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An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
The photon parton distribution function (PDF) of the proton is crucial for precise comparisons of LHC cross sections with theoretical predictions. However, it was previously affected by very large uncertainties of around ${\cal O}(100\%)$…
We calculate the electron structure functions, aka parton distribution functions (PDFs), to NNLO in QED. The calculation is based on the definition of the PDFs in terms of operator matrix elements in soft collinear effective theory (SCET)…
We study the spatially-resolved stellar specific angular momentum $j_*$ in a high-quality sample of 24 CALIFA galaxies covering a broad range of visual morphology, accounting for stellar velocity and velocity dispersion. The shape of the…
We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies…
Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because…
The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a recent paper, we showed how the photon PDF could be determined in terms of the electromagnetic proton structure…
The next-to-leading order (NLO) evolution of the parton distribution functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive…
We conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the…
We demonstrate the utility of dendrograms at representing the essential features of the hierarchical structure of the isosurfaces for molecular line data cubes. The dendrogram of a data cube is an abstraction of the changing topology of the…
The parton distributions functions (PDFs) derived from the NNLO QCD analysis of existing light-targets deep-inelastic-scattering data are presented. The NLO and NNLO PDFs are compared in order to analyze perturbative stability of 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…
We review the current state of the art in the determination of the parton substructure of the nucleon, as expressed in terms of parton distribution functions (PDFs), and probed in high-energy lepton-hadron and hadron-hadron collisions, and…
Molecular clouds exhibit lognormal probability density functions (PDF) of mass densities, which are thought to arise as a consequence of isothermal, supersonic turbulence. Star formation is then widely assumed to occur in perturbations in…
This paper investigates the effect of initial volume fraction on the runout characteristics of collapse of granular columns on slopes in fluid. Two-dimensional sub-grain scale numerical simulations are performed to understand the flow…
Modern global analyses of the structure of the proton include collider measurements which probe energies well above the electroweak scale. While these provide powerful constraints on the parton distribution functions (PDFs), they are also…
The total mass estimate of molecular clouds suffers from the uncertainty in the H$_2$-CO conversion factor, the so-called $X_{\rm CO}$ factor, which is used to convert the $^{12}$CO (1--0) integrated intensity to the H$_2$ column density.…
Numerical simulations within a cold dark matter (DM) cosmology form halos whose density profiles have a steep inner slope (`cusp'), yet observations of galaxies often point towards a flat central `core'. We develop a convolutional mixture…
Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…