ICIAM 2019 SEMA SIMAI Springer Series

Systems, Patterns and Data Engineering with Geometric Calculi

Editors: Xambó-Descamps, Sebastià (Ed.)

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  • Integrated perspective of mathematical engineering based on geometric calculi
  • A comprehensive formalism for deep neural networks based on geometric algebras
  • Coverage of relevant algorithms, particularly for automatic learning, and of advanced computational aspects
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  • ISBN 978-3-030-74486-1
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About this book

The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra.

The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.


About the authors

​Sebastià Xambó-Descamps is an Emeritus Full Professor of Mathematics at the Universitat Politècnica de Catalunya/Barcelonatech and is currently visiting the Barcelona Supercomputer Center. Previously, he held positions at the Universidad Complutense de Madrid (Full Professor) and at the Universitat de Barcelona (Associate Professor). His main research interests are algebraic geometry (intersection theory and enumerative geometry), information theory (coding theory and code-based post-quantum cryptography), computational methods (computer mathematics and symbolic computation), mathematical models in physics and engineering, geometric calculus and its applications to deep learning. Author of Block Error-Correcting Codes, A Computational Primer and Real Spinorial Groups, A Short Mathematical Introduction.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • New Perspectives on Robotics with Geometric Calculus

    Pages 1-17

    Zaplana, Isiah

  • Recent Advances on Oriented Conformal Geometric Algebra Applied to Molecular Distance Geometry

    Pages 19-30

    Lavor, Carlile (et al.)

  • Geometric Calculus Applications to Medical Imaging: Status and Perspectives

    Pages 31-46

    Franchini, Silvia (et al.)

  • Optimal Combination of Orientation Measurements Under Angle, Axis and Chord Metrics

    Pages 47-88

    Dorst, Leo

  • Space-Bending Lattices: Parameterization and Rationalization of Cyclidic Volumes Through Conformal Transformation of Principal Contact Elements

    Pages 89-110

    Colapinto, Pablo

Buy this book

eBook 117,69 €
price for Spain (gross)
  • ISBN 978-3-030-74486-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 145,59 €
price for Spain (gross)
  • ISBN 978-3-030-74485-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Systems, Patterns and Data Engineering with Geometric Calculi
Editors
  • Sebastià Xambó-Descamps
Series Title
ICIAM 2019 SEMA SIMAI Springer Series
Series Volume
13
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-74486-1
DOI
10.1007/978-3-030-74486-1
Hardcover ISBN
978-3-030-74485-4
Series ISSN
2662-7183
Edition Number
1
Number of Pages
IX, 179
Number of Illustrations
26 b/w illustrations, 38 illustrations in colour
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