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Let L be an estimate of the upper bound of possible scaffold length (e.g. an estimated upper bound of the length of the entire genome or the longest chromosome).
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In particular, one consequence is the existence of proper n-edge-colourings of both Kn+1 (for n odd) and Kn,n with a constant bound on the length of two-colored cycles.
If both the number of inputs and that of outputs are bounded by 2 and all regulatory functions are biased, then 10 n / 4 is an upper bound on the length of periodic orbits in n-dimensional networks.
Mmax is essentially an upper bound on the length of all channels in the system.
And without an upper bound on the length of such a string, it is not even clear how to solve the problem by an exhaustive search.
Second, next-generation sequencing machines have a lower bound on the length of the reads.
An upper bound on the length of the pattern and a maximum length difference between subsequences compared leads to a very efficient algorithm.
Turns typically last <4 s, which limits the length of stimulus history that can be used in a linear filter, which thus puts a ∼4-s upper bound on the length of stimulus response that can be predicted.
For the fragments at the end of sequences we relaxed equation Equation (1 ) to a version where the absolute value is not taken, i.e we only test an upper bound on the length of fragments.
Here consider the same affine estimators of the form F (w ) = w ∗ + ∑ j = 1 N w j Y j, but assume f(x) is a sigmoidal function exp{ ao + a · x}/(1 + exp{ ao + a · x}) with a prescribed bound on the length of a, and then get a bound on the mean squared error at xo.
In addition, jobs may run for too long, risking eviction from the machines they are running on – non-dedicated machines in the pool are normally only available when they would otherwise be idle, such as overnight and at weekends – meaning there is often an upper bound on the length of time a job can run for.
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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