Complex system properties in the spreading of COVID-19 pandemic

The objective of the present study was to show that the spread of the COVID-19 pandemic around the world shows complex system properties such as lognormal laws, temporal fluctuation scaling, and time correlation. First, the daily cumulative number of confirmed cases and deaths is distributed among countries as lognormals such that the time series exhibit a temporal fluctuation scaling. Second, the daily return time series of cases and deaths per day have associated Levy stable distributions and they have time correlation. The idea was to draw attention to the fact that the spread of the COVID-19 pandemic can be seen as a complex system, and, thus, contribute to the identification of the structural properties of this system, which is relevant as it is expected that future stochastic models describing the spread of the COVID-19 pandemic from a microscopic dynamics perspective should be able to explain the emergence of the structural properties identified here.

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

We generalize Taylor’s law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power (2−α)/(1−α)>2. The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power (2−α2)/(1−α). These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli–Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor’s law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

Scaling of Measure Fluctuations on a Flapping Flag Device in the Open Channel Around a Cylinder At $Re=10^4$ : Taylor's Law Approach

Experimental evidence showed how various complex systems, characterized by a fluctuation scaling, satisfy the well-known Taylor's law. The present work aims to apply for the first time Taylor's law, given its general treatment, for a flow field at $Re$ around $10^4$, since activity of each fluid particle is highly fluctuating, especially in the context of vortex shedding. In addition, the further element of innovation is the use of an innovative thin-films based device consisting of an elastic piezoelectric flapping flag that is proposed as a measuring instrument of the flow field. The oscillations of the flapping flag, due to the vortexes release downstream to an obstacle of cylindrical shape, generate an alternating piezoelectric voltage whose time history is similar to the chaotic components of the fully developed turbulent speed. Preliminary experimental results about the use of thin-films based device in a flume channel are reported together with a second order analysis on the voltage difference and a scaling law of the exponent scale.

Heavy-tailed distributions, correlations, kurtosis and Taylor’s Law of fluctuation scaling

Pillai & Meng (Pillai & Meng 2016 Ann. Stat. 44 , 2089–2097; p. 2091) speculated that ‘the dependence among [random variables, rvs] can be overwhelmed by the heaviness of their marginal tails ·· ·’. We give examples of statistical models that support this speculation. While under natural conditions the sample correlation of regularly varying (RV) rvs converges to a generally random limit, this limit is zero when the rvs are the reciprocals of powers greater than one of arbitrarily (but imperfectly) positively or negatively correlated normals. Surprisingly, the sample correlation of these RV rvs multiplied by the sample size has a limiting distribution on the negative half-line. We show that the asymptotic scaling of Taylor’s Law (a power-law variance function) for RV rvs is, up to a constant, the same for independent and identically distributed observations as for reciprocals of powers greater than one of arbitrarily (but imperfectly) positively correlated normals, whether those powers are the same or different. The correlations and heterogeneity do not affect the asymptotic scaling. We analyse the sample kurtosis of heavy-tailed data similarly. We show that the least-squares estimator of the slope in a linear model with heavy-tailed predictor and noise unexpectedly converges much faster than when they have finite variances.

A calibrated measure to compare fluctuations of different entities across timescales

A common way to learn about a system’s properties is to analyze temporal fluctuations in associated variables. However, conclusions based on fluctuations from a single entity can be misleading when used without proper reference to other comparable entities or when examined only on one timescale. Here we introduce a method that uses predictions from a fluctuation scaling law as a benchmark for the observed standard deviations. Differences from the benchmark (residuals) are aggregated across multiple timescales using Principal Component Analysis to reduce data dimensionality. The first component score is a calibrated measure of fluctuations—the reactivityRA of a given entity. We apply our method to activity records from the media industry using data from the Event Registry news aggregator—over 32M articles on selected topics published by over 8000 news outlets. Our approach distinguishes between different news outlet reporting styles: high reactivity points to activity fluctuations larger than expected, reflecting a bursty reporting style, whereas low reactivity suggests a relatively stable reporting style. Combining our method with the political bias detector Media Bias/Fact Check we quantify the relative reporting styles for different topics of mainly US media sources grouped by political orientation. The results suggest that news outlets with a liberal bias tended to be the least reactive while conservative news outlets were the most reactive.