Related papers: Benford distributions in NMR
Recently, we demonstrated the validity of anomalous numbers law, known as Newcomb-Benford's law, at the mammalian neuromuscular transmission, considering different extracellular calcium concentrations arXiv:2002.01986. The present work…
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…
Surface deformations of optical cavities and plasmonic nanoparticles are inevitable in nanophotonics. The random morphology changes of different realizations modify the associated resonance frequencies and quality factors, which may be…
We study multi-digit correlations in Benford sequences b^n for integer bases 2 <= b <= 1000, measuring dependence via conditional mutual information (CMI). A resonance ratio derived from the continued fraction expansion of log_10(b)…
Let $\mathcal{I} \subset \mathbb{N}$ be an infinite subset, and let $\{a_i\}_{i \in \mathcal{I}}$ be a sequence of nonzero real numbers indexed by $\mathcal{I}$ such that there exist positive constants $m, C_1$ for which $|a_i| \leq C_1…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first…
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique that is sensitive to the local atomic structure of matter. Computational predictions of NMR parameters can help to interpret experimental data and validate structural…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
Motivated by giving a meaning to "The probability that a random integer has initial digit d", we define a URI-set as a random set E of natural integers such that each n>0 belongs to E with probability 1/n, independently of other integers.…
We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum…
Nuclear Magnetic Resonance (NMR) spectrometry uses electro-frequency pulses to probe the resonance of a compound's nucleus, which is then analyzed to determine its structure. The acquisition time of high-resolution NMR spectra remains a…
The famous \emph{circular law} asserts that if $M_n$ is an $n \times n$ matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution (ESD) of the normalized matrix $\frac{1}{\sqrt{n}} M_n$…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
We study the parton distribution of nucleon and nuclear EMC effect in a statistical model. We find when we choose the parameters appropriately, the predictions given by pure statistical laws can fit the experimental data well in most range…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
Internet research on search engine quality and validity of results demand much concern. Thus, the focus in our study has been to measure the impact of quotation marks usage on the internet search outputs in terms of google search outcomes…