🍩 Database of Original & Non-Theoretical Uses of Topology
(found 5 matches in 0.002552s)
Persistent Homology in Cosmic Shear - II. A Tomographic Analysis of DES-Y1 (2022)Sven Heydenreich, Benjamin Brück, Pierre Burger, Joachim Harnois-Déraps, Sandra Unruh, Tiago Castro, Klaus Dolag, Nicolas Martinet
AbstractWe demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the first-year data of the Dark Energy Survey. To obtain these constraints, we analyse the topological structure of the matter distribution by extracting persistence diagrams from signal-to-noise maps of aperture masses. This presents a natural extension to the widely used peak count statistics. Extracting the persistence diagrams from the cosmo-SLICS, a suite of \textlessi\textgreaterN\textlessi/\textgreater-body simulations with variable cosmological parameters, we interpolate the signal using Gaussian processes and marginalise over the most relevant systematic effects, including intrinsic alignments and baryonic effects. For the structure growth parameter, we find , which is in full agreement with other late-time probes. We also constrain the intrinsic alignment parameter to \textlessi\textgreaterA\textlessi/\textgreater = 1.54 ± 0.52, which constitutes a detection of the intrinsic alignment effect at almost 3\textlessi\textgreaterσ\textlessi/\textgreater.
Persistent Homology in Cosmic Shear: Constraining Parameters With Topological Data Analysis (2021)Sven Heydenreich, Benjamin Brück, Joachim Harnois-Déraps
AbstractIn recent years, cosmic shear has emerged as a powerful tool for studying the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods such as peak count statistics offer competitive results. Here we show that persistent homology, a tool from topological data analysis, can extract more cosmological information than previous methods from the same data set. For this, we use persistent Betti numbers to efficiently summarise the full topological structure of weak lensing aperture mass maps. This method can be seen as an extension of the peak count statistics, in which we additionally capture information about the environment surrounding the maxima. We first demonstrate the performance in a mock analysis of the KiDS+VIKING-450 data: We extract the Betti functions from a suite of \textlessi\textgreaterN\textlessi/\textgreater-body simulations and use these to train a Gaussian process emulator that provides rapid model predictions; we next run a Markov chain Monte Carlo analysis on independent mock data to infer the cosmological parameters and their uncertainties. When comparing our results, we recover the input cosmology and achieve a constraining power on that is 3% tighter than that on peak count statistics. Performing the same analysis on 100 deg\textlesssup\textgreater2\textlesssup/\textgreater of \textlessi\textgreaterEuclid\textlessi/\textgreater-like simulations, we are able to improve the constraints on \textlessi\textgreaterS\textlessi/\textgreater\textlesssub\textgreater8\textlesssub/\textgreater and Ω\textlesssub\textgreaterm\textlesssub/\textgreater by 19% and 12%, respectively, while breaking some of the degeneracy between \textlessi\textgreaterS\textlessi/\textgreater\textlesssub\textgreater8\textlesssub/\textgreater and the dark energy equation of state. To our knowledge, the methods presented here are the most powerful topological tools for constraining cosmological parameters with lensing data.
Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics (2020)Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami, Yasin Ozcan
AbstractWhere do ﬁrms innovate? Mapping their locations in technological space is diﬃcult, because it is high dimensional and unstructured. We address this issue by using a method in computational topology called the Mapper algorithm, which combines local clustering with global reconstruction. We apply this method to a panel of 333 major ﬁrms’ patent portfolios in 1976–2005 across 430 technological areas. Results suggest the Mapper graph captures salient patterns in ﬁrms’ patenting histories, and our measures of their uniqueness (the length of “ﬂares”) are correlated with ﬁrms’ ﬁnancial performances in a statistically and economically signiﬁcant manner. We then compare this approach with a widely used clustering method by Jaﬀe (1989) to highlight additional ﬁndings.
Interdisciplinary Approaches to Automated Obstructive Sleep Apnea Diagnosis Through High-Dimensional Multiple Scaled Data Analysis (2019)Giseon Heo, Kathryn Leonard, Xu Wang, Yi Zhou