A Random Categorization Model for Hierarchical Taxonomies

Abstract

A taxonomy is a standardized framework to classify and organize items into categories. Hierarchical taxonomies are ubiquitous, ranging from the classification of organisms to the file system on a computer. Characterizing the typical distribution of items within taxonomic categories is an important question with applications in many disciplines. Ecologists have long sought to account for the patterns observed in species-abundance distributions (the number of individuals per species found in some sample), and computer scientists study the distribution of files per directory. Is there a universal statistical distribution describing how many items are typically found in each category in large taxonomies? Here, we analyze a wide array of large, real-world datasets – including items lost and found on the New York City transit system, library books, and a bacterial microbiome – and discover such an underlying commonality. A simple, non-parametric branching model that randomly categorizes items and takes as input only the total number of items and the total number of categories is quite successful in reproducing the observed abundance distributions. This result may shed light on patterns in species-abundance distributions long observed in ecology. The model also predicts the number of taxonomic categories that remain unrepresented in a finite sample.

Charge Transport Characteristics of Surface‐Complexed Quantum Dot in a Thin Film Transistor

“…In p-doped ZnS, the dopant atoms occupy the Zn 2+ substitutional sites that are proposed to promote hole transport. [38] Such kinds of p-type conductivity are also known to occur in Mn 2+ -doped ZnO, As-and Sb-doped ZnS and ZnSe. [39][40][41] In Mn 2+ -doped ZnS Qdots, Mn 2+ ions occupy the Zn 2+ lattice cites and S 2− ions tetrahedrally coordinate the Mn 2+ ion.…”