Related papers: Persistent homology in cosmic shear: constraining …
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
The objective of this study is to detect and quantify the periodic behavior of the signals using topological methods. We propose to use delay-coordinate embeddings as a tool to measure the periodicity of signals. Moreover, we use persistent…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
The clustering of galaxy clusters is a powerful cosmological tool, which can help to break degeneracies between parameters when combined with other cosmological observables. We aim to demonstrate its potential in constraining cosmological…
We present the first "clipped" cosmic shear measurement using data from the Kilo-Degree Survey (KiDS-450). "Clipping" transformations suppress the signal from the highest density, non-linear regions of cosmological fields. We demonstrate…
Precise cosmological inference from next-generation weak lensing surveys requires extracting non-Gaussian information beyond standard two-point statistics. We present a hybrid machine-learning (ML) framework that integrates field-level…
We evaluate the potential for current and future cosmic shear measurements from large galaxy surveys to constrain the impact of baryonic physics on the matter power spectrum. We do so using a model-independent parameterization that…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…
In this paper, we use a newly compiled sample of ultra-compact structure in radio quasars and strong gravitational lensing systems with quasars acting as background sources to constrain six spatially flat and non-flat cosmological models…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a…
This study details an approach for the analysis of social media collected political data through the lens of Topological Data Analysis, with a specific focus on Persistent Homology and the political processes they represent by proposing a…
We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By…
Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
In this paper we study a new metric for comparing Betti numbers functions in bidimensional persistent homology, based on coherent matchings, i.e. families of matchings that vary in a continuous way. We prove some new results about this…