Related papers: Probing Dark Energy with Alpha Shapes and Betti Nu…
While the statistical and resilience properties of the Internet are no more changing significantly across time, the Darknet, a network devoted to keep anonymous its traffic, still experiences rapid changes to improve the security of its…
In this work, we consider the possibility that the dynamical dark energy hinted at by recent DESI data may be mimicked by the effects of additional components in the universe, potentially arising from topological defects. We find that the…
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…
The distribution of angles subtended between pairs of galaxies and the line of sight,which is uniform in real space, is distorted by their peculiar motions, and has been proposed as a probe of cosmic expansion. We test this idea using…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
Our standard model of the Universe predicts the distribution of dark matter to $1\%$ at the scales needed for upcoming experiments, yet our predictions for how the luminous matter -- which has interactions besides gravity -- is distributed…
Precise cosmic web classification of observed galaxies in massive spectroscopic surveys can be either highly uncertain or computationally expensive. As an alternative, we explore a fast Machine Learning-based approach to infer the…
We perform an analysis of the Cosmic Web as a complex network, which is built on a $\Lambda$CDM cosmological simulation. For each of nodes, which are in this case dark matter halos formed in the simulation, we compute 10 network metrics,…
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…
We describe an implementation of the structure functions of Babul \& Starkman, in order to quantify the ``sheet-like'' nature of a distribution of matter. We test this statistic on a toy model describing cosmic string wakes, and show that…
While $f(T)$ gravity has shown considerable potential in addressing cosmological tensions, we explore previously overlooked solution spaces that hold further promise. We examine the case where the customary assumption of a strictly positive…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density…
Galaxies are biased tracers of the underlying cosmic web, which is dominated by dark matter components that cannot be directly observed. The relationship between dark matter density fields and galaxy distributions can be sensitive to…
We perform an empirical consistency test of General Relativity/dark energy by disentangling expansion history and growth of structure constraints. We replace each late-universe parameter that describes the behavior of dark energy with two…
The standard framework within which cosmological measurements are confronted and interpreted nowadays, called Lambda Cold Dark Matter, presents a Universe dominated by unknown forms of energy and matter. My Thesis is devoted to investigate…
The analysis of optical images of galaxy-galaxy strong gravitational lensing systems can provide important information about the distribution of dark matter at small scales. However, the modeling and statistical analysis of these images is…
We apply methods of topological analysis to the attention graphs, calculated on the attention heads of the BERT model ( arXiv:1810.04805v2 ). Our research shows that the classifier built upon basic persistent topological features (namely,…
Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulation-based analysis of a set of…