Ultraslow diffusion in language: Dynamics of appearance of already popular adjectives on Japanese blogs

TL;DR

This study analyzes the appearance dynamics of popular adjectives in Japanese blogs over six years, revealing that ultraslow diffusion driven by a power-law forgetting process explains the observed long-memory effects.

Contribution

It introduces a random diffusion model based on the power-law forgetting process to explain word appearance dynamics, capturing ultraslow diffusion and other statistical properties.

Findings

Word appearance follows ultraslow diffusion with logarithmic growth of mean squared displacement.

The power-law forgetting process model reproduces fluctuation scaling and spectral density.

The model accurately captures the statistical properties of the time series data.

Abstract

What dynamics govern a time series representing the appearance of words in social media data? In this paper, we investigate an elementary dynamics, from which word-dependent special effects are segregated, such as breaking news, increasing (or decreasing) concerns, or seasonality. To elucidate this problem, we investigated approximately three billion Japanese blog articles over a period of six years, and analysed some corresponding solvable mathematical models. From the analysis, we found that a word appearance can be explained by the random diffusion model based on the power-law forgetting process, which is a type of long memory point process related to ARFIMA(0,0.5,0). In particular, we confirmed that ultraslow diffusion (where the mean squared displacement grows logarithmically), which the model predicts in an approximate manner, reproduces the actual data. In addition, we also show that the model can reproduce other statistical properties of a time series: (i) the fluctuation scaling, (ii) spectrum density, and (iii) shapes of the probability density functions.