Related papers: Persistent topology of protein space
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…
Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology.…
Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…
The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of…
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point…
We present a topology-informed approach for classifying particle jets using persistent homology, a framework that captures the structural properties of point clouds. Particle jets produced in proton-proton collisions consist of cascades of…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale,…