We can find the optimal smoothing parameter by minimizing the expression of (C.17) with respect to h.
These figures show both the AMMSEs of the asymptotically optimal HDA systems (labeled analytical) obtained by minimizing the expression (18) with respect to ρ and θ o, as well as the experimental AMMSE of actual HDA-PQ and HDA-TC systems which use these (ρ,θ o ) values.
We learn about the function f(x) by minimizing the expression λ ∑ i = 1 n L (y i − f (x i ) ) + 1 2 ‖ w ‖ 2. L denotes the loss function that measures the quality of the estimation.
Although noise-propagation is a plausible explanation for the general association between noise and regulation, its effects are detrimental to the accuracy of expression regulation, and one might thus expect natural selection to have acted to minimize its effects, for example, by minimizing the expression fluctuations in regulators.
Thus, the contribution of each individual (i.e., the number of offspring that each individual leaves for the next generation) was optimized by minimizing the following expression: ∑ i = 1 N ∑ j = 1 N c i c j f ij 2 N 2 where c i is the contribution of individual i and f ij is the coancestry between individuals i and j.
For each point, we define { x i, y i}, i = 1, …, n, the moving M-regression inclusion function, as Thus, the moving M-regression line can be found by minimizing the following expression: Function F is not differentiable at all points (x i, y i) such that y i = ax i + b − d1 and y i = ax i + b + d2.
The equation of graded structure under the in-plane thermal load is derived by minimizing the total potential energy expression.
Lee et al. [61] incorporated sparseness in the factorization process by minimizing the L1 norm, shown in Expression 13, in the factorization process begin{aligned} l_1 varvec{x}|varvec{y}) = sum _{n=1}^N Vert x_n - y_n Vert.
In order to obtain the best set of parameters for the system, we fitted all MD intermolecular potential energy points {r AB, u A, u B, U LJ } with the Gay-Berne expression by minimizing the total squared residuals ∑A,B A≠B[U LJ (A, B) - U GB (A, B ]2.
Surprisingly, a weak, but significant negative correlation of mRNA length (and protein length) with expression level was found in all studied organisms [ 1, 2, 5, 6, 71- 74], which is also generally explained by minimizing the energetic cost of gene expression.
We can solve for f by minimizing the following: (8) In this expression, the first term is the loss function and represents the difference between initial and final labels.
