Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models

Seenivasan, Pavithraa; Easwaran, Soumya; Sridhar, S.; Sinha, Sitabhra

doi:10.3389/fphys.2015.00390

Cited by 8 publications

(6 citation statements)

References 51 publications

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“…The Benford distribution is an empirical observation that the first significant digits (FSD) from certain sets of naturally occurring data (i.e., with minimal human intervention) follow a discrete logarithmic probability distribution (Figure 1, Table 1). The NBL has been applied in the natural sciences for decades [11][12][13][14][15][16][17][18], with little ecological attention. Potential ecological applications arise from reports the dynamic equilibrium of physical and social systems (defined sensu Thoms et al [19] as long-term balanced fluctuations about short-term constantly changing system conditions) can be well described by the Benford FSD sequence (Table 2 [14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

“…The NBL has been applied in the natural sciences for decades [11][12][13][14][15][16][17][18], with little ecological attention. Potential ecological applications arise from reports the dynamic equilibrium of physical and social systems (defined sensu Thoms et al [19] as long-term balanced fluctuations about short-term constantly changing system conditions) can be well described by the Benford FSD sequence (Table 2 [14][15][16][17][18]). The recursive theme is that interactions of system components that maintain structural stability [20] (i.e., persistence, constancy, resilience) can be represented by the informational distance between two discrete probability distributions, one from a FSD transformation of random measurements on system variables, the second from the regularity of FSD probabilities predicted by the Newcomb-Benford law (see Appendix Figures 1-4).…”

Section: Introductionmentioning

confidence: 99%

“…Atmospheric stability Li and Fu, 2016 [14] Stability of cardiac processes Seenivasan et al, 2016 [15] Persistent economic patterns Villas-Boas et al, 2015 [16] Recurrence of seismic event times Sttili, et al, 2012 [17] Quantum phase transitions De and Sen, 2011 [18]…”

Section: Introductionmentioning

confidence: 99%

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Correspondence of Newcomb-Benford Number Law with Ecological Processes

Davic

2022

Preprint

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The Newcomb-Benford number law has been applied in the natural sciences for decades, with little ecological attention. Empirical data reveal statistical correspondence between the discrete Benford probability distribution and physical systems in dynamic equilibrium along a continuum of stability. Analytic methods are presented to detect this mathematical representation across multiple levels of ecological organization and spatial scale. Case studies demonstrate novel application to help identify bidirectional regime changes to alternative states of dynamic equilibrium. Widespread documentation of the surprising phenomenon is anticipated as ecologists revisit historic sets of random measurement data and design future sampling protocols. Controlled experiments with measurement variables that span multiple orders of magnitude would be well suited for future empirical and theoretical inquiry.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Correspondence of Newcomb-Benford Number Law with Ecological Processes

Davic

2022

Preprint

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“…This observation is particularly suitable in time series analysis from physiological data [28]. In Physiology, NBL confirmation involves dynamical transitions in cardiac models and brain electrical activity [36,37]. Nevertheless, even though this law has been attested in different biological systems, it remains to be verified at the synaptic level.…”

Section: Introductionmentioning

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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“…BL has been observed in different kinds of statistical data found in physical constants, number of cells in colonies of the cyanobacterium, alpha decay half-lives and fraud-detection [9][10][11][12]. In Physiology, BL applications involve dynamical transitions in cardiac models and brain electrical activity [13,14]. Nevertheless, BL and gBL remaining to be verified in another genuine complex system: the synaptic terminal.…”

Section: Introductionmentioning

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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Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models

Cited by 8 publications

References 51 publications

Correspondence of Newcomb-Benford Number Law with Ecological Processes

Correspondence of Newcomb-Benford Number Law with Ecological Processes

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

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