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We numerically investigate non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two-point and three-point probability distribution function (PDF) of phase and modulus,…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
We study the dependence of the transverse mass distribution of the charged lepton and the missing energies on the parton distributions (PDFs) adapted to the $W$ boson mass measurements at the CDF and ATLAS experiments. We compare the shape…
The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure -- the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly…
Weak gravitational lensing is a powerful probe of the large-scale cosmic matter distribution. Wide-field galaxy surveys allow us to generate the so-called weak lensing maps, but actual observations suffer from noise due to imperfect…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
Accurate estimation of the covariance matrix of cosmic shear statistics is essential for cosmological analyses using current and upcoming wide-area weak lensing surveys. In this work, we investigate analytical methods for computing the…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear…
Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Experimental data in particle and nuclear physics, particle astrophysics, and radiation protection dosimetry are collected using experimental facilities that consist of a complex system of sensors, electronics, and software. Measured…
An important limitation in current fits of parton distribution functions (PDFs) is that PDF uncertainties do not include any source of theoretical uncertainty. Here we present a general method for incorporating theoretical uncertainties…
Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
For Poisson-Delaunay triangulations in $d$-dimensional Euclidean space $\mathbb{R}^{d}$, a structured and computationally efficient form of the probability density function (PDF) of the volume of a typical cell is analytically derived in…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an…