The Newcomb–Benford law: Scale invariance and a simple Markov process based on it

Burgos, Andrea; Santos, Andrés

doi:10.1119/10.0004957

Cited by 8 publications

(3 citation statements)

References 99 publications

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“…Previous studies have investigated the presence of BL amongst the sunspot numbers and have revealed general non-compliance to the to the overabundance of numbers having digits 1, 2 and 3 as FSDs. Despite being rather long (more than 59000 records, after excluding days without data or with zero spots), the dynamic range -ratio between the largest and the smallest values of the sunspot number series is limited [Burgos and Santos (2021)]. The maximum number of sunspots recorded is 528 corresponding to August 26, 1870.…”

Section: Discussionmentioning

confidence: 99%

Benford’s law: an application to sunspot data

Mir,

Darzi,

Ishtiaq

et al. 2023

Preprint

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Sunspots, the longest recorded indicators of the solar activity, are fundamental to the understanding of the sun and related solar phenomena. Here we explore whether the data on sunspot areas conforms to Benford’s law (BL) - an empirical observation that in large data the numbers having smaller first significant digits (FSDs) appear far more frequently than do the numbers having larger FSDs. We analyze the areas of individual sunspots, of sunspot groups and total area of all the sunspots visible on the surface of sun at any point of time. Furthermore, we also investigate the daily photometric sunspot index (PSI), the umbral and daily plage areas for conformity to BL. The distribution of FSDs of numbers amongst all the data sets are found to be in good agreement with the predictions of BL except the data on daily plage areas which show some deviations from the law. Interpretation of the obtained results is also given.

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Section: Discussionmentioning

confidence: 99%

Benford’s law: an application to sunspot data

Mir,

Darzi,

Ishtiaq

et al. 2023

Preprint

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“…In practice, this peculiar law has been effectively used to distinguish and diagnose frauds in taxing and accounting (Nigrini 1996;Nigrini & Mittermaier 1997;Geyer & Williamson 2004), and to minimize storage space and speed up calculation in computer science (Barlow & Bareiss 1985;Schatte 1988;Berger & Hill 2007). Theoretically, this law has been well explained by using a central-limit-like theorem for first digits (Hill 1995) and a simple Markov process (Burgos & Santos 2021). In mathematics, Benford's law is scale invariant (Berger et al 2008), which indicates that it is independent of any particular choice of units (Pinkham 1961).…”

Section: Introductionmentioning

confidence: 99%

First Digit Distributions of Gamma-Ray Bursts

Lai,

Wei

2024

Res. Astron. Astrophys.

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The occurrence of the first significant digits from real world sources is usually not equally distributed, but is consistent with a logarithmic distribution instead, known as Benford's law. In this work, we perform a comprehensive investigation on the first digit distributions of the duration, fluence, and energy flux of gamma-ray bursts (GRBs) for the first time. For a complete GRB sample detected by the Fermi satellite, we find that the first digits of the duration and fluence adhere to Benford's law. However, the energy flux shows a significant departure from this law, which may be due to the fact that a considerable part of the energy flux measurements are restricted by lack of spectral information. Based on the conventional duration classification scheme, we also check if the durations and fluences of long and short GRBs (with duration $T_{90}>2$ s and $T_{90}\leq2$ s, respectively) obey Benford's law. We find that the fluences of both long and short GRBs still agree with the Benford distribution, but their durations do not follow Benford's law. Our results hint that the long--short GRB classification scheme does not directly represent the intrinsic physical classification scheme.

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“…Various experimental data have been accumulated in many fields of knowledge, attesting to the compliance with the NBL [17][18][19][20][21]. In particular, spatial invariance can have profound morphological implications in physiology, and it is well documented in the heart, lung, and brain [22].…”

Section: Introductionmentioning

confidence: 99%

Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions

Silva,

Floquet,

Lima

2023

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Recently, we demonstrated the validity of the anomalous numbers law, known as Newcomb–Benford’s law, in mammalian neuromuscular transmission, considering different extracellular calcium. The present work continues to examine how changes in extracellular physiological artificial solution can modulate the first digit law in the context of spontaneous acetylcholine release at the neuromuscular junction. Using intracellular measurements, we investigated if the intervals of miniature potentials collected at the neuromuscular junction obey the law in a hyperkalemic environment. When bathed in standard Ringer’s solution, the experiments provided 22,582 intervals extracted from 14 recordings. On the other hand, 690,385 intervals were obtained from 12 experiments in a modified Ringer’s solution containing a high potassium concentration. The analysis showed that the intervals, harvested from recordings at high potassium, satisfactorily obeyed Newcomb–Benford’s law. Furthermore, our data allowed us to uncover a conformity fluctuation as a function of the number of intervals of the miniature potentials. Finally, we discuss the biophysical implications of the present findings.

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The Newcomb–Benford law: Scale invariance and a simple Markov process based on it

Cited by 8 publications

References 99 publications

Benford’s law: an application to sunspot data

Benford’s law: an application to sunspot data

First Digit Distributions of Gamma-Ray Bursts

Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions

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