arXiv subjects

Paula Pirker-Díaz

Publications and source records attributed to Paula Pirker-Díaz.

3 recordsLinked to original sources

arXiv2026

Critical dynamics govern the evolution of political regimes

The emergence and decline of democratic systems worldwide raises fundamental questions about the dynamics of political change. Contrary to the idea of a stable endpoint of liberal democracy, recent backsliding towards less democratic regimes highlights the non-stationary nature of regime evolution. Here, we analyse the historical trajectories of countries within a two-dimensional regime space derived from the principal components of the Varieties of Democracy dataset. We observe weakly non-ergodic dynamics unfolding in an effective landscape characterised by sparse and shifting basins of stability. Step sizes and sojourn times characterising this dynamics follow heavy-tailed distributions near the critical regime, in which mean values appear to diverge. These facts point to the intermittent and heterogeneous nature of the regime change dynamics. A continuous time random walk model reproduces the dynamics of the three most recent decades with remarkable accuracy. Together, these results suggest that some aspects of political regime evolution follow universal stochastic principles, while remaining punctuated by unique historical pathways.

cond-mat.stat-mech↗

arXiv2026

Nonlinear Dimensionality Reduction with Diffusion Maps in Practice

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones.

cs.LG↗

arXiv2024

Unraveling 20th-century political regime dynamics using the physics of diffusion

Uncertainty persists over how and why some countries become democratic and others do not, or why some countries remain democratic and others 'backslide' toward autocracy. Furthermore, while scholars generally agree on the nature of 'democracy' and 'autocracy', the nature of regimes in-between, and changes between them, are much less clear. By applying the spectral dimensionality-reduction technique Diffusion Map to political-science data from the V-Dem project for the period 1900 to 2021, we identify a low-dimensional non-linear manifold on which all electoral regimes move. Using the diffusion equation from statistical physics, we measure the time scale on which countries change their degree of electoral quality, freedom of association, and freedom of expression depending on their position on the manifold. By quantifying the coefficients of the diffusion equation for each country and over time, we show that democracies behave like sub-diffusive (i.e. slow spreading) particles and that autocracies on the verge of collapse behave like super-diffusive (i.e. fast spreading) particles. We show that regimes in-between exhibit diffusion dynamics distinct from autocracies and democracies, and an overall higher instability. Furthermore, we show that a country's position on the manifold and its dynamics are linked to its propensity for civil conflict. Our study pioneers the use of statistical physics in the analysis of political regimes. Our results provide a quantitative foundation for developing theories about what changes during democratization and democratic backsliding, as well as a new framework for regime-transformation and risk-of-conflict assessment.

physics.soc-ph↗