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This hierarchical modelling combining two different approaches at two different scales (mathematical deterministic equations on a large multi-kilometric scale, and partly stochastic cellular automata on a small hectometric scale), requires methods to validate its results in the field, in the framework of a decision support system.
The elementary building blocks in this model of MTS are the individual tumor cells that behave as partly stochastic automata [21], [22].
Instead, development is partly stochastic [ 7].
Blood vessel formation is a partly stochastic process (Jain, 2003) that is not possible to directly describe in our model.
The data so far indicate that cell fate decisions may be at least partly stochastic processes, but that they occur within a defined transcriptional framework governed by transcription factor networks.
Moreover, while the replication program is clearly reproducible at the level of cell populations, it is not clear whether individual cells activate the same origins in the same precise temporal order or whether origin firing is partly stochastic [ 13– 17].
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This makes DNA replication motion at least partly a stochastic process that is dependent on sequence properties such as length and base composition.
The vegetation on the islands in the Skyros archipelago differs substantially even among nearby islets, which might partly reflect stochastic factors and reveal some degree of community drift [ 75].
The current paper is devoted to random dynamics of stochastic partly dissipative systems perturbed by Lévy noise.
The author in [13] study the stochastic partly FitzHugh-Nagumo systems driven by Gaussian white noise, and show the existence of random attractor by uniform estimates on solution for large space and time variable via a cut-off technique.
It is necessary to point out that, comparing with the main result for (1.1) in [10], the two difficulties we need to tackle are the measurability and the asymptotic compactness of the solutions operators of stochastic partly dissipative systems (1.3).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com