If P is any graph property which is monotone with respect to the subgraph ordering (meaning that if A is a subgraph of B and A satisfies P, then B will satisfy P as well), then the statements "P holds for almost all graphs in G(n, p)" and "P holds for almost all graphs in " are equivalent (provided pn2 → ∞).
After an increase of population since the Second World War, Strausberg has stopped its "growth" remaining at almost 26,000 inhabitants in last one, with a little decrease in early years of 2000.
YAFFS2 marks every newly written block with a sequence number that is monotonically increasing.
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Soon after, Valiant found holographic algorithms with reductions to matchgates for #Pl-Rtw-Mon-3CNF and #7Pl-3/2Bip-VC.
A simple example of an order theoretic property for functions comes from analysis where monotone functions are frequently found.
For some filter classes, such as the Butterworth filter, the insertion loss is still monotonically increasing with frequency and quickly asymptotically converges to a roll-off of 6n dB/8ve, but in others, such as the Chebyshev or elliptic filter the roll-off near the cut-off frequency is much faster and elsewhere the response is anything but monotonic.