“…In the previous work of the author, a non-trivial symmetry of the relative entropy in the information geometry of normal distributions was discovered. The same symmetry also appears in the symplectic/contact geometry of Hilbert modular cusps. …”
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“…The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.…”
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“…Our data show that the geometry of the roots increased in tortuosity from C5 to T1, with no significant differences between sides. …”
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“…We investigate two related geometries on wald space. The first is the geometry of the Fisher information metric of character distributions induced by the two-state symmetric Markov substitution process on each tree. …”
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“…Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we construct networks of European banks and demonstrate that the latent geometry of these financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. …”
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“…One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. …”
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“…Only recently, researchers have started devoting attention to the higher-order architecture of complex financial systems, that can significantly enhance our ability to estimate systemic risk as well as measure the robustness of financial systems in terms of market efficiency. Geometry-inspired network measures, such as the Ollivier–Ricci curvature and Forman–Ricci curvature, can be used to capture the network fragility and continuously monitor financial dynamics. …”
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“…We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. …”
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“…Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. …”
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“…We characterise the geometry of the statistical Roegenian manifold that arises from the equilibrium distribution of an income of noninteracting identical economic actors. …”
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“…The backbone bond lengths, bond angles, and planarity of a protein are influenced by the backbone conformation (φ,Ψ), but no tool exists to explore these relationships, leaving this area as a reservoir of untapped information about protein structure and function. The Protein Geometry Database (PGD) enables biologists to easily and flexibly query information about the conformation alone, the backbone geometry alone, and the relationships between them. …”
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“…Furthermore, shock cluster number and shock chain length or area of low static pressure zone were used to analyze the effect of geometries on ejector performance, which is normally indicated by entrainment ratio (ER, or the ratio between the mass flow rate of secondary flow and the mass flow rate of primary flow). …”
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