相关论文: Maple+GrTensorII libraries for cosmology
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic.…
In recent years, deep learning approaches have achieved state-of-the-art results in the analysis of point cloud data. In cosmology, galaxy redshift surveys resemble such a permutation invariant collection of positions in space. These…
The measurements of the temperature and polarisation anisotropies of the Cosmic Microwave Background (CMB) by the ESA Planck mission have strongly supported the current concordance model of cosmology. However, the latest cosmological data…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
Clusters of galaxies can be used for very different kinds of cosmological tests. I review a few of the methods: determination of cluster masses and dark matter content, metal enrichment and its connection to the origin of the intra-cluster…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as…
The Macaulay2 package NumericalSchubertCalculus provides methods for the numerical computation of Schubert problems on Grassmannians. It implements both the Pieri homotopy algorithm and the Littlewood-Richardson homotopy algorithm. Each…
The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
Astrophysical processes such as feedback from supernovae and active galactic nuclei modify the properties and spatial distribution of dark matter, gas, and galaxies in a poorly understood way. This uncertainty is one of the main theoretical…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
Large scale structure of the Universe becomes a leading source of precision cosmological information. We present two particular tools that can be used in cosmological analyses of the redshift space galaxy clustering data: a new open-source…
As part of the effort to meet the needs of the Large Synoptic Survey Telescope Dark Energy Science Collaboration (LSST DESC) for accurate, realistically complex mock galaxy catalogs, we have developed GalSampler, an open-source python…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…