A Universal Rank-Size Law

Opportune warning of COVID-19 in a Mexican health care worker cohort: Discrete beta distribution entropy of smartwatch physiological records

We present a statistical study of heart rate, step cadence, and sleep stage registers of health care workers in the Hospital General de México "Dr. Eduardo Liceaga" (HGM), monitored continuously and non-invasively during the COVID-19 contingency from May to October 2020, using the Fitbit Charge 3® Smartwatch device. The HGM-COVID cohort consisted of 115 participants assigned to areas of COVID-19 exposure. We introduce a novel biomarker for an opportune signal for the likelihood of SARS-CoV-2 infection based on the Shannon Entropy of the Discrete Generalized Beta Distribution fit of rank ordered smartwatch registers. Our statistical test indicated infection for 94% of patients confirmed by positive polymer chain reaction (PCR+) test, 47% before the test, and 47% in coincidence. These results required innovative data preprocessing for the definition of a new biomarker index. The statistical method parameters are data-driven, confidence estimates were calibrated based on sensitivity tests using appropriately derived surrogate data as a benchmark. Our surrogate tests can also provide a benchmark for comparing results from other anomaly detection methods (ADMs). Biomarker comparison of the negative Immunoglobulin G Antibody (IgG-) subgroup with the PCR+ subgroup showed a statistically significant difference (p < 0.01, effect size = 1.44). The distribution of the uninfected population had a lower median and less dispersion than the PCR+ population. A retrospective study of our results confirmed that the biomarker index provides an early warning of the likelihood of COVID-19, even several days before the onset of symptoms or the PCR+ test request. The method can be calibrated for the analysis of different SARS-CoV-2 strains, the effect of vaccination, and previous infections. Furthermore, our biomarker screening could be implemented to provide general health profiles for other population sectors based on physiological signals from smartwatch wearable devices.

Clustering networked funded European research activities through rank-size laws

This paper treats a well-established public evaluation problem, which is the analysis of the funded research projects. We specifically deal with the collection of the research actions funded by the European Union over the 7th Framework Programme for Research and Technological Development and Horizon 2020. The reference period is 2007-2020. The study is developed through three methodological steps. First, we consider the networked scientific institutions by stating a link between two organizations when they are partners in the same funded project. In doing so, we build yearly complex networks. We compute four nodal centrality measures with relevant, informative content for each of them. Second, we implement a rank-size procedure on each network and each centrality measure by testing four meaningful classes of parametric curves to fit the ranked data. At the end of such a step, we derive the best fit curve and the calibrated parameters. Third, we perform a clustering procedure based on the best-fit curves of the ranked data for identifying regularities and deviations among years of research and scientific institutions. The joint employment of the three methodological approaches allows a clear view of the research activity in Europe in recent years.

Combining rank-size and k-means for clustering countries over the COVID-19 new deaths per million

This paper deals with the cluster analysis of selected countries based on COVID-19 new deaths per million data. We implement a statistical procedure that combines a rank-size exploration and a k-means approach for clustering. Specifically, we first carry out a best-fit exercise on a suitable polynomial rank-size law at an individual country level; then, we cluster the considered countries by adopting a k-means clustering procedure based on the calibrated best-fit parameters. The investigated countries are selected considering those with a high value for the Healthcare Access and Quality Index to make a consistent analysis and reduce biases from the data collection phase. Interesting results emerge from the meaningful interpretation of the parameters of the best-fit curves; in particular, we show some relevant properties of the considered countries when dealing with the days with the highest number of new daily deaths per million and waves. Moreover, the exploration of the obtained clusters allows explaining some common countries' features.

Statistical Analysis of the Membership Management Indicators of the Church of England UK Dioceses during the Recent (XXth Century) “Decade of Evangelism”

The paper focusses on the growth or/and decline in the number of devotees in UK Dioceses of the Church of England during the “Decade of Evangelism” [1990–2000]. In this study, rank-size relationships and subsequent correlations are searched for through various performance indicators of evangelism management. A strong structural regularity is found. Moreover, it is shown that such key indicators appear to fall into two different classes. This unexpected feature seems to indicate some basic universality regimes, in particular to distinguish behaviour measures. Rank correlations between indicators measures further emphasise some difference in evangelism management between Evangelical and Catholic Anglican tradition dioceses (or rather bishops) during that time interval.

Statistical models for identifying frequent hitters in high throughput screening

High throughput screening (HTS) interrogates compound libraries to find those that are “active” in an assay. To better understand compound behavior in HTS, we assessed an existing binomial survivor function (BSF) model of “frequent hitters” using 872 publicly available HTS data sets. We found large numbers of “infrequent hitters” using this model leading us to reject the BSF for identifying “frequent hitters.” As alternatives, we investigated generalized logistic, gamma, and negative binomial distributions as models for compound behavior. The gamma model reduced the proportion of both frequent and infrequent hitters relative to the BSF. Within this data set, conclusions about individual compound behavior were limited by the number of times individual compounds were tested (1–1613 times) and disproportionate testing of some compounds. Specifically, most tests (78%) were on a 309,847-compound subset (17.6% of compounds) each tested ≥ 300 times. We concluded that the disproportionate retesting of some compounds represents compound repurposing at scale rather than drug discovery. The approach to drug discovery represented by these 872 data sets characterizes the assays well by challenging them with many compounds while each compound is characterized poorly with a single assay. Aggregating the testing information from each compound across the multiple screens yielded a continuum with no clear boundary between normal and frequent hitting compounds.

Rank-size Distribution of Cities and Municipalities in Bangladesh

This paper examines and updates the rank-size distribution of cities and municipalities in Bangladesh between 1990 and 2019 based on two criteria: (1) built-up urban areas; and (2) population. The distribution of built-up urban areas and population are compared to provide a robust theoretical underpinning of Zipf’s law for future urban developmental planning framework. The data on built-up urban areas is extracted from land cover classification using Google Earth Engine and the population data is obtained from the decennial censuses. The comparison of the conformity to Zipf’s law indicated contradictory results. While a greater proportion of the population has been increasingly concentrated in the smaller and midsized cities over the last three decades, built-up urban areas, on the other hand, have been mostly clustered in two largest cities— Dhaka and Chittagong—accounting for 50 to nearly 60 percent of the total built-up urban areas. These results shed light on the magnitude of continued spatial inequalities in urban development amongst cities and municipalities in Bangladesh despite there being an overall increase of evenness in the distribution of population over time. These results imply an unsustainable rate of urban expansion in Bangladesh and reinforce the need for the exploration of policies and regulations targeted at guiding the rate and direction of evenness in urban expansion.

Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes

Rank-ordered distributions have been a matter of intense study. Often Zipf type invariant scaling is invoked; however, in the last decade the ubiquity of a Discrete Generalized Beta Distribution, DGBD, with two scaling exponents has been established. This distribution incorporates deviations from the power law at the extremes. A proper understanding of the meaning of these exponents is still lacking. Here, using two families of unimodal maps on the [0,1] interval, we construct binary sequences via standard symbolic dynamics. In both cases, the tent map, which is at the convex-concave border of the mapping families, separates intermittent regimes from chaotic dynamics. We show that the frequencies of n-tuples of the generated symbolic sequences are remarkably well fitted by the DGBD. We argue that in the underlying dynamics an order-disorder competition takes place and that one of the exponents is related to multiple range correlations, while the other is sensitive to disorder. In our study, we implement thermodynamic formalisms with which we can readily calculate n-tuple frequencies, in some particular cases, analytically. We show that for the convex mappings there is a first-order thermodynamic phase transition, while concave mappings have smooth free energy densities. Within our DGBD study, the transition between these two regimes coincides with a zero value for both exponents; in this sense, they may even be considered as indicators of the transition. An analysis of the difference between the exponents reinforces the interpretation we have assigned to them. Furthermore, the two regimes can be identified by the sign of such a difference. We also show that divergences in the invariant densities are responsible for the first order phase transitions observed in a range of the rank-frequency distributions. Our findings give further support to previous studies based on expansion-modification algorithms, birth-death processes, and random variable subtraction dynamics.

Population patterns in World's administrative units

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.