By asking what happened when space, food, or water did limit population growth, students could see the biological and mathematical consequences of assumptions.
Of particular importance was the assessment of the consequences of assumptions used in M&S: assumptions can be violated (e.g., addressed by additional evidence or a better model), mitigated (e.g., by label restriction, treatment regimen adjustment) or managed as potential risks for patients, regulators or sponsors.
The consequence of assumptions about dose levels depends on another assumption, the dose response: the increase in cancer for each unit increase in radiation dose.
This fact is a consequence of assumption (A.3)(a).
The uniqueness of the common fixed point is a consequence of assumption (F2).
Estimate (19) is purely a consequence of Assumption A via Remark 4. [2, Proposition 5.1].
This is in turn a consequence of assumption (3) in Definition 144.
Estimate (19) is purely a consequence of Assumption A via Remark 4. [2, Proposition 5.1] In this proposition, it is shown that there exists C such that if (Pi _y u,r ge C) then begin{aligned} lambda _{r/2}^{1/2}le frac{tilde{C}}{Vert Pi _y u,r Vert _{L^infty (B_1)}}lambda _{r}^{1/2} end{aligned} (20) for some (tilde{C}>0).
Using assumption (12) on Φ, we obtain that for all u ∈ , there exists r u ∈ ( σ, u ) such that ∫ σ + ∞ P ( s ) I s < u Φ ( s, u ) d s ≤ θ P ( r u ) ≤ θ B P ( u ), the second inequality being a consequence of assumption (25) on P. We deduce that there exists a constant C such that ∫ σ ∞ P ( s ) | m ( s, t ) | d s ≤ C ∫ 0 + ∞ P ( s ) ( | M ( s, t ) | + | J ( s, t ) | ) d s. (27).
Different approaches, notation, etc., are used by the authors of those theories, so it is not always straightforward to compare the assumptions made and to assess the quantitative consequences of those assumptions.
A more concise discussion focusing on the main ideas, i.e. the importance of model selection, the assumptions of the Koonin & Wolf model, and the consequences of these assumptions in distinguishing simulated and real data would likely increase readership substantially relative to the present version.
