Sentence examples for with respect to the realization from inspiring English sources

The authors wish to thank Dr. Andrea Walpersdorf for her fundamental competencies with respect to the realization of the RENAG database; Prof. Toshitaka Tsuda for his suggestions and inspiration regarding the heterogeneity index; and Prof. Andrea Mazzino, Dr. Federico Cassola, and Dr. Francesco Ferrari for sharing meteorological simulation data and their support with the WRF model.

Estimates of the velocity are shown in (B), superposing curves corresponding to different angles obtained averaging with respect to the noise realization and indicating the standard deviation (STD).

The estimated modulus of the velocity vector is shown in Figure 3B as a function of the simulated modulus of velocity, superposing curves corresponding to different angles obtained averaging with respect to the noise realization and indicating the standard deviation (STD).

Finally, the proposed approximation of the BER can be obtained by averaging with respect to the channel realization H, thus giving BER d = E 1 2 ∑ s = 1 Q ′ p s ′ Q σ w 2 σ w d 2 ( 1 − c 1 ) − ℜ ( α s ) σ w d 2 2 + 1 2 ∑ s = 1 Q ′ p s ′ Q σ w d 2 σ w d 2 ( 1 − c 1 ) + ℜ ( α s ) σ w d 2 2. For QPSK constellations, it can be shown that Q ′ = 1 c 1, where 1 c 1 = N K is assumed to be integer.

The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations.

where the expectation is taken with respect to the channel realizations.

The expectation in Equation (14) is taken with respect to the channel realizations.

Experimental results show that the proposed algorithms yield significant reductions in the number of adders/subtractors with respect to the original realizations without violating the error constraints, and consequently lead to CMVM designs with less area, delay, and power dissipation.

Our goal is to obtain positioning scheme suitable for all channels, data, and noise realizations by optimizing the positioning scheme with respect to the worst case realizations.

In practical situations, the placement of RRUs has to be carefully conducted, such as to optimize, e.g., the network coverage with respect to the large-scale shadow-fading realization in each cell.

The maximum function in (23) and expectation in (24) are taken with respect to the data symbols, noise, and channel realizations.