Schedule

Data-Driven Recovery of Network Dynamics and Detecting Critical Transitions

Deniz Eroglu (Kadir Has University, TR)

Anticipating critical transitions in complex systems—ranging from brain networks to climate dynamics—depends crucially on our ability to uncover both their internal dynamics and network structure from limited and noisy data. In this talk, I introduce a unified framework for reconstructing governing dynamics and interaction topologies in weakly coupled chaotic networks, leveraging model reduction techniques and recent advances in data-driven system identification. A central insight of our method is to exploit stochastic fluctuations—often regarded as mere noise—as informative fingerprints of the underlying network architecture. Using these, we build effective dynamical models that integrate local node behavior with statistically inferred coupling rules. This approach enables us to accurately forecast critical transitions even when the system is driven far from its observed states [1]. We validate the method on both simulated networks inspired by cortical connectivity and experimental neuronal recordings from the mouse neocortex [2], where the framework captures both topology and dynamics from sparse observations. Notably, it performs well even with short time series, making it suitable for practical scenarios where data is limited. Finally, I will highlight open challenges in network reconstruction from partial and noisy data, and discuss how our work addresses some of these limitations by incorporating ideas from normal form theory and synchronization dynamics [3].

References

[1] D. Eroglu, M. Tanzi, S. van Strien, T. Pereira, Phys. Rev. X 10, 021047 (2020).

[2] I. Topal, D. Eroglu, Phys. Rev. Lett. 130, 117401 (2023).

[3] E. Nijholt, J.L. Ocampo-Espindola, D. Eroglu, I.Z. Kiss, T. Pereira, Nat. Commun. 13, 4849 (2022).

Octopus Reservoir Computing (RC): Combining Tentacle RC with Kuramoto RC

Yuriko Fujihara (Kanazawa University, JP)

Computing in silica comes with drawbacks, including high energy consumption, susceptibility to critical failures in extreme environments, such as high-radiation areas, as well as computational speed limitations which can be troublesome when processing real-time photonic data.  This has sparked significant interest in discovering alternative physical systems that can overcome these limitations. A framework that overcomes this is physical reservoir computing as it allows us to directly harness the computational capabilities of a physical system without requiring a specific architecture which greatly reduces engineering overhead.

In nature networks of coupled oscillators are abundant. Hence, if we find a method to harness coupled oscillators using reservoir computing a wide variety of systems can be used for computing. Based on work in [de Jong et al, 2025] we consider a reservoir computer given by a network of coupled oscillators. We show how the architecture of a coupled oscillator network can greatly influence the performance of the reservoir computer. We take inspiration from the tentacle RC by [Nakajima et al,2015] and the Forced Kuramoto RC from [de Jong et al, 2025]. We combine the two to obtain an octopus like architecture that has high performance.   

Topological bifurcations in random dynamical systems with bounded noise 

Wei Hao Tey (Imperial College, UK)

Noise and uncertainty play a central role in real-world dynamical systems, motivating the study of random dynamical systems (RDS). When noise is bounded, stationary measures are typically non-unique and supported on compact sets. In many cases, the support acts as an attractor: nearby trajectories are drawn to it and remain confined. The ensemble of all random trajectories can be naturally described by a deterministic set-valued dynamical system, where the supports of stationary measures correspond to minimal attractors of this set-valued system. These attractors can change discontinuously, through a topological bifurcation, reflected by sudden jumps - critical transitions - in time-series data. However, set-valued analysis is notoriously challenging; therefore, we propose the study of support boundaries instead. I will present two ideas in this talk:

1) We propose a novel early warning indicator for critical transitions in one-dimensional random dynamical systems with bounded noise. The indicator is based on the derivative of the extremal map, which describes how the boundary of stationary measure supports evolve. By analysing the tail asymptotics of the stationary density, we introduce numerical estimations of the derivative of the extremal map, given time-series data. This provides a quantitative and interpretable measure of the system’s proximity to bifurcation.

2) We show that topological bifurcations can be detected through a classical bifurcation analysis of a single-valued map - the boundary map, a higher-dimensional generalisation of the extremal map that captures the evolution of support boundaries. This connection provides a systematic bridge between random dynamical systems and deterministic bifurcation theory.

Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes

Yin Hao Wu (Shanghai School of Finance and Economics, CN)

Recent empirical findings in high-frequency data reveal that asset volatility exhibits rough paths, characterized by a Hurst parameter $H\approx 0.1$, which is significantly smaller than that of standard Brownian motion. On the modeling side, Score-Driven models have emerged as a powerful framework in data science and econometrics due to their robustness and information-theoretic optimality. However, standard score-driven models are typically Markovian, which implies that the macroscopic behavior they characterize in high-frequency data are constrained to be standard diffusion processes. In this talk, we discuss the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we carry out numerical simulations and option pricing analyses, offering new tools for rough volatility modeling and simulation.

Tilings of Penrose type: projection and substitution

Jeroen Lamb (Imperial College, UK)

The Penrose tiling is a planar tiling with two rhombic tiles, orginally designed by Roger Penrose in the early 1970s to illustrate the fact that local properties of tiles (matching rules) can enforce global aperiodicity.  Penrose demonstrated  this by a renormalization argument that involves a substitution rule. Some ten years later, Nico de Bruijn showed that Penrose's tiling can also be viewed as the projection of a slice of a 5-dimensional lattice. Penrose tilings have received much attention in the context of quasicrystals (that were discovered to exist

in 1984). Despite many other examples of quasicrystaline tilings have been discovered, few shared the remarkable combination of properties of the Penrose tiling.

We present a comprehensive characterisation of all tilings of "Penrose type", i.e. tilings of $R^n$ that, like Penrose's original example, have matching rules, substitutions rules, and can be constructed by De Bruijn's projection method. A generalisation of Rauzy-Veech renormalisation for interval-exchange transformations lies at the foundation of this result. Our results are constructive and reveal an infinity of novel examples of tilings of Penrose type. This is joint work with Edmund Harriss (Arkansas).

More Than Just Hexagons: Does an Einstein Tile Exist in Life? 

Makoto Sato (Kanazawa University, JP)

A tile pattern is a way of covering a surface using repeated shapes without gaps or overlaps. When all the tiles are identical and arranged with translational symmetry—like bathroom tiles or honeycombs—the pattern is called "periodic". In contrast, an "Einstein tile" is a unique shape that can cover a surface using only identical tiles, but in a way that never repeats periodically. This property is called "aperiodicity". For over 50 years, it was unknown whether such a tile could exist, until amateur mathematician David Smith, in collaboration with professional mathematicians, discovered one in 2023.

 So far, Einstein tiles have not been found in nature. In biology, many natural tile patterns, such as honeycombs or insect eyes, tend to show hexagonal symmetry. This is thought to arise from physical constraints like minimizing perimeter and maximizing space filling. For example, the compound eye of Drosophila forms a highly regular hexagonal pattern. Our previous research showed that this regular pattern emerges gradually from an initially irregular arrangement during pupal development (Hayashi et al., Curr. Biol. 2022).

 Interestingly, Einstein tiles share some geometric properties with hexagonal patterns and with the cellular arrangements found in the compound eye. In this talk, we will explore the possible relationship between Einstein tiles and biological systems. We will present intriguing reasons to think that nature favors similar aperiodic arrangements under certain conditions, particularly during the development of the compound eye, which gradually establishes a hexagonal arrangement through intracellular force feedback. 

Riding the wave: swarmalators that sync, divide and proliferate  

Ahmad Mohiuddin (Kanazawa University, JP)

During early embryonic development in many species, a series of cell divisions transforms one cell into a cluster of tens or hundreds of cells. This often occurs by cell divisions with no growth, also known as cleaving divisions. Towards investigating the apparent synchrony of division events, we model the cells as oscillators with spatial degrees of freedom that are coupled to their neighbours. Therefore, we have a model of spatially coupled oscillators that proliferate as they complete full cycles, constituting a biologically-inspired generalization of the classical swarmalator model. We explore the effect of coupling on our cleaving cell model and show that for suitable parameters the model qualitatively resembles the biology.

Dynamics of interfaces in the two-dimensional wave-pinning model 

Taikei Uechi (Kanazawa University, JP)

We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp interface that partitions the domain into high- and low-concentration regions. We perform a detailed asymptotic analysis and derive higher-order approximation equations governing the motion of this interface. Our results show that on a fast timescale, the interface evolves via propagating front dynamics, whereas on a slow timescale, it evolves as an area-preserving mean curvature flow. Furthermore, using the derived free boundary problem, we demonstrate that on a significantly slower timescale, an interface whose endpoints lie on the domain boundary drifts along the boundary toward regions of higher curvature.