Results 41 to 50 of about 3,198,197 (181)
How smooth is quantum complexity?
Journal of High Energy Physics, 2021 The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational ...
Vir B. Bulchandani, S. L. Sondhi
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Liouville Integrability in a Four-Dimensional Model of the Visual Cortex
Journal of Imaging, 2021 We consider a natural extension of the Petitot–Citti–Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account.
Ivan Galyaev, Alexey Mashtakov
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Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry [PDF]
SIAM Journal on Applied Mathematics, 2018 From the point of view of the theory of the partial differential equations, the paper is concerned with the Helmholtz version of the Grushin equation \[ (\partial^2_x+ x^{2r}\partial^2_y) u+ \rho^2u= 0,\quad r=1,2,\dots, \] which, by separation of variables, reduces to the analysis of eigenfunctions of anisotropic harmonic oscillators.
Allan Greenleaf +4 more
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A proof of a trace formula by Richard Melrose
Advanced Nonlinear Studies, 2023 The goal of this article is to give a new proof of the wave trace formula proved by Richard Melrose in an impressive article. This trace formula is an extension of the Chazarain-Duistermaat-Guillemin trace formula (denoted as “CDG trace formula” in this ...
Colin de Verdière Yves
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Curvature and the equivalence problem in sub-Riemannian geometry
Archivum Mathematicum, 2022 These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with ...
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Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
ESAIM: Proceedings and Surveys, 2018 In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information
Boscain Ugo +4 more
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Journal of Differential Geometry, 1986 A sub-Riemannian or singular Riemannian geometry is given by a smoothly varying positive definite quadratic form defined only on a subbundle \(S\) of the tangent bundle \(TM\) of a differentiable manifold, \(S\) being bracket-generating, that is sections of \(S\) together with their Lie brackets generate the \(C^{\infty}(M)\)-module \(V(M)\) of vector ...
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Screen Cauchy–Riemann (SCR)-lightlike submanifolds of metallic semi-Riemannian manifolds [PDF]
Arab Journal of Mathematical SciencesPurposeThe screen Cauchy–Riemann (SCR)-lightlike submanifold is an important class of submanifolds of semi-Riemannian manifolds. It contains various other classes of submanifolds as its sub-cases. It has been studied under various ambient space.
Gauree Shanker +2 more
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Frontiers in Human Neuroscience, 2021 Objective: Tangent Space Mapping (TSM) using the geometric structure of the covariance matrices is an effective method to recognize multiclass motor imagery (MI).
Fan Wu +11 more
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Quantum geometric tensors from sub-bundle geometry [PDF]
QuantumThe geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the
Marius A. Oancea +2 more
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