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Woven fabric is manifestly not a continuum and therefore Darcy's law or its modifications, or any other differential models are invalid theoretically.
Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.
The related question of which models are invalid can be answered if appropriate data are available, i.e. the inability of a model to reproduce a data set renders it invalid.
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In this case, using the Ordinary Least Square method (OLS estimates) to estimate the parameters of network data models is invalid.
Otherwise, model is invalid in minimizing cost terms.
While overlap ratio was larger than 25.7%, excessive overlap resulting in poor surface topography occurred and the prediction model was invalid.
No evidence suggested that the proportional hazards assumption, underlying the Cox model, was invalid.
In case the model is invalid it is updated and then checked again.
Hence, there is no evidence to show that the assumption for the ordinal logistic model was invalid.
On the other hand, we have to acknowledge that our model is invalid during therapy possibly due to reporting bias of progresses and toxic side effects under therapy.
A 2 ms period during which the whisker was slipping off was removed as the quasi-static model is invalid for such highly dynamic events.
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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