Beyond Benford's Law: Distinguishing Noise from Chaos

Computational and experimental modulation of a noisy chaotic neuronal system

In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.

Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis

The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts, the Jensen-Shannon divergence and the encoding scheme based on the sequential ordering of the elements in the data series. The versatility and robustness of this ordinal symbolic distance for characterizing and discriminating different dynamics are illustrated through several numerical and experimental applications. Results obtained allow us to be optimistic about its usefulness in the field of complex time-series analysis. Moreover, thanks to its simplicity, low computational cost, wide applicability, and less susceptibility to outliers and artifacts, this ordinal measure can efficiently handle large amounts of data and help to tackle the current big data challenges.

Flow Regime Recognition and Dynamic Characteristics Analysis of Air-Water Flow in Horizontal Channel under Nonlinear Oscillation Based on Multi-Scale Entropy

Gas-liquid two-phase flow behavior in horizontal channel under heaving motion showed unique dynamic characteristics due to the complex nonlinear interaction. To further establish a description model and investigate the effects of heaving motion on horizontal gas-liquid flow, experiments in a wide range of vibration parameters and working conditions were carried out by combining vibration platform with two-phase flow loop. It was found that the flow regimes under heaving motion showed significant differences compared to the ones expected in steady state flow under the same working conditions. Increasing vibration parameters showed an obvious impact on fluctuation degree of gas-liquid interface by visualizing high-speed photographs. A method based on multi-scale entropy was applied to identify flow regimes and reveal the underlying dynamic characteristics by collecting signals of pressure-difference. The results indicated that the proposed method was effective to analyze gas-liquid two-phase flow transition in horizontal channel under heaving motion by incorporating information of flow condition and change rate of multi-scale entropy, which provided a reliable guide for flow pattern control design and safe operation of equipment. However, for slug-wave and boiling wave flow, an innovative method based on multi-scale marginal spectrum entropy showed more feasible for identification of transition boundary.

An analysis of bibliometric indicators to JCR according to Benford's law

Journal Citation Reports (JCR) is the main source of bibliometric indicators known by the scientific community. This paper presents the results of a study of the distributions of the first and second significant digits according to Benford’s law (BL) of the number of articles, citations, impact factors, half-life and immediacy index bibliometric indicators in journals indexed in the JCR Sciences and Social Sciences Editions from 2007 to 2014. We also performed the data analysis to country’s origin and by journal’s category, and we verified that the second digit has a better adherence to BL. The use of the second digit is important since it provides a more sound, complete and consistent analysis of the bibliometric indicators.