We outline a theory for the calculation of the beam quality factor of an aberrated laser beam. We provide closed-form equations that show that the beam quality factor of an aberrated Gaussian beam depends on all primary aberrations except tilt, defocus, and x-astigmatism. The model is verified experimentally by implementing aberrations as digital holograms in the laboratory.

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance structure.

In this paper we extend the theory of optimal approximations of functions f : R → R in the L1(R)-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and properties of truncated theta functions obtained via the maximum principle for the heat operator. As applicatio...

Microorganisms play critical roles in host health. The advancement of high-throughput sequencing technology provides opportunities for a deeper understanding microbial interactions. However, due to the technological limitations 16S ribosomal RNA sequencing, microbiome data are zero-inflated, and quantitative comparison abundances cannot be made across subjects. By leveraging recent profiling te...

In the current study, model expressions for fifth-order velocity moments obtained from truncated Gram-Charlier series expansions a turbulent flow field probability density function are validated using data direct numerical simulation (DNS) of planar in strained channel. Simplicity expressions, lack unknown coefficients, and their applicability to non-Gaussian flows make this approach attractive...

The crch package provides functions for maximum likelihood estimation of censored or truncated regression models with conditional heteroscedasticity along with suitable standard methods to summarize the fitted models and compute predictions, residuals, etc. The supported distributions include leftor right-censored or truncated Gaussian, logistic, or student-t distributions with potentially diff...

Image segmentation is one of the most important area of image retrieval. In colour image segmentation the feature vector of each image region is ’n’ dimension different from grey level image. In this paper a new image segmentation algorithm is developed and analyzed using the finite mixture of doubly truncated bivariate Gaussian distribution by integrating with the hierarchical clustering. The ...

PURPOSE To determine the appropriateness of statistical models using the truncated Gaussian distribution and gamma distribution for diffusion signal decay, and to assess the correlation between the parameters obtained from the statistical models and estimated glomerular filtration rate (eGFR). METHODS Twenty-nine patients with chronic kidney disease and 21 healthy volunteers were included and...