Zipf–Mandelbrot–Pareto model for co-authorship popularity

Language-like efficiency and structure in house finch song

Communication needs to be complex enough to be functional while minimizing learning and production costs. Recent work suggests that the vocalizations and gestures of some songbirds, cetaceans and great apes may conform to linguistic laws that reflect this trade-off between efficiency and complexity. In studies of non-human communication, though, clustering signals into types cannot be done a priori, and decisions about the appropriate grain of analysis may affect statistical signals in the data. The aim of this study was to assess the evidence for language-like efficiency and structure in house finch (Haemorhous mexicanus) song across three levels of granularity in syllable clustering. The results show strong evidence for Zipf's rank-frequency law, Zipf's law of abbreviation and Menzerath's law. Additional analyses show that house finch songs have small-world structure, thought to reflect systematic structure in syntax, and the mutual information decay of sequences is consistent with a combination of Markovian and hierarchical processes. These statistical patterns are robust across three levels of granularity in syllable clustering, pointing to a limited form of scale invariance. In sum, it appears that house finch song has been shaped by pressure for efficiency, possibly to offset the costs of female preferences for complexity.

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.

On a heuristic point of view concerning the citation distribution: introducing the Wakeby distribution

The paper proposes a heuristic approach to modeling the cumulative distribution of citations of papers in scientific journals by means of the Wakeby distribution. The Markov process of citation leading to the Wakeby distribution is analyzed using the terminal time formalism. The Wakeby distribution is derived in the paper from the simple and general inhomogeneous Choquet–Deny convolution equation for a non-probability measure. We give statistical evidence that the Wakeby distribution is a reasonable approximation of the empirical citation distributions.

AMS Subject Classification: 91D30; 91D99