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A hybrid approach for computing products of high-dimensional geometric algebras

Stéphane Breuils, Vincent Nozick, Laurent Fuchs, Dietmar Hildenbrand, Werner Benger, Christian Steinmetz
2017 Proceedings of the Computer Graphics International Conference on - CGI '17  
Finally, Section 5 details the integration of the hybrid approach as a plug-in into Gaalop, a very advanced geometric algebra tool.  ...  to handle high dimensional space computations.  ... 
doi:10.1145/3095140.3097284 dblp:conf/cgi/BreuilsNFHBS17 fatcat:rhy5paehtbfvtauekb74zhjhzm

Garamon: A Geometric Algebra Library Generator

Stéphane Breuils, Vincent Nozick, Laurent Fuchs
2019 Advances in Applied Clifford Algebras  
While for low dimension vector spaces, precomputing all the Geometric Algebra products is an efficient strategy, it fails for higher dimensions where the operation should be computed at run time.  ...  This paper describes how a prefix tree can be a support for a recursive formulation of Geometric Algebra operations.  ...  For higher dimensional algebra, we tested Garamon on the Quadric Conformal Geometric Algebra [5] built over a 15-dimensional vector space for real-time applications.  ... 
doi:10.1007/s00006-019-0987-7 fatcat:akhjzsdv5regxfstblankgmvzm

Embedding Learning in Hybrid Quantum-Classical Neural Networks [article]

Henry Liu, Junyu Liu, Rui Liu, Henry Makhanov, Danylo Lykov, Anuj Apte, Yuri Alexeev
2022 arXiv   pre-print
In this paper we propose a quantum few-shot embedding learning paradigm, which learns embeddings useful for training downstream quantum machine learning tasks.  ...  Quantum embedding learning is an important step in the application of quantum machine learning to classical data.  ...  This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.  ... 
arXiv:2204.04550v1 fatcat:otncnu5bqndkfn2cy7n4bmyz2u

Gaalop—High Performance Parallel Computing Based on Conformal Geometric Algebra [chapter]

Dietmar Hildenbrand, Joachim Pitt, Andreas Koch
2010 Geometric Algebra Computing  
We present Gaalop (Geometric algebra algorithms optimizer), our tool for high performance computing based on conformal geometric algebra.  ...  An inverse kinematics algorithm of a humanoid robot is described as an example.  ...  Each slice is able to compute all operations of the four-dimensional geometric algebra. The coefficients have now been extended to 32 bit integers.  ... 
doi:10.1007/978-1-84996-108-0_22 fatcat:d2ymfzzfbbau7i2xymhst4vbm4

VUDJOOD Algebra Theory from the Viewpoint of 3D Object Recognition

Amin Mirahmadi, Kamran Vafaee, Behdad Geranmehr
2013 American Journal of Mechanical Engineering  
Objects identifying Algorithm has been studied for a few objects with simple geometry using the experimental tests. Dimensional accuracy of detection results is acceptable.  ...  The goal of VUDJOOD (existence) algebra is to provide the capability of visual intelligence for intelligent machines that are like humans.  ...  Case Study In this section the performance of the proposed approach is evaluated for a user-defined database.  ... 
doi:10.12691/ajme-1-6-1 fatcat:2sgwzylc5zerhc5xcmct4bdwy4

The Breakdown of Topology at Small Scales

Paul S Aspinwall
2004 Journal of High Energy Physics  
The mechanism proposed coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The topology breaks down as one approaches non-geometric phases.  ...  We discuss how a topology (the Zariski topology) on a space can appear to break down at small distances due to D-brane decay.  ...  stability for that decay product. figure.  ... 
doi:10.1088/1126-6708/2004/07/021 fatcat:mip5liviwvdtlekg2iahvdkpb4

Three-dimensional space groups two-dimensional hyperbolic orbifolds and 'sponge' groups

S. T. Hyde, S. Ramsden, V. Robins
2011 Acta Crystallographica Section A Foundations of Crystallography  
The careful analysis of a series high pressure structures showing a pressureinduced shrinking more than 10% along the chain direction, which can describe as spring compressed 10%.  ...  Magneto -structural correlation will be discussed .The coordinated shells of Iron (N4O2) also decrease 0.11 Å about averagely.  ...  We see a need for this, because so far many mainstream crystallographers are relatively unfamiliar with Clifford geometric algebra [6].  ... 
doi:10.1107/s0108767311091641 fatcat:tnd425xr25bifagt4pdzcmba2y

Efficient representation and manipulation of quadratic surfaces using Geometric Algebras [article]

Stéphane Breuils, Laurent Fuchs
2019 arXiv   pre-print
The proposed approach also allows to transform any quadratic surfaces and to compute their intersection and to easily extract some geometric properties .  ...  This paper presents a unification of these frameworks that enables to represent any quadratic surfaces either using control points or from the coefficients of its implicit form.  ...  After presenting the main approaches to represent and manipulate quadratic surfaces, we introduced a new hybrid Geometric Algebra approach.  ... 
arXiv:1903.02444v1 fatcat:luh7m2lep5ek3izgwbvtqmo44a

Hybrid multigrid methods for high-order discontinuous Galerkin discretizations [article]

Niklas Fehn, Peter Munch, Wolfgang A. Wall, Martin Kronbichler
2019 arXiv   pre-print
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems.  ...  This does not only further reduce the problem size of the coarse-grid problem, but also leads to a discretization most suitable for state-of-the-art algebraic multigrid methods applied as coarse-grid solver  ...  priority program "Software for Exascale Computing" (SPPEXA), grant agreement no.  ... 
arXiv:1910.01900v1 fatcat:7dfh25442ngezart4vkhhesaqa

Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

Uzair Aslam Bhatti, Zhaoyuan Yu, Linwang Yuan, Saqib Ali Nawaz, Mughair Bhatti, Anum Mehmood, Qurat Ul Ain, Z. Zeehsan, Luo Wen
2020 IEEE Access  
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.  ...  ACKNOWLEDGMENT This work was supported in part by the National Natural Science Foundation of China under Grant 41625004, 41976186, and Six talent peaks project in Jiangsu Province under Grant RJFW-019.  ...  GA as a feature extraction tool for geospatial Most of our reality exists in high data volume, high dimensionality, non-equilibrium, non-linear, unstructured information systems.  ... 
doi:10.1109/access.2020.3018544 fatcat:dxnehrysjbh3fmsbmolkqnzfbu

Mathematics mechanization and applications after thirty years

Wenjun Wu, Xiaoshan Gao
2007 Frontiers of Computer Science in China  
The characteristic set method for symbolic solution of algebraic, differential, and difference equation systems are first introduced.  ...  Finally, applications in computer-aided geometric design, computer vision, intelligent computeraided design, and robotics are surveyed.  ...  By mapping three-dimensional geometric objects into a five-dimensional space, this algebra provides a unified and compact representation for classical geometric objects and a set of effective algorithms  ... 
doi:10.1007/s11704-007-0001-8 fatcat:7iia43igzrckfnzchtg5jll5eq

Page 8328 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
Conditions on the algebraic multiplicity, geometric multiplicity and the span of the system eigenvalues are obtained for assigning the poles to a given sequence of complex numbers.  ...  Moreover, an algebraic approach (based on the extended interval arithmetic which is developed in [E. Kaucher, in Fundamentals of numerical computation (computer-oriented numerical analysis) (Proc.  ... 

The Monogenic Curvature Scale-Space [chapter]

Di Zang, Gerald Sommer
2006 Lecture Notes in Computer Science  
Combining methods of tensor algebra, monogenic signal and quadrature filter, the monogenic curvature signal, as a novel model for intrinsically two-dimensional (i2D) structures, is derived in an algebraically  ...  In contrast to the Gaussian curvature scale-space, our approach has the advantage of simultaneous estimation of local phase and orientation.  ...  hybrid matrix geometric algebra M (2, R 3 ), which is the geometric algebra of a 2 × 2 matrix with elements in R 3 , see [21] .  ... 
doi:10.1007/11774938_25 fatcat:3p7bgawny5agxmulunsjouegcm

High Order Finite Element Schemes And Domain Decomposition Solvers For Large-Scale Simulations In Electromagnetics

Stéphane Lanteri
2017 Zenodo  
We report on our work aiming at enabling large-scale simulations of frequency-domain electromagnetic wave propagation based on a recently developed innovative simulation software combining a high order  ...  The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential  ...  The simulation software named HORSE (High Order solver for Radar cross Section Evaluation) for implements an innovative high order finite element type method for solving the system of three-dimensional  ... 
doi:10.5281/zenodo.830354 fatcat:zdaf5nmg3bbntevadby5i737ym

Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)

Michael Breuß, Alfred M. Bruckstein, Christer Oscar Kiselman, Petros Maragos, Michael Wagner
2019 Dagstuhl Reports  
In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a  ...  New developments from tropical geometry have a high potential for use in shape analysis.  ...  For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model  ... 
doi:10.4230/dagrep.8.10.87 dblp:journals/dagstuhl-reports/BreussBKM18 fatcat:qzsc5ihgsfhzlmooaukqjo2rcy
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