, and numerical methods, offering both theoretical insights and practical implementations. Moreover, it delves into the fascinating field of inverse problems, where mathematical tools help extract hidden information from data?a crucial approach in fields such as climate science and biomedical modeling.
Ideal for researchers, and advanced students, this book provides a comprehensive and accessible introduction to modern optimization and control methodologies with direct applications to science and engineering.
Bianchini.- Boccardo.- Boussaid.- Camasta.- Di Pierro "Dirichlet".- Di
Pierro "Neumann".- Floridia.- Kian.- Leugering.- Paolucci.
Format: Hardback, 304 pages, height x width: 235x155 mm, 1 Illustrations, color;
2 Illustrations, black and white; XIV, 304 p. 3 illus., 1 illus. in color., 1 Hardback
Series: Applied Mathematical Sciences 222
Pub. Date: 06-May-2025
ISBN-13: 9783031891410
Inverse problems lie at the core of scientific discovery, enabling us to determine causes from observed consequences. They are fundamental to both theoretical research and technological innovation, making them a central topic in the mathematical sciences. This book explores a cutting-edge area of inverse problems?those related to integro-differential operators, also known as nonlocal operators. Due to their unique theoretical properties and vast practical applications, nonlocal inverse problems have garnered significant interest in recent years, making this an ideal time for a dedicated research monograph.
Focusing on nonlocality in space, this book provides a systematic study of both forward and inverse problems associated with integro-differential operators. It introduces key properties of forward problems?well-posedness, maximum principles, and unique continuation?before delving into inverse problems, including modeling, unique identifiability, stability analysis, and reconstruction methods. The discussion bridges mathematical theory with real-world applications, offering insights into pioneering contributions as well as recent advances by the authors and their collaborators.
As an evolving field, nonlocal inverse problems present a wealth of open challenges and emerging applications. This book not only provides a comprehensive introduction but also aims to inspire future research with fresh perspectives and novel insights. It is an invaluable resource for graduate students and early-career researchers looking to enter the field, as well as a valuable reference for experienced mathematicians working in inverse problems and mathematical analysis.
Preface.- Introduction.- Integro-differential operators.- Part
1.
Inverse problems for linear integro-differential operators.- Inverse problems
for the fractional SchrOodinger equation.- Inverse problems for the
fractional SchrOodinger equation with drift.- Inverse problems for variable
coefficients nonlocal equations.- Inverse problems for the fractional wave
equation.- Part
2. Inverse problems for nonlinear
integro-differential operators.- Inverse problems for fractional semilinear
elliptic equations.- Montonicity-based inversion formula with power type
nonlinearities.- Summary and some open questions.- Bibliography.