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Exact(1)
This upper bound can be approximated by [9] P e | H ≈ ∏ i = 1 d w i − 1 E s 4 N t N 0 − d, (9).
Similar(59)
When is far less than, the detection probability low-bound can be approximated by (22).
However, an approximate lower bound can be found by imposing similar assumptions as in [22, 23].
The upper bound can be obtained as N<1 when d is infinitely approximate to 0 or 1.
This bound can be derived from the half-duplex cut-set bound in [52].
Assuming no ribosomal interference during translation, the expected number of ribosomes bound to each mRNA can be approximated by solving the differential equation (2) d R i b d t = ρ i − R i b ϵ i where ρ i and ϵ i are the rates of initiation and total elongation of the i th mRNA, respectively.
Assuming no ribosomal interference during translation, the expected number of ribosomes bound to each mRNA can be approximated by solving the differential equation (2) d R i b d t = ρ i − R i b ϵ i where ρ i and ϵ i are the rates of initiation and total elongation of the ith mRNA, respectively.
Similarly, the EE can be approximated by the lower bound in (49) when the antenna-array scale M is large enough.
Using the lower bound of R k, the EE η k can be approximated by η k ≈ log 1 + s k p k i k p k + I k p k + p c, (8).
In [21], it was shown that erfc can be approximated to a tighter bound than Chernoff-Rubin bound, Q ( y ) ≤ 1 6 e - y + 1 2 e - 4 3 y (33).
Determination of 'upper bound PTP' and 'lower bound PTP' have enabled calculations of PTP throughout the respiratory cycle so that total energy expenditure can be approximated (Fig. 10).
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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