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The use of cross section data makes it necessary for some assumptions to be made.
The theory of multistage carcinogenesis and the ensuing notion of transformation resistance of cells as the countdown trigger of carcinogenesis (see above) lay the basis for some assumptions.
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Those who don't know the history of hatha yoga's rise in the west might be forgiven for making some assumptions.
For example, some assumptions (e.g., directionality or monotonicity of treatment effects) are readily stated via counterfactuals but require augmentations to our causal diagrams.
The ancient canon of gradual evolution is certainly valuable for demonstrating that some assumptions are met for the hypothesis that natural selection generates complexity, serving as a colorful and graphical example (Dawkins 1996).
For system (2.1), some assumptions are given in the following: (A1) For (i,jin mathcal{N}), (a_{i}(t)>0), (b_{ij}(t)), (c_{ij}(t)) and (I_{i}(t)) are bounded continuous functions defined on (R_).
Second, even if all assumptions hold, the method potentially proves that for at least some assumptions (the assessed input variables), the assumed cause-effect-relations are statistically highly uncertain.
Next, we recall briefly some lemmas used to prove the well-posedness of the solutions and the existence of the uniform (w.r.t. σ ∈ Σ ) attractors for (1 - 3) under some assumptions on f.
This study has several limitations, for instance because some assumptions were needed in our analyses.
For data analysis, some assumptions were made (e.g., upper and lower MEP limits) which may have biased the results.
Using the theory of foliations, we derive necessary and sufficient conditions for global exponential observers for nonlinear systems under some assumptions.
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CEO of Professional Science Editing for Scientists @ prosciediting.com