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After an ensemble of calibrated model realizations is identified using the GA, the ensemble is reduced via a cluster analysis to define a variance-preserving subset of the members for the second step of local, higher-resolution parameter calibration.

Mandelbrot used a fractional volatility to define a fractional Brownian Motion whose variance is auto-correlated, Laskin (2003) applied a Liouville fractional operator to the set of differential-equations that defined Poisson processes (see also Baleanu et al. 2010, Podlubny, 1999)., Meltzer and Klafter 2004 applied fractional operators to Fokker Planck partial differential equations, and so on.

The extended methods use patterns in the contrast variance to define a minimum depth below which comparison pairs were excluded [see Additional file 2].

The final LUR models for BTEX and each species were identified as having a combination of variables with the highest coefficient of determination, R. Independent variables retained in the models had to have significant t-score (p < 0.05) and low collinearity with other variables (defined by a variance inflation factor < 2.0).

In order to exploit the local contrast information of the reference image, we define the variance of a local region as a weight in the pooling stage w(m,n =frac{1}{R+1}sum_{p=m-R}^{m+R}sum_{q=n-R}^{n+R} ri p,q)-theta(m,n))^{2} (6) Fig. 4 a R+1}sum_{p=m-R}^{m+R}sum_{q=n-R}^{n+R} ri phe 3×3 region.

Details are provided in Additional File 1, but in brief we define the variance of a physician's cost profile as: This assumes that the variance of the sum of the expected costs is small compared to the sum of the observed costs because it is based on all the data.

For each subject, one of two values, a large or small value, was used to define the variance for that experiment's prior.

For a threshold t, s min < t < s max , define the variance ε(t) between the moving target's independent flow and the background's independent flow as.

Next, we define the variance reduction to discriminate between acceptable and unacceptable matching accuracy.

We can interpret this as an iterative quadratic regularization inversion followed by the estimation of variances τ j which are used in the next iteration to define the variance matrix D.

We can interpret this as an iterative quadratic regularization inversion followed by the estimates of variances τ j which are used in the next iteration to define the variance matrix D. This algorithm is simple to implement.

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