Characterization and classification of dynamical states of a system using persistent homology (PH) is proving to be rather fruitful in recent years. The marked success of the approach lies in mapping ...

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 ...

Abstract: We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical ...

HiDeF is a method for robustly resolving the hierarchical structures of networks based on multiscale community detection and the concepts of persistent homology. HiDeF is described in the following ...

We present a topological method for the detection and quantification of bone microstructure from non-linear microscopy images. Specifically, we analyse second harmonic generation (SHG) and two photon ...

Ripser.py is a lean persistent homology package for Python. Building on the blazing fast C++ Ripser package as the core computational engine, Ripser.py provides an intuitive interface for computing ...

Quantifying and comparing complex spatial biological datasets is crucial for medical applications and remains an active area of research. As datasets become more heterogeneous and complicated, so must ...

Our current work builds upon the idea that persistent homology can be used to detect objects in images 5. However, many real-world images contain outliers, as well as irrelevant objects, which ...