Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.

Sub-Riemannian Geometry: General Theory and Examples (Encyclopedia of Mathematics and its Applications, Series Number 126)

Reference

CALIN, OVIDIU

Chang, Der-Chen

Encyclopedias & Subject Guides

Cambridge University Press

*  A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter  * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis)

Science & Math

Mathematics

Birkhauser

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques (Applied and Numerical Harmonic Analysis)

Furutani, Kenro

Iwasaki, Chisato

Evolution

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)

World Scientific Publishing Co Pte Ltd

Deep Learning Architectures: A Mathematical Approach (Springer Series in the Data Sciences)

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates.&nbsp; In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject. &nbsp; &nbsp;

Computers & Technology

Computer Science

Springer

Product Description 
This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. 
This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.\nReview 
“This book is useful to students who have already had an introductory course in machine learning and are further interested to deepen their understanding of the machine learning material from the mathematical point of view.” (T. C. Mohan, zbMATH 1441.68001, 2020) 
 From the Back Cover 
This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. 
This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.\nAbout the Author 
Ovidiu Calin, a graduate from University of Toronto, is a professor at Eastern Michigan University and a former visiting professor at Princeton University and University of Notre Dame. He has delivered numerous lectures at several universities in Japan, Hong Kong, Taiwan, and Kuwait over the last 15 years. His publications include over 60 articles and 8 books in the fields of machine learning, computational finance, stochastic processes, variational calculus and geometric analysis.

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields.
This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able toprovide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Geometric Modeling in Probability and Statistics

Udrişte, Constantin

Informal Introduction To Stochastic Calculus With Applications, An (second Edition)

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory. The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus. The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods. This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises. This edition has also improved presentation from the first edition in several chapters, including new material.

Informal Introduction to Stochastic Calculus with Applications, an (Second Edition)

World Scientific Pub Co Inc

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory. The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus. The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods. This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises. This edition has also improved presentation from the first edition in several chapters, including new material.

WSPC

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Books by CALIN, OVIDIU

See the best price to sell, buy, or rent books by CALIN, OVIDIU. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Sub-Riemannian Geometry: General Theory and Examples (Encyclopedia of Mathematics and its Applications, Series Number 126)

Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis)

Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques (Applied and Numerical Harmonic Analysis)

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)

Deep Learning Architectures: A Mathematical Approach (Springer Series in the Data Sciences)

Deep Learning Architectures: A Mathematical Approach (Springer Series in the Data Sciences)

Geometric Modeling in Probability and Statistics

Geometric Modeling in Probability and Statistics

Informal Introduction to Stochastic Calculus with Applications, an (Second Edition)

Informal Introduction To Stochastic Calculus With Applications, An (second Edition)