Related papers: Gerberto e la Geografia Tolemaica
For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all…
Modern mobile applications such as navigation services and ride-sharing platforms rely heavily on geospatial technologies, most critically predictions of the time required for a vehicle to traverse a particular route, or the so-called…
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
This paper describes a flexible approach to short term prediction of meteorological variables. In particular, we focus on the prediction of the solar irradiance one hour ahead, a task that has high practical value when optimizing solar…
Although the standard cosmological model is capable of explaining most current observational data, it faces some theoretical and observational issues. This is the main motivation for exploring alternative cosmological models. In this paper,…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
Following a technique of Galileo we compute the height on a mountain on the Moon. It is based on a simple observation that precisely on a half Moon day, the Earth, the Moon, and the Sun form the vertices of a right triangle with the Moon at…
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…
Time is a parameter playing a central role in our most fundamental modeling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motions and on the strength of the…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is, out of a set of exponentially small measure in the space of…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
Understanding our place in the universe is an eternal quest. Through the analysis of the 3D structures of 66 nearby open clusters using Gaia DR3 data, we discovered an intriguing pattern: most clusters show their elongation directions…
A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the BRST cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling…
High resolution information on climatic conditions is essential to many applications in environmental and ecological sciences. Here we present the CHELSA Climatologies at high resolution for the earths land surface areas data of downscaled…
This paper introduces two astronomical methods developed through computational simulation to evaluate the historical dating of ancient astronomical sources. The first identifies a 1151-year planetary cycle based on the recurrence of visible…
Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more…