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In Section 4, an achievable rate region as well as a rate region outer bound based on the cut-set bound are provided.
This bound was first proposed in [11], and an improved version was presented in [12], which separates the constellation points into groups located on one or multiple concentric rings and computes the phase bound based on the current sphere radius and previously detected symbols (hat {s}_{k}) and r i,k.
Also, a lower bound based on the performance metric has been designed to compare the performance of the heuristics developed.
The frequency coefficients have been determined using: (1) the differential quadrature method; (2) the finite element technique; (3) an optimized and/or improved Rayleigh quotient method; and (4) a lower bound based on the Stodola Vianello method.
A similar (even more conservative) bound based on the power spectrum of the driving process has already been proposed by Butterweck [24] and reads in our notation 0< mu_{text{Butterweck}} le frac1{m_{mathrm{x}}^{(2)} M max_{Omega} |C e^{jOmega})|^{2}}. (63).
We estimated the total number of OTUs (>99% sequence identity) of all fungi to be 60±22; the data on chytrid fungi alone was insufficient for direct richness estimation, but a conservative lower bound (based on the equal-OTU-abundance or unmixed Poisson model) for the number of chytrid fungi OTUs was 14±2.
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Zhou and Zhong [29]) modeled to minimize total train travel time with three techniques to reduce the search space; i) Lagrangian lower bound estimate, ii) exact lower bound based on remaining conflicts in the partial schedule and, iii) Upper bound using beam search heuristic.
Liang and Li [13] derived the Berry-Esseen type bound based on linear process errors under negatively associated random variables.
The second strategy is an effective lower bound based on linear programming (LP).
The goal is to obtain a bound based only on the system parameters and not on the optimization parameter ρ.
Evidently, the number of size classes of protein families, N, should be finite, although intrinsic features that could determine the value of N so far have not been considered (the impossibility of an infinite genome is self-evident but one would expect a much tighter bound based, e.g., on the limited time and resources available for genome replication and expression).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com