The original Landau hydrodynamic model is, to our best knowledge, the only model suggesting some certain shape for pseudorapidity distributions of produced particles in both nucleon-nucleon and nucleon-nucleus collisions at very high energies, Gaussian distribution
. Of course, it is necessary to note that only in the case of a very high multiplicity does the pseudorapidity distribution of produced particles in an individual event become a meaningful concept.
Impact of the number of the Gaussian distributions
on localization accuracy Number of the Gaussian distributions
Localization error (%) 2 0.383 3 0.352 4 0.349 5 0.345 6 0.342 7 0.34 8 0.338 Note: Table made from bar graph.
The Euclidean distance (dissimilarity) is most frequently used by the k-means family, and, moreover, is derived using the log likelihood of an isotropic Gaussian distribution
. Therefore, the k-means using the Euclidean distance will be able to appropriately partition data sampled from isotropic Gaussian distributions
but not other distributions.
The method has several advantages: (1) the outcome of the region growing approach is provided automatically as the initial contour of level set evolution method; (2) the global Gaussian distribution
with different means and variances is integrated into level set framework.
In some schemes the noise is added without concerning the covariance of the data, but the uniform distribution or Gaussian distribution
is directly declared [12, 13].
Some causal processes can simulate Gaussian distribution
The GMM algorithm has been proposed by Stauffer and Grimson, , with the target of efficiently dealing with multimodal Bg by using a statistical model composed by a mixture of Gaussian distributions
. The GMM algorithm has been modified and included in the OpenCV libraries.
He later called the Gaussian distribution
"a model child," one "which is commonly called 'normal,' but in fact deserves less and less to be considered as such."
We add a little zero mean Gaussian noise to this to get the action which we actually perform [a.sub.t] = [a.sup.opt.sub.t] + [mu] where [mu] is drawn from a zero mean Gaussian distribution
. It has been found essential for accurate convergence that [mu] is very small in magnitude so typically [mu] ~ N(0, 0.01).
The software quickly calculates: (a) the mean value and the standard deviation of all the measurement values; (b) the Log-Normal distribution; (c) the Gaussian distribution
; (d) the deviations from the Log-Normal and Gaussian distributions
in terms of the Kolmogoroff-Smirnov and Chi-square tests; (e) skewness; and (f) excess of the measured distribution.
They are obviously two-dimensional Gaussian distributions
. Zhao et al.
In addition, we assume that both the spatial and the unstructured variability have Gaussian distributions
, which are independent in the latter case.