Results 21 to 30 of about 944,650 (244)
On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds
Entropy, 2020 We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat ...
Frank Nielsen
doaj +1 more source
Entropy, 2020 A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework.
Florio M. Ciaglia +2 more
doaj +1 more source
Diffeological Statistical Models, the Fisher Metric and Probabilistic Mappings
Mathematics, 2020 We introduce the notion of a C k -diffeological statistical model, which allows us to apply the theory of diffeological spaces to (possibly singular) statistical models.
Hông Vân Lê
doaj +1 more source
Information-Theoretic Models for Physical Observables
Entropy, 2023 This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular ...
D. Bernal-Casas, J. M. Oller
doaj +1 more source
The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location
Journal of Computational Mathematics, 2023 In our previous work [Chen el al., J. Comput. Phys., 373(2018)], the quadratic Wasserstein metric is successfully applied to the earthquake location problem. The actual earthquake hypocenter can be accurately recovered starting from initial values very far from the true ones.
Zhou, Datong +4 more
openaire +3 more sources
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
doaj +1 more source
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
openaire +6 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source