Life sciences through mathematical models
This article discusses some of the basic principles of mathematical modeling in life sciences, and in particular the special features that make the modeling task fundamentally different from the traditional reductive modeling. The intricacies of the modeling in living systems are elucidated by simple and tractable examples that underline the problems of parametric models and the issue of non-scalability of the models.
KeywordsComplex systems Parametric models Agent-based models Computational statistics
The work of Daniela Calvetti was partly supported by Grant number 246665 from the Simons Foundation, and the work of Erkki Somersalo was partly supported by NSF Grant DMS 1016183.
- Calvetti D, Somersalo E (2010) Subjective knowledge or objective belief? An oblique look to bayesian methods. In: Large-scale inverse problems and quantification of uncertainty. Wiley, New York, pp 33–70Google Scholar
- Calvetti D, Somersalo E (2012) Computational mathematical modeling: an integrated approach across scales (vol. 17). SIAM, PhiladelphiaGoogle Scholar
- Calvetti D, Somersalo E (2013) Quantitative in silico analysis of neurotransmitter pathways under steady state conditions. Front Endocrinnol 4:137Google Scholar
- Calvetti C, Cheng Y, Somersalo E (2015) A spatially distributed computational model of brain cellular metabolism. J Theor Biol (to appear)Google Scholar
- Gilbert N (2008) Agent-based models (No. 153). Sage, New YorkGoogle Scholar
- Hadamard J (1902) Sur les problèmes aux dérivèes partielles et leur signification physique. Princeton Univ Bull 13(1902):49–52Google Scholar
- Newton RG (1993) What makes nature tick?. Harvard University Press, CambridgeGoogle Scholar
- Von Neumann J (1951) The general and logical theory of automata. Cereb Mech Behav 1:41Google Scholar
- Wigner EP (1995) The unreasonable effectiveness of mathematics in the natural sciences. In: philosophical reflections and syntheses. Springer, Berlin Heidelberg, pp 534–549Google Scholar
- Wolfram S (2002) A new kind of science. Wolfram Media, ChapaignGoogle Scholar