Sentence examples for a constrained sum from inspiring English sources

(A) Histogram of Cy5 intensities for substrates exhibiting FRET onset (blue curve), fit to a constrained sum of Gaussians (red curve) to estimate the intensity of a single Cy5 molecule (see Methods).

We evaluated the significance of the overlap of each triplet using a constrained sum involving a product of two hypergeometric distributions.

The article also describes a novel iterative transmission power/energy adaptation scheme to maximize the sum capacity of the downlink for a single user, when using discrete transmission rates and a constrained total transmission power.

As, and both q and π must sum to 1, q lies in a constrained set Ω.

Observing that this is a constrained maximization since (sum _{k=1}^{K}phi _{textit {nm}} (k) =1), we first take the corresponding derivative: begin{array}{*{20}l} frac{partial mathcal{L}}{partial phi_{nm} (k)} &=Psi (eta_{n} (k))-Psi left(sumlimits_{j=1}^{K}eta_{n} (j) right)+log beta (k,w_{nm})&quad-log phi_{nm} (k -1 end{array}.

Equation  1 was fitted by the Nelder-Mead simplex direct search method with bound constraints (Table  1), which performs a constrained non-linear minimisation of the sum of the squared residuals [ 27, 28].

The sum rate bounds under a constrained backhaul and imperfect channel knowledge are important [18] and it is part of our future work.

In order to obtain the sum capacity, we need to make a constrained optimization first, {C}_{mathrm{sum}-d}=underset{left{{p}_kright}}{max }{log}_2det left({I}_M+{rho}_d{GD}_p{G}^Hright) (4) sum limits_{k=1}^K{p}_k=1,{p}_kge 0 (5)where D p is a diagonal matrix whose diagonal elements constitute a K × 1 vector p. The power limit is given by Eq. (5), and the sum power is limited to 1.

With reliable transmission power control for the secondary transmitter, the power allocation problem of the CR system is modeled into a constrained Lagrange multipliers optimization problem to guarantee reliable sum rate maximization.

LASSO is a constrained form of ordinary least squares with a bound on the sum of the absolute values of the coefficients (Tibshirani 1996).

Then, to provide the SUs with satisfactory quality of service (QoS), and optimize the sum rate of the MCR system as well, a constrained two-variable nonlinear optimization problem (OP) is formulated.