Persistence homology is an important tool for topological data analysis(TDA), and a persistence diagram is a visualization tool of persistent homology. We can compute the geometric features of the data quantitatively using persistence diagrams. When using persistence diagrams, we often want to know which part of the input data is related to the geometric features shown in the persistence diagram. In this paper, we show some approaches to the problem.
Elastic-wave turbulence has been used for a testbed for the weak turbulence theory, since it can be examined by numerical and laboratory experiments. The elastic-wave turbulence has distinctive characteristics as a wave turbulence system, one of which is the coexistence of the weak and strong turbulence. Recent researches on the elastic-wave turbulence are reviewed, not restricted to the weak turbulence properties, with focusing on energy transfers under large-scale external forcing.