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The calculation of gradient g t, k can be decomposed to the projection part and cepstral part.
In addition, the calculation of gradient of (11) with respect to B is computationally expensive due to the existence of the Hadamard product.
The gradient norm ||∇f|| of the color image f is easy to compute as follows since it perceives image structures successfully [14, 15] (see Figure 10): Figure 10 Calculation of gradient norms: considering only the lightness channel L of the image in CIE-Lab color space (a) and considering all the information contained in each of the color channels (b).
Another advantage of our model is its fast calculation of gradient and torque of overlap energy allowing an efficient gradient-based local search to be easily implemented.
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The general, algebraic framework allows for the calculation of gradients using both the Direct and Adjoint derivative methods.
The designed MEA geometry facilitates positioning near a 2D cell culture setup, and the proposed in situ transient calibration minimizes the effects of sensitivity variability, thus allowing for calculation of gradients based on concentration differences between closely spaced electrodes.
Reduced-order models, like those based on the harmonic balance concept, in combination with the calculation of gradients via adjoint methods, are proposed for the efficient solution of a certain class of aerodynamics optimization problems.
For example, the gradient-based algorithms have high computational efficiency and fast convergence rate, but the calculation of gradients requires detailed knowledge of the numerical simulators.
The findings of Ubuz (2001) in her research on first year engineering students' understanding of tangency, numerical calculation of gradients and the approximate value of a function at a point through computers reveal that students have the following misconceptions about the derivative: The derivative at a point gives the function at a point.
The search direction is determined using a centroid solution of existing neighbor solutions without making explicit calculations of gradient information.
The calculation of the gradient of the cost function is a key point when a gradient based method is used.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com