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The problem is NP-hard even when restricted to just not equal constraints.
Even when restricted laser sources are employed, a small number of color codes can be expressed simultaneously.
Even when restricted to images in specific domains such as music score recognition, solving image processing problems usually requires the design of customized algorithms.
At the end of the paper, we show that the mixed domination problem is NP-complete even when restricted to split graphs, a subclass of chordal graphs.
We use the language and techniques of quantum probability but, even when restricted to the classical case, our results seem to be new.
Such courage of endurance calls not simply for the zest of external attack, but for a deep inner movement of the soul that allows us to keep moving even when restricted in place.
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A tailored lay-up exhibiting spatially distirbuted stacking sequences is implemented to achieve multi-stability even when restricting two opposing edges.
The first point to be made then is that the geographic distribution of known early archeological sites does not readily conform to the distribution predicted from the traditional colonization scenario, even when restricting attention to the widely accepted sites and dates across the Americas.
The positive correlations between EPC number and hypertension, Hba1c and triglycerides remain significant even when restricting the analyses to subjects without any medication, which indicates that these unexpected trends are not confounded by drug therapy.
However, as our group has recently reported in a smaller subset of participants (n = 30) [34], HIV controllers also had significantly higher frequencies of activated (CD38+ HLA-DR+) CD8+ T cells (Figure 1A) and CD4+ T cells (Figure 1B) than HIV-uninfected participants (P<0.001 for both), even when restricting to HCV-uninfected individuals (P<0.001).
Thus, even when restricting to time-feasible solutions, this number can remain huge.
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CEO of Professional Science Editing for Scientists @ prosciediting.com