Related papers: Constructing PDFs of spatially dependent fields us…
We employ the LuxQED approach to compute the polarized photon PDF (photon pPDF). This approach expresses the pPDF in terms of the structure functions $g_1$ and $g_2$. Different models for the structure functions are employed according to…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…
We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot…
In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
At any given scale, 3$\times$2-point statistics extract only three numbers from the joint distribution of the cosmic matter density and galaxy density fluctuations: their variances and their covariance. It is well known that the full shape…
The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations…
We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable…
This paper presents a novel method for analytical derivations of marginal densities using the fractional derivatives of moment-generating functions. Although the method requires likelihood functions to take specific forms, its assumptions…
This paper analyses the finite element component of the error when using preintegration to approximate the cdf and pdf for uncertainty quantification (UQ) problems involving elliptic PDEs with random inputs. It is a follow up to Gilbert,…
We present a discussion on the methods for extracting a given parameter from measurements of hadronic data, with particular focus on determinations of the strong coupling constant. We show that when the PDF dependency on the determination…
In our recent study we have determined two new spatially dependent nuclear PDF (nPDF) sets, EPS09s and EKS98s. With these, the hard-process cross-sections can be calculated in different centrality classes consistently with the globally…
SIL (Safety Integrity Level) allocation plays a crucial role in defining the design requirements for Safety Functions (SFs) within high-risk industries. SIL is typically determined based on the estimated Probability of Failure on Demand…
The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…
A general spherical harmonics method is described for extracting anisotropic pair distribution functions (PDF) in this work. In the structural study of functional crystallized materials, the investigation of the local structures under the…
We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e., tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time…
Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides $\langle x \rangle$, face severe challenges from…