Related papers: Persistent homology in cosmic shear: constraining …
Maximising the information that can be extracted from weak lensing measurements is a key goal for upcoming surveys such as LSST and Euclid. This is typically achieved through statistics that are complementary to the cosmic shear two-point…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…
Persistent homology is one of the most active branches of Computational Algebraic Topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this paper, we report on the formal…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
We quantify the cosmological constraining power of the `lensing PDF' - the one-point probability density of weak lensing convergence maps - by modelling this statistic numerically with an emulator trained on $w$CDM cosmic shear simulations.…
(abridged) We present the Significant Cosmic Holes in Universe (SCHU) method for identifying cosmic voids and loops of filaments in cosmological datasets and assigning their statistical significance using techniques from topological data…
We explore the cosmological constraints from cosmic shear using a new way of modelling the non-linear matter correlation functions. The new formalism extends the method of Angulo & White (2010), which manipulates outputs of $N$-body…
The persistent Betti numbers are used in topological data analysis to infer the scales at which topological features appear and disappear in the filtration of a topological space. Most commonly by means of the corresponding barcode or…
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We study the statistics of peaks in a weak lensing reconstructed mass map of the first 450 square degrees of the Kilo Degree Survey. The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated…
Context. Weak lensing and clustering statistics beyond two-point functions can capture non-Gaussian information about the matter density field, thereby improving the constraints on cosmological parameters relative to the mainstream methods…
Context. Gravitational lensing is one of the leading tools in understanding the dark side of the Universe. The need for accurate, efficient and effective methods which are able to extract this information along with other cosmological…
Shear peak statistics has gained a lot of attention recently as a practical alternative to the two point statistics for constraining cosmological parameters. We perform a shear peak statistics analysis of the Dark Energy Survey (DES)…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…