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The reason why we formulated this as a hypothesis rather than a theorem is that we assumed that the significant (molecular) interaction path follows the shortest path connecting two genes.
For this purpose, we formulated this as a two-step integer optimization problem, where in the first step by perturbing all the genes in a given circuit, minimal numbers of circuits that can bring about the cellular transitions are identified.
To detect long regions of focal epigenetic states, we formulated this as a problem of finding an optimal set of disjoint (non-overlapping) regions in a sequence that maximizes the sum of similarity scores in all regions.
The reason why we formulated this as a hypothesis rather than a theorem is that hypothesis 6 is based on many assumptions (2 – 4) which are difficult to proof theoretically.
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Setting begin{aligned} M_2 = sup limits _Omega |D^2 u|, quad M^prime _2 = sup limits _{partial Omega } sup limits _{|tau | = 1, tau cdot nu =0} |u_{tau tau }|, end{aligned}we formulate this as follows.
But I had not formulated this concept as tactfully as I could have, and now it was the casting agent's turn to be insulted.
We formulate this as a landmark identification problem, where a set of landmarks specifies the boundaries of the parts.
Ikeda and Jefferys formulate this as P(F|N&L;) = 1, but I prefer the more direct expression P(N&~F&L;) = 0.
We formulate this as a schema matching problem, finding appropriate paths in the data model for each required visualization attribute in a visualization template.
We'll formulate this as an existenceanduniqueness property of Lz-transform.
Of course, one could in principle formulate this as a high dimensional meta-population ODE model with many patches and coupling coefficients.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com