🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001066s)

  1. HiDeF: Identifying Persistent Structures in Multiscale ‘Omics Data (2021)

    Fan Zheng, She Zhang, Christopher Churas, Dexter Pratt, Ivet Bahar, Trey Ideker
    Abstract In any ‘omics study, the scale of analysis can dramatically affect the outcome. For instance, when clustering single-cell transcriptomes, is the analysis tuned to discover broad or specific cell types? Likewise, protein communities revealed from protein networks can vary widely in sizes depending on the method. Here, we use the concept of persistent homology, drawn from mathematical topology, to identify robust structures in data at all scales simultaneously. Application to mouse single-cell transcriptomes significantly expands the catalog of identified cell types, while analysis of SARS-COV-2 protein interactions suggests hijacking of WNT. The method, HiDeF, is available via Python and Cytoscape.

  2. Community Structures in Simplicial Complexes: An Application to Wildlife Corridor Designing in Central India -- Eastern Ghats Landscape Complex, India (2020)

    Saurabh Shanu, Shashankaditya Upadhyay, Arijit Roy, Raghunandan Chundawat, Sudeepto Bhattacharya
    Abstract The concept of simplicial complex from Algebraic Topology is applied to understand and model the flow of genetic information, processes and organisms between the areas of unimpaired habitats to design a network of wildlife corridors for Tigers (Panthera Tigris Tigris) in Central India Eastern Ghats landscape complex. The work extends and improves on a previous work that has made use of the concept of minimum spanning tree obtained from the weighted graph in the focal landscape, which suggested a viable corridor network for the tiger population of the Protected Areas (PAs) in the landscape complex. Centralities of the network identify the habitat patches and the critical parameters that are central to the process of tiger movement across the network. We extend the concept of vertex centrality to that of the simplicial centrality yielding inter-vertices adjacency and connection. As a result, the ecological information propagates expeditiously and even on a local scale in these networks representing a well-integrated and self-explanatory model as a community structure. A simplicial complex network based on the network centralities calculated in the landscape matrix presents a tiger corridor network in the landscape complex that is proposed to correspond better to reality than the previously proposed model. Because of the aforementioned functional and structural properties of the network, the work proposes an ecological network of corridors for the most tenable usage by the tiger populations both in the PAs and outside the PAs in the focal landscape.