B.Saulnier

Phd thesis

I did my PhD in the Computer science lab. of ENS (Equipe CIM, Dpt. d'Informatique DI, Ecole Normale Supérieure ENS).

My advisors were Giuseppe Longo (opens new window) (Computer science) and Francis Bailly (opens new window) (Physics).

PhD committee:

Summary

In a first part, this thesis contributes to a theoretical analysis of the foundations of dynamics and states inference in biology. We use different entropies to give a precise mathematical form to the information quantity associated to a measurement process, and develop a unified theoretical framework, from the static or dynamical point of view.

We make explicit the causal completeness hypothesis that underlies the use of interaction networks in biocomputing. Existing works do not make this hypothesis explicit, and do not justify it. We show that this hypothesis can not be justified from the analysis of histograms produced experimentally. Actually, a theory is needed to guarantee the reproducibility of an experiment, control the experimental variability, and allow the reconstruction of a probability distribution from the measurement of frequencies.

To escape this reproducibility pitfall, the dynamical approach allows to deal with data produced by one unique experiment. We show, within symbolic dynamics, that the different information quantities one can associate to a data source are equivalent. But their effective calculation needs infinite data sequences. Therefore, rebuilding a dynamics needs a prior theoretical characterization.

In the second part of the thesis, we then use methods from statistical physics, to show that entropy, seen as a missing information, is relative to a given scale. Therefore, one deals with hierarchies of entropies. If scales are separable, then a phenomenological description, like interaction networks, with few variables and autonomous equations, is possible. If not, the statistical treatment of fluctuations must be adapted.

In this last case, we show that only the relation between scales is objective. To develop this idea, we build a model, related to scaling laws which govern biological thermodynamics. We show that, if scaling laws exist in biology, then, within an organism, the massic enthalpy equals the product of the characteristic groth time and of the metabolism scaling coefficient. This result is experimentally confirmed, so that the model contributes to a theoretical justification of scaling laws observed in biology.

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Please contact me for more information or the full thesis.

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