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In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological structures coming from biological phenomena in datasets of CCC contact maps.
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $mathbb{Z}_2
The probability of two loci, separated by a certain genome length, being in contact can be inferred using the Chromosome Conformation Capture (3C) method and related Hi-C experiments. How to go from the contact map, a matrix listing the mean contact
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular pieces-ca
Data analysis often concerns not only the space where data come from, but also various types of maps attached to data. In recent years, several related structures have been used to study maps on data, including Reeb spaces, mappers and multiscale map
The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constit