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The Newcomb-Benford Law, which is also called the first digit phenomenon, has applications in diverse phenomena ranging from social and computer networks, engineering systems, natural sciences, and accounting. In forensics, it has been used to determine intrusion in a computer server based on the measured expectations of first digits of time varying values of data, and to check whether the information in a data base has been tampered with. There are slight deviations from the law in certain natural data, as in fundamental physical constants, and here we propose a more general bin distribution of which the Newcomb-Benford Law is a special case so that it can be used to provide a better fit to such data, and also open the door to a mathematical examination of the origins of such deviations.
The coronavirus disease 2019 bursted out about two months ago in Wuhan has caused the death of more than a thousand people. China is fighting hard against the epidemics with the helps from all over the world. On the other hand, there appear to be dou
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 literature on effic
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 $|a_i| leq C_1 cdot i^m$ for all $i i
Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and prosperous future.
We report on the existing connection between power-law distributions and allometries. As it was first reported in [PLoS ONE 7, e40393 (2012)] for the relationship between homicides and population, when these urban indicators present asymptotic power-