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

  • Domenico Napoletani
  • Emanuel Petricoin
  • Daniele C. Struppa
Part of the Springer Proceedings in Mathematics book series (PROM, volume 16)


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.


Path Integral Meaningful Condition Radon Transform Path Integral Formalism Phase Interference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Mirco Mannucci, Roman Buniy, and the referee for very useful comments.


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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Domenico Napoletani
    • 1
    • 2
  • Emanuel Petricoin
    • 1
  • Daniele C. Struppa
    • 2
  1. 1.Center for Applied Proteomics and Molecular MedicineGeorge Mason UniversityManassasUSA
  2. 2.Schmid College of Science and TechnologyChapman UniversityOrangeUSA

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