🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001131s)

  1. Characterising Epithelial Tissues Using Persistent Entropy (2019)

    N. Atienza, L. M. Escudero, M. J. Jimenez, M. Soriano-Trigueros
    Abstract In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by \$\$\alpha \$\$α-complexes and persistent homology. After using some statistical tests, we can guarantee the existence of significant differences in the studied tissues.

  2. A Topological Measurement of Protein Compressibility (2015)

    Marcio Gameiro, Yasuaki Hiraoka, Shunsuke Izumi, Miroslav Kramar, Konstantin Mischaikow, Vidit Nanda
    Abstract In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels and cavities. The persistence diagrams of this alpha filtration capture the sizes and robustness of such tunnels and cavities in a compact and meaningful manner. From these persistence diagrams, we extract a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties. Due to recent advances in combinatorial topology, this measure is efficiently and directly computable from information found in the Protein Data Bank (PDB). Our main result establishes a clear linear correlation between the topological measure and the experimentally-determined compressibility of most proteins for which both PDB information and experimental compressibility data are available. Finally, we establish that both the topological measurement and the linear correlation are stable with respect to small perturbations in the input data, such as those arising from experimental errors in compressibility and X-ray crystallography experiments.