Organizers: Stefanie Winkelmann, Maximilian Engel

Abstract:

Interacting particle systems appear in physics, biology, and social dynamics, often leading to high-dimensional models. This minisymposium focuses on recent advances in model reduction techniques that enable efficient simulation, analysis, and interpretation of such systems. Approaches include mean-field models and stochastic PDEs, transfer-operator frameworks and Markov state models, hybrid multiscale models, coherent structure analysis, as well as data-driven techniques. The session aims to bring together theoretical and applied perspectives on efficient representations of complex, many-body systems.

Speakers:

14:30h: Vaishnavi Jayakumar (University of Potsdam)

The Physics of Political Change: Diffusion, Stability, and Regime Dynamics

Understanding the dynamics of political regimes is central to navigating contemporary complexity at the intersection of social, economic, and institutional processes. Contrary to equilibrium-based perspectives that treat liberal democracy as a stable endpoint, empirical evidence from the past century points to fundamentally non-stationary and heterogeneous regime evolution. In this talk, we demonstrate how tools from statistical physics and biostatistics provide a unifying framework to characterize and model these dynamics across scales.

Leveraging the high-dimensional Varieties of Democracy (V-Dem) dataset, we first construct low-dimensional representations of political regimes using linear and nonlinear dimensionality reduction techniques. The latter, specifically Diffusion Maps, reveal that regime indicators lie on a curved, low-dimensional manifold, enabling the definition of a latent regime coordinate that preserves nonlinear structure and improves predictive resolution for outcomes such as intra-state conflict and child mortality.

Building on this understanding, we show that long-term regime dynamics obey scaling laws characteristic of diffusive processes, with different dynamical regimes emerging across political contexts: super-diffusive behavior in destabilizing autocracies, near-random-walk dynamics in hybrid regimes, and sub-diffusive dynamics in more stable systems. Furthermore, we find heavy-tailed step sizes and waiting times near critical regions of the regime space, suggesting that political transitions exhibit universal properties akin to anomalous diffusion.

Complementary survival analysis of regime lifetimes further reveals insight into asymmetry between autocracies and democracies, and the long-term stability of different governance types, dependent on economic and institutional factors. These findings point to distinct stability mechanisms operating across the regime spectrum. Together, these results suggest that political systems, despite their historical and cultural specificity, can be fruitfully understood through the lens of stochastic processes, scaling, and universality.

By integrating methods from statistical physics and biostatistics with large-scale political data, this work advances an interdisciplinary approach to complex societal systems and offers new quantitative insights into regime stability, transformation, and the conditions under which political order becomes fragile.

15:00h: Narcicegi Kiran (University of Hamburg)

Network Recoverability under Aggregation and Smoothing

In the natural sciences, from neuroscience to geophysics and chemistry, observations are often aggregated to reduce system size and filtered to mitigate noise. We address the inverse problem of recovering the underlying network from such observations. We first show how the smoothing filter enables the recovery of the effective system obtained through averaging. We then consider recovery from mean-field measurements, a problem typically regarded as ill-posed. By leveraging a pinching-type initialization, we derive theoretical conditions guaranteeing the uniqueness of the recovered network, along with numerical experiments demonstrating robustness across different connectivity regimes. Together, these results provide theoretical and computational foundations for network recovery from aggregated and noisy observation.

15:30: Ralph Gregor Andrzejak (Universitat Pompeu Fabra)

Effective directional interdependence in homogeneous non-directionally coupled networks – a simple model and analogies to neuronal dynamics

In this presentation, I will consider oscillator networks in which all nodes are identical, all nodes have the same arrangement of links connecting them to other nodes, and all links are symmetric-bidirectional. Such networks can exhibit a rich variety of collective dynamics, including so-called chimera states, for which the network segregates into mutually synchronized and desynchronized nodes. Accordingly, despite the homogeneity of the network’s nodes and connectivity, heterogeneous dynamics can arise. In this talk, we take a data-driven approach to these networks. We apply a signal analysis measures to the state variables of the network nodes. One might expect this approach to extract the homogeneity of the network connectivity structure. Likewise, it may infer the heterogeneity of the network's dynamics by finding strong and weak interdependence between synchronized and desynchronized nodes, respectively. However, we show that in chimera states this approach actually reveals a directional interdependence of the desynchronized nodes on synchronized ones. This illustrates that the impact of interactions among network nodes not only depends on their connectivity but also on their respective states. Symmetric-bidirectional network links can effectively act like a driver-response coupling. In closing, we will briefly discuss analogies to the notions of structural, functional and effective connectivity in neuroscience and the study of electroencephalographic signals from epilepsy patients.

The authors acknowledges the Grant PID2024-159709OB-I00 funded by MICIU/AEI/10.13039/501100011033 and by 'ERDF A way of making Europe'.