This software paper gives an overview of the features supported by the Topology ToolKit (TTK), which is an open-source library for topological data analysis (TDA). TTK implements, in a generic and efficient way, a substantial collection of reference algorithms in TDA. Since its initial public release in 2017, both its user and developer bases have grown, resulting in a significant increase in the number of supported features. In contrast to the original paper introducing TTK [40] (which detailed the core algorithms and data structures of TTK), the purpose of this software paper is to describe the list of features currently supported by TTK, ranging from image segmentation tools to advanced topological analysis of high-dimensional data, with concrete usage examples available on the TTK website [42].
The contour tree is one of the principal tools in scientific visualisation. It captures the connectivity of level sets in scalar fields. In order to apply the contour tree to exascale data we need efficient shared memory and distributed algorithms. Recent work has revealed a parallel performance bottleneck caused by substructures of contour trees called W-structures. We report two novel algorithms that detect and extract the Wstructures. We also use the W-structures to show that extended persistence is not equivalent to branch decomposition and leafpruning.
The contour tree is a tool for understanding the topological structure of a scalar field. Recent work has built efficient contour tree algorithms for shared memory parallel computation, driven by the need to analyze large data sets in situ while the simulation is running. Unfortunately, methods for using the contour tree for practical data analysis are still primarily serial, including single isocontour extraction, branch decomposition and simplification. We report data parallel methods for these tasks using a data structure called the hyperstructure and a general purpose approach called a hypersweep. We implement and integrate these methods with a Cinema database that stores features as depth images and with a web server that reconstructs the features for direct visualization.
The ionized gas flow in the boundary layer on bodies of revolution with porous contour is studied in this paper. The gas electroconductivity is assumed to be a function of the longitudinal coordinate , x. The problem is solved using Saljnikov's version of the general similarity method. This paper is an extension of Saljnikov's generalized solutions and their application to a particular case of magnetohydrodynamic flow. Generalized boundary layer equations have been numerically solved in a four-parametric localized approximation and characteristics of some physical quantities in the boundary layer has been studied.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.