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Those that resulted in the lowest cost function were considered optimal for each sequence and are shown in Table 2.
The 'best' solution was defined as the execution which resulted in the lowest cost function output of the independent runs (i.e. the smallest error).
The parameters were then re-estimated and we compared the estimates from the best fit after grid optimization (i.e. the fit with the lowest cost function value and therefore the highest likelihood, see Equation 4) and the mean, median, and mode of the Monte Carlo ensemble with the "true" parameter values from the initial simulation.
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The model performance with respect to parameter changes as revealed in the course of annealing, is illustrated in fig 3. Low cost function parameter sets (good solutions) are coloured green to blue whereas worse solutions are in red colours (see colour bar and not the logarithmic scale).
Using the Kronecker product, the high-cost MUSIC function is further reformulated as an eigenvector-based optimization problem, and a new low-complexity cost function with spatial aliasing is derived.
The narrow-band signal model and the conventional MUSIC algorithm are introduced in Section 2. In Section 3, the steering vector of a ULA that used in the standard MUSIC is firstly reconstructed as two other steering vectors, based on which the proposed low-complexity cost function with spatial aliasing is addressed.
The optimal countermeasure strategy is the combination of individual countermeasures (and when and where they are implemented) which gives the lowest value of the cost function.
In order to avoid local minimum, for random initialization, we repeated the algorithm 10 times with random initial conditions and chose the results with lowest value of the cost function (4).
In the low-frequency band, a quadratic cost function is minimized in accordance with the observation that the low-frequency components of chrominance slowly vary within an object region.
Although this technique leads to an improvement of the precision of the estimate (Figure 4), the algorithm is still sensitive to local minima, or to local low-sensitivity areas of the cost function that can occur also for the in-plane pose parameters, such as for (Figure 3).
However, indirect selection for beneficial mutations could still substantially increase the mutation rate in sexual organisms if the replication accuracy cost function has low slope (i.e. the physiological cost of increasing replication accuracy to bring about a unit reduction in mutation rate is low) (Johnson 1999).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com