Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

Domenico Napoletani*, Emanuel Petricoin, Daniele C. Struppa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain.We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes.

Original languageEnglish
Pages (from-to)247-260
Number of pages14
JournalSpringer Proceedings in Mathematics
StatePublished - 2012
Externally publishedYes


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