Related papers: Persistent homology in cosmic shear: constraining …
This is the third in a series of papers that develop a new and flexible model to predict weak-lensing (WL) peak counts, which have been shown to be a very valuable non-Gaussian probe of cosmology. In this paper, we compare the cosmological…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
Proposing scoring functions to effectively understand, analyze and learn various properties of high dimensional hidden representations of large-scale transformer models like BERT can be a challenging task. In this work, we explore a new…
We compare the cosmological constraints that can be obtained from halo clustering on non-linear scales ($2 h^{-1}$ Mpc < $r$ < $50 h^{-1}$ Mpc) using Betti curves, a topological summary statistic, and $k$-th nearest neighbor ($k$NN)…
We present a re-analysis of cosmic shear and galaxy clustering from first-year Dark Energy Survey data (DES Y1), making use of a Hybrid Effective Field Theory (HEFT) approach to model the galaxy-matter relation on weakly non-linear scales,…
Future large scale cosmological surveys will provide huge data sets whose analysis requires efficient data compression. Calculating accurate covariances is extremely challenging with increasing number of statistics used. Here we introduce a…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
In this paper, we propose a new method to use the strong lensing data sets to constrain a cosmological model. By taking the ratio…
Standard cosmological weak lensing analyses using cosmic shear are inevitably sensitive to small-scale, non-linear clustering from low-redshift structures. The need to adequately model the clustering of matter on this non-linear regime,…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as `the hierarchical algorithm'. The idea of this method is to combine information from WL maps sequentially smoothed with a…
In tomographic weak lensing surveys, the presence of nulling properties reveals symmetries inherent in the data, which rely solely on the geometrical properties of the Universe. Ensuring its validity thus provides us with constraints on the…
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions.…