🍩 Database of Original & Non-Theoretical Uses of Topology
(found 5 matches in 0.001747s)
Atom-Specific Persistent Homology and Its Application to Protein Flexibility Analysis (2020)David Bramer, Guo-Wei Wei
AbstractRecently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of topological representations of the molecule. However, persistent homology is rarely employed for the analysis of atomic properties, such as biomolecular flexibility analysis or B-factor prediction. This work introduces atom-specific persistent homology to provide a local atomic level representation of a molecule via a global topological tool. This is achieved through the construction of a pair of conjugated sets of atoms and corresponding conjugated simplicial complexes, as well as conjugated topological spaces. The difference between the topological invariants of the pair of conjugated sets is measured by Bottleneck and Wasserstein metrics and leads to an atom-specific topological representation of individual atomic properties in a molecule. Atom-specific topological features are integrated with various machine learning algorithms, including gradient boosting trees and convolutional neural network for protein thermal fluctuation analysis and B-factor prediction. Extensive numerical results indicate the proposed method provides a powerful topological tool for analyzing and predicting localized information in complex macromolecules.
Deep Learning With Topological Signatures (2017)Christoph Hofer, Roland Kwitt, Marc Niethammer, Andreas Uhl
Topological Characteristics of Oil and Gas Reservoirs and Their Applications (2017)V. A. Baikov, R. R. Gilmanov, I. A. Taimanov, A. A. Yakovlev
AbstractWe demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.
Persistent Brain Network Homology From the Perspective of Dendrogram (2012)Hyekyoung Lee, Hyejin Kang, Moo K. Chung, Bung-Nyun Kim, Dong Soo Lee
AbstractThe brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes, and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales. By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms. As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attention-deficit hyperactivity disorder children, 26 autism spectrum disorder children, and 11 pediatric control subjects.