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When more than two observations that satisfy the above conditions exist, a vector detected at the closest distance is chosen, and the others are removed by an assumption that they were detected because of indirect reflections.
Table 12 in the "Appendix" section displays the eigenvalues of the Hessian matrix at the sample means and the percentage of observations that satisfy concavity for both modeling approaches, all four samples and different parametrizations of the model14.
Table 11 Exploring the complementarity result between energy and capital Open image in new window Notes: The table displays the degree of complementarity between capital and energy and the rate of observations that satisfy concavity as well as mean factor shares for different energy intensity subsets.
A challenge was to identify regions within the extreme 5% of observations that satisfy defined criteria.
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The aim is to evaluate the topological structure of the underlying signalling network and to identify and analyse model parameterisations that satisfy observations from a set of genetic knockout experiments.
In our real data applications, we show empirically that equation (31) holds even in networks that satisfy the assumptions of Observation 8 only approximately.
Designs that satisfy certain conditions are proved to be uniquely E-optimal designs when the number of observations n≡2(mod4).
Did that satisfy the Republicans?
The most likely geologic process that satisfied these observations was subduction of the oceanic crust.
Kernel density estimation places a kernel, i.e a function that satisfies probability density axioms on each observation sample.
Indeed it may be thought that the requirements of such a theory are satisfied by the observations that a judgement that p is correct only if p, and that the proposition that p is true only if p. If arguments in metaphysics or epistemology persuade us that there are facts, then we may perhaps appeal to facts in giving accounts of correctness and of truth.
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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