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However, voting behaviour is messy - it will be distributed among all the different possible combinations (including invalid and blank ballots), uncoordinated and in several cases voters won't include more than one preference.
If the cluster of average points is too small (i.e. it contains very few points), but is near the threshold S, all other routes (including invalid ones) outside the cluster are inspected for a starting point near the average point of the cluster which minimizes the distance.
* Lack of sufficient personnel to manage contracts and insufficient contract oversight including invalid invoices as well as inadequate performance.
The remaining participants were not contacted for various reasons (including invalid or changed telephone number, telephone not answered, and patient moved).
All clinical data were reviewed; this allowed us to avoid including invalid data from the computerized databases, for example, incorrect blood pressure measured during sampling blood from an arterial line.
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"We've disclosed that our rate, before hiring Click Forensics, was between 12 and 15percentt," a number that includes invalid clicks, or traffic that an advertiser should not pay for, he said.
Fourth, we excluded records that include invalid data.
A reason for this might be that it is possible to include invalid trellis paths in the calculation by using the BB detection approach [15].
Defects in title may include invalid powers of attorney, deeds by minors, improperly recorded documents, undisclosed heirs, gaps in the chain of title, false impersonations, incorrect legal descriptions, errors in the tax records, IRS or other tax liens and even forged documents.
We must include invalid stops in regular CompStat reports.
Approximately 10% of the compiled records included invalid or nonresidential (including urban post office boxes) postal codes and were excluded from the residential history assignment.
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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