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Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra [PDF]
Advances in Applied Clifford Algebras, 2021 We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA objects which is important especially for software implementation and symbolic calculations.
Jaroslav Hrdina +2 more
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The elastic theory of shells using geometric algebra [PDF]
Royal Society Open Science, 2017 We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation.
A. L. Gregory, J. Lasenby, A. Agarwal
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Multi-Modal Medical Image Fusion With Geometric Algebra Based Sparse Representation [PDF]
Frontiers in Genetics, 2022 Multi-modal medical image fusion can reduce information redundancy, increase the understandability of images and provide medical staff with more detailed pathological information.
Yanping Li +4 more
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Traffic-Data Recovery Using Geometric-Algebra-Based Generative Adversarial Network [PDF]
Sensors, 2022 Traffic-data recovery plays an important role in traffic prediction, congestion judgment, road network planning and other fields. Complete and accurate traffic data help to find the laws contained in the data more efficiently and effectively.
Di Zang +6 more
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Graph Geometric Algebra networks for graph representation learning [PDF]
Scientific ReportsGraph neural networks (GNNs) have emerged as a prominent approach for capturing graph topology and modeling vertex-to-vertex relationships. They have been widely used in pattern recognition tasks including node and graph label prediction.
Jianqi Zhong, Wenming Cao
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Chirality in Geometric Algebra
Mathematics, 2021 We define chirality in the context of chiral algebra. We show that it coincides with the more general chirality definition that appears in the literature, which does not require the existence of a quadratic space.
Michel Petitjean
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Geometric Algebra-Based ESPRIT Algorithm for DOA Estimation [PDF]
Sensors, 2021 Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding ...
Rui Wang +4 more
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A Survey of Geometric Algebra and Geometric Calculus [PDF]
Advances in Applied Clifford Algebras, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alan Macdonald, Macdonald Alan
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Dual-arm admittance control using conformal geometric algebra [PDF]
Frontiers in Robotics and AIWe propose a task-space admittance controller for dual-arm robotic systems using conformal geometric algebra. The controller is a reinterpretation of a previous work using dual quaternion algebra.
Tobias Löw +5 more
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Geometric Algebra Jordan–Wigner Transformation for Quantum Simulation [PDF]
EntropyQuantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the
Grégoire Veyrac, Zeno Toffano
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