Abstract
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.
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Refer to Remarks 5 an 6 for outstanding issues related to the definition of geometric path integrals.
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Acknowledgement
We would like to thank Mirco Mannucci, Roman Buniy, and the referee for very useful comments.
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This paper is dedicated to the memory of Leon Ehrenpreis 1930–2010.
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Napoletani, D., Petricoin, E., Struppa, D.C. (2012). Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness. In: Sabadini, I., Struppa, D. (eds) The Mathematical Legacy of Leon Ehrenpreis. Springer Proceedings in Mathematics, vol 16. Springer, Milano. https://doi.org/10.1007/978-88-470-1947-8_16
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DOI: https://doi.org/10.1007/978-88-470-1947-8_16
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