We study the geometric decomposition of the (reduced) Persistent Homology Transform (PHT). We focus on two special classes of objects, star shapes and cutouts. We prove that the PHT_0 of the former ...

Ritwik is a passionate gamer who has a soft spot for JRPGs. He's been writing about all things gaming for six years and counting. No matter how great a title's gameplay may be, there's always the ...

Understanding individual differences in brain dynamics is a central goal in neuroscience. While conventional time series features capture signal properties of local brain regions, they often fail to ...

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Article subjects are automatically applied from the ACS Subject Taxonomy and describe the scientific concepts and themes of the article. To evaluate the defect formation energies, first-principles ...

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In past years, elections in the U.S. have been marked by stories of long waiting lines at the voting polls. Add other barriers, like long commutes and inadequate transportation, and voting can become ...

Abstract: While persistent homology has been successfully used to provide topological summaries of point cloud data, the question of computing persistent homology of graphs or networks remains unclear ...

This article describes a non-parametric clustering algorithm with an outlier removal step. Our method is based on tools from topological data analysis: we define a new filtration on metric spaces ...