With this expansion, the frequency shift of the clutter can be derived directly by computing the root square of CED for one complex signal.
To compute the optimal spectrum sensing window length for CR-UWB spectral efficiency enhancement under the constrains of P f ̄ and P d ̄, we use linear programming to calculate the optimized value of τ s by computing the root for f r ( τ s ) = d F r ( τ s ) d τ s = 0, where f r ( τ s ) = - 1 T txop - Q ′ ( τ s ) - 1 T ( Q ( f ( τ s ) ) + Q ′ ( f ( τ s ) ) ) = 0, (16).
The fit of the GKE model networks was then assessed by computing the root mean square error (RMSE) between these mean values and those given by the scaling relationships (24) and (25) for the tested sizes of network n.
The optimum number of factors was determined by computing the root mean square error of approximation (RMSEA) [ 20], the Comparative Fit Index [ 21], and the Tucker Lewis Index [ 22].
The global minimum ui,j can be obtained by computing the roots of its derivative and selecting the one yielding the smallest value of (24).
The global minimum ti,j can be obtained by computing the roots of its derivative and selecting the one yielding the smallest value of J ~ ( t i, j ).
The convergence of the string calculation can be monitored by computing the root-mean-squared deviation of the string in CV-space as well as by computing the average string deviation over different iterations.
In the first comparative study, the state variables (the enzyme CadA, the transport protein CadB, the regulatory protein CadC and lysine Lys for a model of the Cad System in E. coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data.
In the first comparative study, the state variables (the enzyme CadA, the model cadBA, the cadaverine Cadav and the lysine Lys for a model of the Cad System in Escherichia coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data.
It is worth remarking that by computing the square root of expressions in (4), (5), and (7), RMSD α (i), RMSPD λ (i), and RMSPD ϕ (i) could be obtained, which convey an immediate indication of the error (in degrees) and of the relative error (as a percentage) in estimating brushstroke orientation, length, and width, respectively.
If dispersal distance has evolved in response to changes in range size (e.g. reduced dispersal for island individuals), a positive correlation between the dispersal distances estimated in PhyloMapper analyses and range size estimated by computing the square root of the potential range area within a basin should be observed.
