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A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
Binary neural networks (BNNs) constrain weights and activations to +1 or -1 with limited storage and computational cost, which is hardware-friendly for portable devices. Recently, BNNs have achieved remarkable progress and been adopted into…
A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with…
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments.…
A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
Spin defects in two-dimensional materials hold significant potential for quantum information technologies and sensing applications. The negatively charged boron vacancy (VB-) in hexagonal boron nitride (hBN) has attracted considerable…
Introduction: Normalised prediction distribution errors (npde) are used to graphically and statistically evaluate continuous responses in non-linear mixed effect models. Here, our aim was to extend npde for categorical data and to evaluate…
In these lectures we give a concise introduction to the ideas of renormalon calculus in QED and QCD. We focus in particular on the example of the Adler D function of vacuum polarization, and on relations between perturbative renormalon…
A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization…
While binary neural networks (BNNs) offer significant benefits in terms of speed, memory and energy, they encounter substantial accuracy degradation in challenging tasks compared to their real-valued counterparts. Due to the binarization of…
A subring pair B < A has right depth 2n if the n+1'st relative Hochschild bar resolution group is isomorphic to a direct summand of a multiple of the n'th relative Hochschild bar resolution group as A-B-bimodules; depth 2n+1 if the same…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
We consider and reformulate a recent definition of multiplication between distributions. We show that this definition can be adopted, in particular, to prove biorthonormality of some distributions arising when looking to the (generalized)…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
In this short review paper, we discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron production data in e+e-, deep inelastic scattering…
The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
A fast and flexible $k$NN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments…