Benford’s law, its applicability and breakdown in the IR spectra of polymers

Bormashenko, Edward; Shulzinger, Evgeny; Whyman, Gene; Bormashenko, Yelena

doi:10.1016/j.physa.2015.10.090

Cited by 12 publications

(5 citation statements)

References 22 publications

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“…Finally, Bormashenko asked why NBL is frequently observed in statistical data [54]. According to his view, like NBL, many systems entropically governed are described by a logarithm dependence.…”

Section: Discussionmentioning

confidence: 99%

On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission

Silva

Floquet

Santos

et al. 2020

Physica A: Statistical Mechanics and its Applications

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A B S T R A C TThe neuromuscular junction represents a relevant substrate for revealing important biophysical mechanisms of synaptic transmission. In this context, calcium ions are important in the synapse machinery, providing the nervous impulse transmission to the muscle fiber. In this work, we carefully investigated whether intervals of spontaneous electrical activity, recorded in seven different calcium concentrations, conform Newcomb-Benford law. Our analysis revealed that electrical discharge of neuromuscular junction obeys the expected values for Newcomb-Benford law for first and second digits, while first-two digits do not perfectly follows the law. We next examined previous theoretical studies, establishing a relation between the law and lognormal and Weibull distributions. We showed that Weibull distribution is more appropriate to fit the intervals as compared to lognormal distribution. Altogether, the present findings strongly suggest that spontaneous activity is a base-scale invariant phenomenon.

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Section: Discussionmentioning

confidence: 99%

On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission

Silva

Floquet

Santos

et al. 2020

Physica A: Statistical Mechanics and its Applications

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“…In this sense, how such exocytotic machinery can organize themselves into an invariant scale scenario will be the focus of further research. Bormashenko asked why BL is frequently observed in statistical data [48].…”

Section: Discussionmentioning

confidence: 99%

On the distribution of spontaneous potentials intervals in nervous transmission

Silva¹,

Floquet²,

Lima³

2018

Preprint

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One of the main challenges in Biophysics teaching consists on how to motivate students to appreciate the beauty of theoretical formulations. This is crucial when the system modeling requires numerical calculations to achieve realistic results. In this sense, due to the massive use of software, students often become a mere users of computational tools without capturing the essence of formulation and further problem solution. It is, therefore, necessary for instructors to find innovating ways, allowing students developing of their ability to deal with mathematical modelling. To address this issue one can highlight the use of Benford's law, thanks to its simple formulation, easy computational implementation and wide possibility for applications. Indeed, this law enables students to carry out their own data analysis with use of free software packages. This law is among the several power or scaling laws found in biological systems. However, to the best of our knowledge, this law has not been contemplated in Cell Biophysics yet. Beyond its vast applications in many fields, neuromuscular junction represents a remarkable substrate for learning and teaching of complex system. Thus, in this work, we applied both classical and a generalized form of Benford's Law, to examine if electrophysiological data recorded from neuromuscular junction conforms the anomalous number law. The results indicated that nerve-muscle communications conform the generalized Benford's law better than the seminal formulation. From our electrophysiological measurements a biological scenario is used to interpret the theoretical analysis.

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“…His studies resulted in him stating that it would not hold for conventional sets of numbers, such as atomic weights and specific heats of compounds and materials, as his distributions showed, but it was a good fit * E-mail: ep14btech11001@iith.ac.in † E-mail: shantanud@iith.ac.in for quantities such as the numerals from the front pages of newspapers. Over the following years, the distribution has garnered a considerable amount of interest from a variety of specialists, from an assortment of fields, such as biology [5,6], finance [7,8], geophysics [9], seismology [10], spectroscopy [11,12] and astrophysics [13][14][15]. This law also has been used for practical applications in detecting banking frauds [8].…”

Section: Introductionmentioning

confidence: 99%

“…Over the following years, the distribution has garnered a considerable amount of interest from a variety of specialists, from an assortment of fields, such as biology [5,6], finance [7,8], geophysics [9], seismology [10], spectroscopy [11,12] and astrophysics [13][14][15]. This law also has been used for practical applications in detecting banking frauds [8].…”

Section: Introductionmentioning

confidence: 99%

Do τ lepton branching fractions obey Benford’s Law?

Dantuluri

Desai

2018

Physica A: Statistical Mechanics and its Applications

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According to Benford's law, the most significant digit in many datasets is not uniformly distributed, but obeys a well defined power law distribution with smaller digits appearing more often. Among one of the myriad particle physics datasets available, we find that the leading decimal digit for the τ lepton branching fraction shows marginal disagreement with the logarithmic behavior expected from the Benford distribution. We quantify the deviation from Benford's law using a χ 2 function valid for binomial data, and obtain a χ 2 value of 16.9 for nine degrees of freedom, which gives a p-value of about 5%, corresponding to a 1.6σ disagreement. We also checked that the disagreement persists under scaling the branching fractions, as well as by redoing the analysis in a numerical system with a base different from 10. Among all the digits, '9' shows the largest discrepancy with an excess of 4σ. This discrepancy is because the digit '9' is repeated for three distinct groups of correlated modes, with each group having a frequency of two or three, leading to double-counting. If we count each group of correlated modes only once, the discrepancy for this digit also disappears and we get pristine agreement with Benford distribution.

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Benford’s law, its applicability and breakdown in the IR spectra of polymers

Cited by 12 publications

References 22 publications

On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission

On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission

On the distribution of spontaneous potentials intervals in nervous transmission

Do τ lepton branching fractions obey Benford’s Law?

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