Results 21 to 30 of about 1,115,323 (244)
The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location
Journal of Computational Mathematics, 2023 In this paper, we apply the Wasserstein-Fisher-Rao (WFR) metric from the unbalanced optimal transport theory to the earthquake location problem. Compared with the quadratic Wasserstein ($W_2$) metric from the classical optimal transport theory, the advantage of this method is that it retains the important amplitude information as a new constraint ...
Zhou, Datong +4 more
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From the Jordan Product to Riemannian Geometries on Classical and Quantum States
Entropy, 2020 The Jordan product on the self-adjoint part of a finite-dimensional C * -algebra A is shown to give rise to Riemannian metric tensors on suitable manifolds of states on A , and the covariant derivative, the geodesics, the Riemann tensor,
Florio M. Ciaglia +2 more
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Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum [PDF]
Open Systems & Information Dynamics, 2018 The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise ...
Florio M. Ciaglia +5 more
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Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric
Calculus of Variations and Partial Differential Equations, 2022 This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves, surfaces and measures by complementing diffeomorphic deformations with a transformation process on the varifold weights.
Hsi-Wei Hsieh, Nicolas Charon
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On the Geodesic Distance in Shapes K-means Clustering
Entropy, 2018 In this paper, the problem of clustering rotationally invariant shapes is studied and a solution using Information Geometry tools is provided. Landmarks of a complex shape are defined as probability densities in a statistical manifold.
Stefano Antonio Gattone +3 more
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Information Geometry in Roegenian Economics
Entropy, 2022 We characterise the geometry of the statistical Roegenian manifold that arises from the equilibrium distribution of an income of noninteracting identical economic actors.
Constantin Udriste, Ionel Tevy
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Information Geometry of Complex Hamiltonians and Exceptional Points
Entropy, 2013 Information geometry provides a tool to systematically investigate the parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian, then there ...
Dorje C. Brody, Eva-Maria Graefe
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NeuroImage: Clinical, 2016 Tumor heterogeneity is a crucial area of cancer research wherein inter- and intra-tumor differences are investigated to assess and monitor disease development and progression, especially in cancer. The proliferation of imaging and linked genomic data has
Abhijoy Saha +9 more
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Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
CoRR, 2017 We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of the new capacity measure, through
Liang, T +3 more
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Fisher-Rao geometry of Dirichlet distributions
, 2021 International audienceIn this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has everywhere negative sectional curvature.
Puechmorel, Stéphane +2 more
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