Related papers: Benford distributions in NMR
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in…
For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…
In this paper, we derive limit laws for the empirical spectral distributions of random band and block matrices with correlated entries. In the first part of the paper, we study band matrices with approximately uncorrelated entries. We…
This paper proposes a novel approach for statistical modelling of a continuous random variable $X$ on $[0, 1)$, based on its digit representation $X=.X_1X_2\ldots$. In general, $X$ can be coupled with a latent random variable $N$ so that…
We investigate the average sizes of the $n$ largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte…
Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g. about cell membranes. While it has been shown in recent articles, that these…
Nuclear Magnetic Resonance (NMR) spectra are widely used in metabolomics to obtain profiles of metabolites dissolved in biofluids such as cell supernatants. Methods for estimating metabolite concentrations from these spectra are presently…
Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic properties of atomic nuclei to discover the structure, reaction state and chemical environment of molecules. We propose a probabilistic generative model and inference…
In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse…
We use a large single particle tracking data set to analyze the short time and small spatial scale motion of quantum dots labeling proteins in cell membranes. Our analysis focuses on the jumps which are the changes in the position of the…
A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data…
Diffusion-encoded magnetic resonance (MR) experiments can provide important insights into the microstructural characteristics of a variety of biological tissues and other fluid- or gas-filled porous media. The physics of diffusion encoding…
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Some of the progress in determining the phase boundaries of the nuclear phase diagram, the location of the critical point of the nuclear fragmentation phase transition, and the values of the critical exponents of this transition is…
We developed a novel direct algorithm to derive the mass-ratio distribution (MRD) of short-period binaries from an observed sample of single-lined spectroscopic binaries (SB1). The algorithm considers a class of parameterized MRDs and finds…