🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.00111s)

  1. Topological Data Analysis of Single-Cell Hi-C Contact Maps (2020)

    Mathieu Carrière, Raúl Rabadán
    Abstract Due to recent breakthroughs in high-throughput sequencing, it is now possible to use chromosome conformation capture (CCC) to understand the three dimensional conformation of DNA at the whole genome level, and to characterize it with the so-called contact maps. This is very useful since many biological processes are correlated with DNA folding, such as DNA transcription. However, the methods for the analysis of such conformations are still lacking mathematical guarantees and statistical power. To handle this issue, we propose to use the Mapper, which is a standard tool of Topological Data Analysis (TDA) that allows one to efficiently encode the inherent continuity and topology of underlying biological processes in data, in the form of a graph with various features such as branches and loops. In this article, we show how recent statistical techniques developed in TDA for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological structures coming from biological phenomena, such as the cell cyle, in datasets of CCC contact maps.

  2. Two-Tier Mapper, an Unbiased Topology-Based Clustering Method for Enhanced Global Gene Expression Analysis (2019)

    Rachel Jeitziner, Mathieu Carrière, Jacques Rougemont, Steve Oudot, Kathryn Hess, Cathrin Brisken
    Abstract MOTIVATION: Unbiased clustering methods are needed to analyze growing numbers of complex datasets. Currently available clustering methods often depend on parameters that are set by the user, they lack stability, and are not applicable to small datasets. To overcome these shortcomings we used topological data analysis, an emerging field of mathematics that discerns additional feature and discovers hidden insights on datasets and has a wide application range. RESULTS: We have developed a topology-based clustering method called Two-Tier Mapper (TTMap) for enhanced analysis of global gene expression datasets. First, TTMap discerns divergent features in the control group, adjusts for them, and identifies outliers. Second, the deviation of each test sample from the control group in a high-dimensional space is computed, and the test samples are clustered using a new Mapper-based topological algorithm at two levels: a global tier and local tiers. All parameters are either carefully chosen or data-driven, avoiding any user-induced bias. The method is stable, different datasets can be combined for analysis, and significant subgroups can be identified. It outperforms current clustering methods in sensitivity and stability on synthetic and biological datasets, in particular when sample sizes are small; outcome is not affected by removal of control samples, by choice of normalization, or by subselection of data. TTMap is readily applicable to complex, highly variable biological samples and holds promise for personalized medicine. AVAILABILITY AND IMPLEMENTATION: TTMap is supplied as an R package in Bioconductor. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.