Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on claim that situation improved when enhanced to super-integrability, i.e. explicit formulas Gaussian averages of characters. In this case, are equivalent simple recursive formulas, which have appropriate combinations characters as their solutions. Moreover...

Gaussian mixture models (GMMs) are a convenient and essential tool for the estimation of probability density functions. Although GMMs are used in many research domains from image processing to machine learning, this statistical mixture modeling is usually complex and further needs to be simplified. In this paper, we present a GMM simplification method based on a hierarchical clustering algorith...

in this paper, the effect of size on melting temperature of metallic nanoparticles (au, pb and bi) is theoretically simulated and explained. in this regard, the cause of difference in various experimental data is introduced, which is the difference between nanoparticles’ grain gaussian distribution. this volume-depended model with the help of the gaussian distribution can describe the relation ...