Related papers: Quantum Informatics View of Statistical Data Proce…
Statistical nuclear spectroscopy (also called spectral distribution method), introduced by J.B. French in late 60's and developed in detail in the later years by his group and many other groups, is based on the Gaussian forms for the state…
Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…
We obtain asymptotic counting results with error terms for complex orthospectrum for Schottky groups and orbit counting function for quadratic polynomials. Moreover, we prove equidistribution of holonomy associated to these dynamical…
We report on two machine learning experiments in search of statistical relationships between Dirichlet coefficients and root numbers or analytic ranks of certain low-degree $L$-functions. The first experiment is to construct interpretable…
Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to…
The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…
Nowadays data compressors are applied to many problems of text analysis, but many such applications are developed outside of the framework of mathematical statistics. In this paper we overcome this obstacle and show how several methods of…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
Gaussian radial basis functions can be an accurate basis for multivariate interpolation. In practise, high accuracies are often achieved in the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by Cucker, Krick, Malajovich, and Wschebor - we establish new…
We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system - a frequency- and spatially degenerate two-photon field. The method of statistical estimation of the quantum state…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…