English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Mark Kac asked a famous question in 1966 entitled Can one hear the shape of adrum?, a spectral geometry problem that has intrigued mathematicians for thelast six decades and is important to many other fields, such as architecturalacoustics, audio forensics, pattern recognition, radiology, and imagingscience. A related question is how to hear the shape of a drum. We show thatthe answer was given in the set of 65 Zenghouyi chime bells dated back to475-433 B.C. in China. The set of chime bells gradually varies their sizes andweights to enable melodies, intervals, and temperaments. The same designprinciple was used in many other musical instruments, such as xylophones, panflutes, pianos, etc. We reveal that there is a fascinating connection betweenthe progression pattern of many musical instruments and filtration (or spectralsequence) in topological data analysis (TDA). We argue that filtration-inducedevolutionary de Rham-Hodge theory provides a new mathematical foundation formusical instruments. Its discrete counterpart, persistent Laplacians and manyother persistent topological Laplacians, including persistent sheaf Laplaciansand persistent path Laplacians are briefly discussed.

Topological data analysis hearing the shapes of drums and bells