AbstractDeep convolutional networks have proved to be extremely powerful in image analysis. However.they tend to be biased toward local features such as texture and often fail to capture the globalstructure of image and volume data. Persistent homology (PH), a tool from the emerging field oftopological data analysis, has been successfully used to detect global characteristics of data thatare ov...
AbstractThe past decade has seen large literatures develop around two novel invariants of directedgraphs: magnitude homology (due to Leinster, Hepworth and Wilerton) and the path homology ofGLMY theory. Though their origins are quite separate, Asao proved in 2022 that in fact thesehomology theories are intimately related. To every directed graph one can associate a certainspectral sequence - th...