Related papers: Benford distributions in NMR
The deviation of the electron density around the nuclei from spherical symmetry determines the electric field gradient (EFG), which can be measured by various types of spectroscopy. Nuclear Quadrupole Resonance (NQR) is particularly…
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of…
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…
Prediction of chemical shift in NMR using machine learning methods is typically done with the maximum amount of data available to achieve the best results. In some cases, such large amounts of data are not available, e.g. for heteronuclei.…
Nuclear physics has been playing an important role in modern astrophysics and cosmology. Since the early 1950's it has been successfully applied for the interpretation and prediction of astrophysical phenomena. Nuclear physics models helped…
We estimate the local laws of the distribution of the middle prime factor of an integer, defined according to multiplicity or not. An asymptotic estimate with effective remainder is provided for a wide range of values. In particular this…
The simple one-parameter nearest neighbor-spacing distribution (NNSD) is suggested for statistical analysis of nuclear spectra. This distribution is derived within the Wigner-Dyson approach in the linear approximation for the level…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
In acoustics, ultrasonics and in electromagnetic wave propagation, the crossed medium can be often modelled by a linear invariant filter (LIF) which acts on a wide-sense stationary process. Its complex gain follows the Beer-Lambert law i.e…
A simple and quick general test to screen for numerical anomalies is presented. It can be applied, for example, to electoral processes, both electronic and manual. It uses vote counts in officially published voting units, which are…
This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath component (MPC) parameters based on radio signals. Under dynamic channel conditions with moving transmitter/receiver, the…
Using the sum invariance property of Benford random variables, we prove that an $n$-digit Benford variable converges to a Benford variable as $n$ approaches infinity.
Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…
Let $\log^Cn\le d\le n/2$ for a sufficiently large constant $C>0$ and let $A_n$ denote the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices. We prove that as $n$ tends to infinity, the empirical spectral…
In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of…
Nuclear magnetic resonance (NMR) is a widely used nondestructive method to study random motion of spin-bearing particles in different systems. In the long-time limit the theoretical description of the NMR experiments is well developed and…
A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or…
Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…
Existing music generation models are mostly language-based, neglecting the frequency continuity property of notes, resulting in inadequate fitting of rare or never-used notes and thus reducing the diversity of generated samples. We argue…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…