Related papers: Spectral Representation and the Averaging Problem …
The recently introduced Spatial Spectral Compressive Spectral Imager (SSCSI) has been proposed as an alternative to carry out spatial and spectral coding using a binary on-off coded aperture. In SSCSI, the pixel pitch size of the coded…
We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial…
We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially…
Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new…
The extra space paradigm plays a significant role in modern physics and in cosmology as the specific case. In this review, the relation between the main cosmological parameters - Planck mass and Cosmological constants - and a metric of…
Swarm robotics promises adaptability to unknown situations and robustness against failures. However, it still struggles with global tasks that require understanding the broader context in which the robots operate, such as identifying the…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
In addressing the cosmological constant problem, we propose that the discrepancy between the theoretical and observed values can be ascribed to the inherent uncertainty in the spacetime metric. Mach's principle, which posits that mass…
Assuming the universe is spatially homogeneous on the largest scales lays the foundation for almost all cosmology. This idea is based on the Copernican principle, that we are not at a particularly special place in the universe.…
Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
A long standing problem in weak lensing is about how to construct cosmic shear estimators from galaxy images. Conventional methods average over a single quantity per galaxy to estimate each shear component. We show that any such shear…
Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called "flatness problem", which is…
Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with…
The matching of our epoch of existence with the approximate equality of dark energy and dark matter energy densities is an apparent further fine-tuning, beyond the already troubling 120 orders of magnitude that separate dark energy from the…
Since the Universe is inhomogeneous on scales well below the Hubble radius, light bundles from distant galaxies are deflected and distorted by the tidal gravitational field of the large-scale matter distribution as they propagate through…
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…
In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of…
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…