The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry

This chapter provides a few examples of representations of the universe on a large scale—a first step in constructing a cosmological model. It first discusses the Copernican principle, which is an approximation/hypothesis about the matter distribution in the observable universe. The chapter then turns to the cosmological principle—a hypothesis about the geometry of the Riemannian spacetime representing the universe, which is assumed to be foliated by 3-spaces labeled by a cosmic time t which are homogeneous and isotropic, that is, ‘maximally symmetric’. After a discussion on maximally symmetric space, this chapter considers spacetimes with homogenous and isotropic sections. Finally, this chapter discusses Milne and de Sitter spacetimes.

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On the expected diameter, width, and complexity of a stochastic convex hull

Computational Geometry ◽

10.1016/j.comgeo.2019.04.002 ◽

2019 ◽

Vol 82 ◽

pp. 16-31 ◽

Cited By ~ 2

Author(s):

Jie Xue ◽

Yuan Li ◽

Ravi Janardan

Keyword(s):

Convex Hull

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Publisher’s Note: Eternal time machine in (2+1)-dimensional anti–de Sitter space [Phys. Rev. D66, 084020 (2002)]

Physical Review D ◽

10.1103/physrevd.67.069902 ◽

2003 ◽

Vol 67 (6) ◽

Cited By ~ 4

Author(s):

Simon DeDeo ◽

J. Richard Gott

Keyword(s):

De Sitter Space ◽

De Sitter ◽

Time Machine

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Spherical object recognition based on the number of contour edges extracted by fitting and convex hull processing

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/0954407020969502 ◽

2020 ◽

pp. 095440702096950

Author(s):

Bochang Zou ◽

Huadong Qiu ◽

Yufeng Lu

Keyword(s):

Convex Hull ◽

Target Object ◽

Identification Accuracy ◽

Detection Accuracy ◽

Morphological Operations ◽

Circle Detection ◽

Spherical Object ◽

Single Feature ◽

Contour Fitting ◽

Rgb Images

The detection of spherical targets in workpiece shape clustering and fruit classification tasks is challenging. Spherical targets produce low detection accuracy in complex fields, and single-feature processing cannot accurately recognize spheres. Therefore, a novel spherical descriptor (SD) for contour fitting and convex hull processing is proposed. The SD achieves image de-noising by combining flooding processing and morphological operations. The number of polygon-fitted edges is obtained by convex hull processing based on contour extraction and fitting, and two RGB images of the same group of objects are obtained from different directions. The two fitted edges of the same target object obtained at two RGB images are extracted to form a two-dimensional array. The target object is defined as a sphere if the two values of the array are greater than a custom threshold. The first classification result is obtained by an improved K-NN algorithm. Circle detection is then performed on the results using improved Hough circle detection. We abbreviate it as a new Hough transform sphere descriptor (HSD). Experiments demonstrate that recognition of spherical objects is obtained with 98.8% accuracy. Therefore, experimental results show that our method is compared with other latest methods, HSD has higher identification accuracy than other methods.

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Systematics of type IIA moduli stabilisation

Journal of High Energy Physics ◽

10.1007/jhep11(2020)113 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Fernando Marchesano ◽

David Prieto ◽

Joan Quirant ◽

Pramod Shukla

Keyword(s):

Scalar Potential ◽

Systematic Search ◽

Stability Criteria ◽

De Sitter ◽

Large Subset

Abstract We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

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