Non-metric geometry as the origin of mass in gauge theories of scale invariance [PDF]
The European Physical Journal C, 2022 We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric ( $$\nabla _\mu g_{\alpha \beta }\!\not =\!0$$ ∇ μ g α β ≠ 0 ...
D. Ghilencea
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Algebraic Geometry Codes in the Sum–Rank Metric [PDF]
IEEE Transactions on Information Theory, 2023 We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study the
Elena Berardini, X. Caruso
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A spectral metric for collider geometry [PDF]
Journal of High Energy Physics, 2023 By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry.
A. Larkoski, J. Thaler
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Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States [PDF]
Europhysics letters, 2021 This paper introduces a novel approach to spatio-temporal data analysis using metric geometry to study the propagation of COVID-19 across the United States.
N. James, Max Menzies, H. Bondell
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Metric geometry of spaces of persistence diagrams [PDF]
Journal of Applied and Computational Topology, 2021 Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams.
Mauricio Che +3 more
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A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations [PDF]
Annales de l'Institut Fourier, 2021 For any polarized variety (X,L), we show that test configurations and, more generally, R-test configurations (defined as finitely generated filtrations of the section ring) can be analyzed in terms of Fubini-Study functions on the Berkovich ...
S. Boucksom, Mattias Jonsson
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CAJAL enables analysis and integration of single-cell morphological data using metric geometry
Nature Communications, 2023 High-resolution imaging has revolutionized the study of single cells in their spatial context. However, summarizing the great diversity of complex cell shapes found in tissues and inferring associations with other single-cell data remains a challenge ...
Kiya W. Govek +8 more
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Projective Metric Geometry and Clifford Algebras [PDF]
Results in Mathematics, 2021 Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group.
H. Havlicek
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Survey on the metric SYZ conjecture and non-archimedean geometry [PDF]
International Journal of Modern Physics A, 2022 We survey the metric aspects of the Strominger-Yau-Zaslow conjecture on the existence of special Lagrangian fibrations on Calabi-Yau manifolds near the large complex structure limit.
Yang Li
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Design of 3D Metric Geometry Study and Research Activities within a BIM Framework
Mathematics, 2022 This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences.
José M. Olmos-Noguera +2 more
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