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In this case, the path y → x′ → ϕ → t is a path from y to t in G f (again, the existence of all edges of this path in G f can be asserted from the flow conservation constraints).
Nevertheless, it can be asserted from the lemmas in Section 'Reducing MCM to Min-Cost Max-Flow', Proposition 1, and their proofs, that for an optimal flow f′ in N x, y, MCM(X ∖ { x}, Y ∖ { y}, w) = c o s t(f′) + w X ∖ { x }, Y ∖ { y }.
The correctness of the observation can be asserted from the fact that A is an isomorphic alignment between a smoothed subtree of T that contains v, x, and y, and a smoothed subtree of S that contains v′, x′, and y′.
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As such, all that can be asserted from these experiments is the changes in RNA length.
It is simple to observe that f M is a valid flow in N (satisfying the capacity and flow conservation constraints), where its maximality is asserted from the fact that it saturates the cut ({ s}, V ∖ { s}).
One commonly used approach for setting up such "ground truth" is by spiking in bacterial synthetic transcripts with known concentrations in series of dilutions over a large dynamic range [ 22], however, the limitation of this approach is that the information is asserted from very limited transcripts, and it is also very prone to experimental artifacts.
It is asserted from various studies that noticeable numbers of senior citizens are of critical concern about their privacy.
Apart from all that, (perhaps) most importantly, the measure 'density' does not possess the capability to view proteins as nonlinear complex systems, as have been asserted (from various perspectives) in recent studies [28] [30].
Annotations can be asserted manually from the literature by biocurators or computationally by automated methods.
From this, it can be asserted that the PAI index seems to be higher when a smaller bandwidth is implemented irrespective of time-of-day.
"Confidentiality shouldn't be asserted to shield the government from accountability," said Judge J. Michael Luttig, former head of the Office of Legal Counsel in the first Bush administration, "but by the same token, confidential advice to the president is essential to the proper functioning of the executive branch".
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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