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 ...

In forecasting economic time series, statistical models often need to be complemented with a process to impose various constraints in a smooth manner. Systematically imposing constraints and retaining ...

Machine learning has become an essential tool in computational drug design, enabling models to uncover patterns in molecular data and predict protein–ligand interactions. This study introduces a novel ...

Introduction: 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 ...

Dendritic structures that emerge during the growth of thin films are a major obstacle in large-area fabrication, a key step towards commercialization. However, current methods of studying dendrites ...

Introduction: Mild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity. In this paper, the applicability of persistent ...

Persistent Systems Ltd. has its fingers in many pies, with the goal of spurring digital transformation across diverse industries. The technology services company, which has been operating for over 30 ...

The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding.

Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ...