It was rather chaotic at first, but as time went on, things became regularized according to schedules".
These fluid, shifting organic forms would soon become more regularized, but continue to emphasize the power of ambiguous color units to resonate.
The next summer, the dance became more regularized.
Through Figure 1, Figure 2, Figure 3, and Table 1, it is clear that as the measuring error ε becomes small, the regularized solution gets ever more close to the exact one.
"Aspects of Emergent have become popular in Mainline Protestantism, and more regularized in pockets of evangelicalism," said Daniel Treier, a theology professor at Wheaton College outside Chicago.
Thus, in the limit α→ ∞ the regularized objective function becomes a convex function.
When α=0, the regularized optimization (7) becomes the original problem (6) and the variance of the estimated parameters dominates the prediction error (10).
In the case of noise-added data, it is possible to expand Eq. (12) by adding noise to the final term on the right-hand-side and then demonstrate that at a certain noise level, the improvement in crosstalk are gradually minimized as the effect of noise on the (un-regularized) spectral matrix becomes dominant.
With the LIBLINEAR solver, the efficient training of large-scale graph-regularized multi-task problems becomes feasible.
Thus, the modified regularized solution of problem (2.2) becomes v^{delta,ast}_{alpha} x, t):=sum ^{+infty}_{n=-infty}frac{cosh (sqrt{in}x)}{1+alpha^{2}|cosh(sqrt{in})|^{2}} bigl(f^{delta}(t),e^{int} bigr) e^{int}.
