相关论文: Constructing a Space from the System of Geodesic E…

Random fields are mathematical structures used to model the spatial interaction of random variables along time, with applications ranging from statistical physics and thermodynamics to system's biology and the simulation of complex systems.…

Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…

Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a…

Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system…

The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions. Even though Ricardo's formula can…

Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…

We survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. We also propose several open problems.

Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…

Random fields are ubiquitous mathematical structures in physics, with applications ranging from thermodynamics and statistical physics to quantum field theory and cosmology. Recent works on information geometry of Gaussian random fields…

Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…

This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational…

We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages…

The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to…

The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…

Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…

We determine the Christoffel's symbols for the Siegel-Jacobi ball endowed with the balanced metric. We study the equations of geodesics on the Siegel-Jacobi ball. We calculate the covariant derivative of one-forms in the variables in which…

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is…

A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…