with exponent 2 for some unbounded distribution in the plane. the case of unbounded distributions is important both from a mathematical and an applied point of view. in particular we consider the case of the gaussian, the case of the maxwellian and we give some hints on the case of other ...
The change from formula (5) is quite useful, because it allows to apply the perturbative expansion to the quantum action. Indeed, let us substitute decomposition (5) into the path integral from (4) and calculate the standard Gaussian integrals, see [33]. Then, using the fact that the fiel...
(15) of the parameters, assuming that the results of the parameters conform to an ideal Gaussian distribution, and are therefore ellipse-like. The numerical results are listed on the first four rows of Table 1. It is evident that ξγ1 γ1ξγ1 γ1 itself does not constrain S8S8 and ...
In a post process step, the spurious interactions between periodically repeated images is removed from the total energy using an electrostatic correction scheme that involves a Gaussian approximation to the localised charge distribution and a model for the dielectric function of the material21. While ...
4d), shows a single peak in the distribution, mimicking the behavior of conductance through a metallic SET island. In the second array (Fig. 4e), in contrast, the single peak in the distribution evolves into a broad distribution, exhibiting conductance that occurs via single addition electrons ...
std::uniform_real_distribution<float> dist(0, 1); auto engine = phi::GetCPURandomEngine(0); u = dist(*engine); } else { u = random_u; } alpha_height = static_cast<float>(input_height - pool_height) / (output_height - (pool_height > 0 ? 1 : 0)); alpha_width = static_...
In case of the 8 Gaussian dataset, we have an analytical formula for the true data distribution. We can evaluate the MSE of the log density learned by the energy model versus the true data distribution. The plot below shows the MSE on the8gaussianstraining dataset. ...
Thus, the output image obtained by the proposed AtomGAN is closer to the gray distribution of the target segmentation result shown in Figure 6(b). In other words, the images generated by the proposed AtomGAN retain the basic atomic information of the input domain and better integrate the ...
c, Microregion distribution in the spatially distinct cohort at the section level coloured by cancer type (left), microregion size group (middle) and primary versus metastasis (right). Each circle indicates one microregion. The size of each circle represents the size of the microregion. d, ...
To do so, firstly we generated a great many configurations () with different topological characteristics. We placed in a fixed domainpoints randomly sampled from Gaussian distributions where the number, mean, and standard deviation of the distributions were varied over large intervals. Then, we conne...