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It is not clear that the above equation is a sufficient condition for constructing equivalence classes.
This is a necessary condition for constructing a reversible evolutionary Hidden Markov model (HMM) from pair-HMMs along the branches of τ.
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The underlying logic is that correlation is a necessary, but not sufficient, condition for construct validity.
Moreover, this characterization suggests very simple sufficient conditions for constructing tight frames from multiresolution.
The sufficient conditions for constructing the underdetermined mixing matrix for encryption are then described.
But Deutsch's two conditions for constructing the idea of nationhood were amply fulfilled in the 20th century, when two great wars gave the British fresh opportunity to hate their neighbours and to misunderstand their own history.
Thai officials have bristled at China's proposed conditions for constructing the rail link, including Chinese management of its operations, rights to develop land along the 870-kilometer route, and a 4percentt interest rate on related loans.
Some sufficient conditions for constructing upper and lower solutions are given in each section for applications.
Conditions for constructing a Riesz wavelet basis are given by the following lemma.
Structural conditions for constructing such UP-equivalent PMs are proposed, which results in numerous new architectures of UP-equivalent PMs.
In particular, sufficient conditions for constructing temporally smoothed matrices to resolve K>2 incompletely polarized (IP) monochromatic signals with a single vector sensor have been established.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com