Related papers: Geometric Methods for Spherical Data, with Applica…
Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly…
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of…
This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine…
The complexity and accuracy of current and future precision cosmology observational campaigns has made it essential to develop an efficient technique for directly combining simulation and observational datasets to determine cosmological and…
Geological processes determine the distribution of resources such as critical minerals, water, and geothermal energy. However, direct observation of geology is often prevented by surface cover such as overburden or vegetation. In such…
Spatial scientometrics has attracted a lot of attention in the very recent past. The visualization methods (density maps) presented in this paper allow for an analysis revealing regions of excellence around the world using computer programs…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
A solid sphere is considered, with a uniformly distributed infinity of points. Two points being pseudorandomly chosen, the analytical probability density that their separation have a given value is computed, for three types of the…
Geometry constrains but does not dictate the topology of the 3--dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
Methods based on machine learning have recently made substantial inroads in many corners of cosmology. Through this process, new computational tools, new perspectives on data collection, model development, analysis, and discovery, as well…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
These lecture notes delve into field-level inference, a framework offering a robust way to extract more information and avoid biases compared to traditional methods for cosmological data analysis. The core idea is to analyse uncompressed…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Astrometry, the precise measurement of star motions, offers an alternative avenue to investigate low-frequency gravitational waves through the spatial deflection of photons, complementing pulsar timing arrays reliant on timing residuals.…
We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
Cosmography is a model-independent phenomenological approach to observational cosmology, relying on Taylor series expansions of physical quantities as a function of the cosmological redshift or other analogous variables. A recent work…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
A flood of reliable seismic data will soon arrive. The migration to larger telescopes on the ground may free up 4-m class instruments for multi-site campaigns, and several forthcoming satellite missions promise to yield nearly uninterrupted…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…