Abstract
Tychastic viability is defined in an uncertain dynamical framework and used for providing a “viability risk eradication measure”, first, by delineating the set of initial conditions from which all evolutions satisfy viability constraints, second, for the other “risky” initial states, by introducing their duration index. This approach provides an alternative to the stochastic representation of chance and these two measures replace the statistical measures (expectation, variance, etc).
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Notes
This assumption requires that the components of the variables are equipped with units of measure for being measured by real numbers. Embedding any set in the space of discrete measures (in particular, probabilities) is a way to fulfill this requirement, which may be too audacious. A qualitative representation of states should be designed for describing life sciences variables. See the forthcoming [9, Evaluation and Quotations of Sets] by O. Dordan and the author.
What was God doing before He created the Heavens and the Earth? asked Augustine of Hippo in his confessions. Is His eternity only forward in time and not backward? Introducing the concepts of temporal windows and duration function bypasses the question of origin of time.
Actually, when the Epicurean Lucretius observed what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways \({\ldots}\) their dancing is an actual indication of underlying movements of matter that are hidden from our sight in De rerum natura.
Who also discovered photosynthesis and cellular respiration.
Originating in the French “randon”, from the verb “randir”, sharing the same root than the English “to run” and the German rennen. When running too fast, one looses the control of himself, the race becomes a poor ”random walk”, bumping over scandala (stones scattered on the way) and falling down, cadere in Latin, a matter of chance since it is the etymology of this word.
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The author is grateful to Luxi Chen, Giuseppe Da Prato, Olivier Dordan, Halim Doss and H. Frankowska for their recent and older cooperation on “tychastic approach” to uncertainty. This work was partially supported by the Commission of the European Communities under the 7th Framework Programme Marie Curie Initial Training Network (FP7-PEOPLE-2010-ITN), project SADCO, contract number 264735.
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Aubin, JP. Tychastic Viability. Acta Biotheor 61, 329–340 (2013). https://doi.org/10.1007/s10441-013-9194-4
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DOI: https://doi.org/10.1007/s10441-013-9194-4