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Barcoding Invariants and Their Comparison
Emerson G. Escolar, Woojin Kim
The persistence barcode, which can be obtained from the interval decomposition of a persistence module, plays a pivotal role in applications of persistent homology. For multi-param…
A topological analysis of the space of recipes
Emerson G. Escolar, Yuta Shimada, Masahiro Yuasa
In recent years, the use of data-driven methods has provided insights into underlying patterns and principles behind culinary recipes. In this exploratory work, we introduce the us…
Bipath Persistence
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this se…
Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
Mickaël Buchet, Emerson G. Escolar
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is th…