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Since these equations are not independent, they cannot be independently brought to zero, and therefore, only the node that has the maximum gradient value is moved.
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Moreover, statistics of slope angles of each mound (mean, minimum, maximum, standard deviation) were also examined using the slope maps (maximum gradient values per pixel scale, in degrees) directly converted from HiRISE-derived DEMs (Table 2).
Of course, using only the maximum gradient values leads to spurious points along each surface.
Shown also in Fig. 4, left, are the maximum gradient values of the restitution plots.
The parameters which can be modified, aiming to optimize the training procedure with Levenberg Marquardt method of each network are the adaptive Marquardt value mu, the mu decrease and mu increase factors, the final target mean squared error, the minimum gradient value and the maximum mu value.
The parameters which can be modified to optimize each network's training procedure with the Bayesian method are the adaptive Marquardt mu, the mu decrease and mu increase factors, the final target mean squared error, the minimum gradient value and the maximum mu value.
209 PCBs were minimized under the Tripos force field with MMFF94 [35] atomic partial charges by the Powell method, with a maximum iteration of 10,000 to reach a convergence gradient value of 0.001 kcal mol−1 Å.
For the purposes of illustration, however, a threshold was applied to each map (RSFC-Snowballing aggregate peak density map and RSFC-Boundary Mapping gradient map following nonmaxima suppression) to identify the vertices with the highest peak values (threshold of 0.05 which corresponds to >5% of maximum peak value) and highest gradient values (mean gradient value >0.03), respectively.
Generally, training stops when one of the following conditions is fulfilled: the maximum epoch number is reached, the maximum training time is reached, the desired mean squared error is achieved, the gradient value becomes smaller than its minimum value and as mentioned above when the adaptive Marquardt overruns its maximum value.
The tensile modulus (E) was defined as the slope of a tangent to the curve at 5% strain, 20% strain and high values of strain (where the maximum gradient was reached).
For each subject, 15 DW images were collected using the "medium" gradient scheme provided by the manufacturer, with a maximum gradient strength of 22 mT m−1 and a b-value of 1,000 s mm−2.
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