ﻻ يوجد ملخص باللغة العربية
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases studies: street networks in Shanghai and hotspots of COVID-19 infections. We then summarize our results and provide an outlook on TDA in spatial systems.
Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for observations
Jeongganbo is a unique music representation invented by Sejong the Great. Contrary to the western music notation, the pitch of each note is encrypted and the length is visualized directly in a matrix form in Jeongganbo. We use topological data analys
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fund
Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persistent homology to capture changes in combinatorial dynamical systems. The
Deep generative models have emerged as a powerful tool for learning informative molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. Deep generative auto-encoders de