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Systems, patterns and data engineering with geometric calculi

Record Type:	Electronic resources : Monograph/item
Title/Author:	Systems, patterns and data engineering with geometric calculiedited by Sebastia Xambo-Descamps.
other author:	Xambo-Descamps, Sebastia.
Published:	Cham :Springer International Publishing :2021.
Description:	ix, 179 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Engineering mathematics.
Online resource:	https://doi.org/10.1007/978-3-030-74486-1
ISBN:	9783030744861$q(electronic bk.)

Systems, patterns and data engineering with geometric calculi
Systems, patterns and data engineering with geometric calculi[electronic resource] /edited by Sebastia Xambo-Descamps. - Cham :Springer International Publishing :2021. - ix, 179 p. :ill. (some col.), digital ;24 cm. - SEMA SIMAI Springer series. ICIAM 2019 SEMA SIMAI Springer series ;v.13. - SEMA SIMAI Springer series.ICIAM 2019 SEMA SIMAI Springer series ;v.10..

1 I. Zaplana, New Perspectives on Robotics with Geometric Calculus -- 2 C. Lavor and R. Alves, Recent advances on oriented conformal geometric algebra applied to molecular distance geometry -- 3 S. Franchini and S. Vitabile, Geometric Calculus Applications to Medical Imaging: Status and Perspectives -- 4 L. Dorst, Optimal Combination of Orientation Measurements Under Angle, Axis and Chord Metrics -- 5 P. Colapinto, Space-Bending Lattices through Conformal Transformation of Principal Contact Elements -- 6 L. A. F. Fernandes, Exploring Lazy Evaluation and Compile-Time Simplifications for Efficient Geometric Algebra Computations -- 7 E. U. Moya-Sanchez et al., A Quaternion Deterministic Monogenic CNN Layer for Contrast Invariance -- 8 S. Xambo-Descamps et al., Geometric Calculi and Automatic Learning: An Overview.

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.

ISBN: 9783030744861$q(electronic bk.)

Standard No.: 10.1007/978-3-030-74486-1doiSubjects--Topical Terms:

182072
Engineering mathematics.

LC Class. No.: TA331 / .S97 2021

Dewey Class. No.: 620.00151

Systems, patterns and data engineering with geometric calculi
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505 0 $a 1 I. Zaplana, New Perspectives on Robotics with Geometric Calculus -- 2 C. Lavor and R. Alves, Recent advances on oriented conformal geometric algebra applied to molecular distance geometry -- 3 S. Franchini and S. Vitabile, Geometric Calculus Applications to Medical Imaging: Status and Perspectives -- 4 L. Dorst, Optimal Combination of Orientation Measurements Under Angle, Axis and Chord Metrics -- 5 P. Colapinto, Space-Bending Lattices through Conformal Transformation of Principal Contact Elements -- 6 L. A. F. Fernandes, Exploring Lazy Evaluation and Compile-Time Simplifications for Efficient Geometric Algebra Computations -- 7 E. U. Moya-Sanchez et al., A Quaternion Deterministic Monogenic CNN Layer for Contrast Invariance -- 8 S. Xambo-Descamps et al., Geometric Calculi and Automatic Learning: An Overview.
520 $a 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.
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