🍩 Database of Original & Non-Theoretical Uses of Topology

1. Homological Scaffold via Minimal Homology Bases (2021)

   Marco Guerra, Alessandro De Gregorio, Ulderico Fugacci, Giovanni Petri, Francesco Vaccarino

   Abstract

   The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.

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   • Connectome
   • Quantitative Biology
   • Correlation matrix
   • Networks
   • Neuronal network
   • fMRI
   • Homological scaffolds
   • Network