Sentence examples for smooth reduced from inspiring English sources
Assume z is a smooth, reduced 12 Gaussian random field from (mathbb{D}), which almost surely has no degenerate zero 13 in (mathcal {A}); then mathbb{E} { mathcal {N}_{mathcal {A}} } = frac{1}{2pi} int _{mathcal {A}} mathbb{E} bigl{ bigl| det dmathbf{z}(p) bigr| | mathbf{z}(p) = 0 bigr},dp (here the integral is Lebesgue integral, and the integrand is a conditional expectation).
Azaïs and Wschebor's theorem (Theorem 6.2 in [29]), in the particular case of a smooth reduced Gaussian field, is the following equality: mathbb{E}(mathcal{P}_{mathcal{A}}) = frac {1}{2pi}int _{mathcal{A}} mathbb{E} bigl{ biglvert operatorname{det} d mathbf{z}(p) bigrvert | mathbf{z}(p) = 0 bigr},dp.
Removing edge effects caused by the smoothing reduced the number of measuring points in each profile from 60 to 48.
This smoothing reduced spatial resolution but enabled analysis of the intrinsically noisy images provided by the clinic.
It is reasonable that atmPrf2013 shows a positive ∆T CPT because height smoothing reduces the sharp temperature fluctuations.
For instance, the configurations using FaceDetection with and without ImageSmoothing have an average processing time of 252.78 ms and 306.81 ms respectively in parallel execution, what shows that smoothing reduces face detection response time considerably.
Smoothing reduces spatial resolution.
We demonstrated that Gaussian smoothing reduces this effect, at the expense of degradation of the spatial resolution.
However, for single municipalities, without fully eliminating it, the use of Bayesian smoothing reduces the probability to detect narrow areas with specifically high or low risk.
Although smoothing reduces variability relative to measured concentrations, Gryparis et al. (2008) show this is a type of Berkson measurement error that should not cause substantial bias toward the null.
We employ the time-domain filtering described in the IKK method also here, replacing θ(t) with θ̃(t) in eq 7. The time-filtering results in a spectral smoothing reducing the noise and not systematically influencing the phase outside spectral resonances.
