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Theory of overparametrization in quantum neural networks
The prospect of achieving quantum advantage with quantum neural networks (QNNs) is exciting. Understanding how QNN properties (for example, the...
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Canonical Hamiltonian Systems in Symplectic Statistical Manifolds
What is named Hamiltonian system in a symplectic manifold \((M, \omega )\)...
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Symplectic Foliation Transverse Structure and Libermann Foliation of Heat Theory and Information Geometry
We introduce a symplectic bifoliation model of Information Geometry and Heat Theory based on Jean-Marie Souriau's Lie Groups Thermodynamics to...
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Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier–Stokes equation
The current study dedicated to the compressible isentropic Navier–Stokes equations in one-dimensional with a general pressure law. The Lie Group...
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Algebra
This chapter discusses algebra, and we discuss simple and simultaneous equations, including the method of elimination and the method of substitution...
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Engel’s Theorem in Mathlib
We discuss the theory of Lie algebras in Lean’s Mathlib library. Using nilpotency as the theme, we outline a computer formalisation of Engel’s...
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MomentaMorph: Unsupervised Spatial-Temporal Registration with Momenta, Shooting, and Correction
Tagged magnetic resonance imaging (tMRI) has been employed for decades to measure the motion of tissue undergoing deformation. However,...
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Algorithms for Multi-conditioned Conic Fitting in Geometric Algebra for Conics
We introduce implementations of several conic fitting algorithms in Geometric algebra for conics. Particularly, we incorporate additional conditions...
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Differential Geometry and Mechanics: A Source for Computer Algebra Problems
AbstractIn this paper, we discuss the possibility of using computer algebra tools in the process of modeling and qualitative analysis of mechanical...
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Characterization of Invariant Inner Products
In several situations in differential geometry, one can be interested in determining all inner products on a vector space that are invariant under a...
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Implementation of Analytic Projective Geometry for Computer Graphics
AbstractIn their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and...
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A Non-formal Formula for the Rankin-Cohen Deformation Quantization
Don Zagier’s superposition of Rankin-Cohen brackets on the Lie group...
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Algebraic Informatics 9th International Conference, CAI 2022, Virtual Event, October 27–29, 2022, Proceedings
This book constitutes the proceedings of the 9th International Conference on Algebraic Informatics, CAI 2022, held as virtual event, in October...
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On Singular Value Decomposition and Polar Decomposition in Geometric Algebras
This paper is a brief note on the natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in...
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Distributive Laws Between the Operads \({{\,\mathrm{\textit{Lie}}\,}}\) and \({{\,\mathrm{\textit{Com}}\,}}\)
We apply computer algebra, especially linear algebra over polynomial rings and Gröbner bases, to classify inhomogeneous distributive laws between the...
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Analysing ‘Simple’ Image Registrations
Processes such as growth and atrophy cause changes through time that can be visible in a series of medical images, following the hypothesis that form...
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Degröbnerization: a political manifesto
Computer Algebra relies heavily on the computation of Gröbner bases, and these computations are primarily performed by means of Buchberger’s...
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Symmetric and asymmetric cryptographic key exchange protocols in the octonion algebra
We propose three cryptographic key exchange protocols in the octonion algebra. Using the totient function, defined for integral octonions, we...
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Splossoms: Spherical Blossoms
This paper provides an overview of spherical blossoms, called splossoms, and some of its implications. The blossom of a polynomial is a multi-affine...