Inferring the dynamics of infectious diseases enables prediction and intervention. During early monitoring, available information may comprise digital contact data that partly resolve the interaction network and intermittent screening data that leave the states of some nodes unresolved. Learning-based methods can introduce further information loss by compressing available network and state information into summary statistics. To retain the correspondence between node states and network positions, we develop Graph-Sequence Transformer Attention (GTA), which uses observed node states, network topology, and observation times to infer infection and recovery probabilities for susceptible–infectious–recovered spreading. We compare GTA with summary-based XGBoost and a one-dimensional convolutional neural network and with maximum-likelihood estimation of the recovery probability. Across four synthetic network classes and five empirical topologies, the three learning methods often perform comparably and respond similarly to changes in network size, mean degree, and observation timing. GTA is usually most accurate for estimating infection on sparse, heterogeneous networks, whereas summary-based methods often match or outperform it on denser, more homogeneous networks. For a fixed number of observations, wider spacing can initially improve inference by covering more of the spreading trajectory, but eventually increases error as intermediate transitions are missed. Maximum-likelihood estimation can outperform learning methods when recovery transitions are well resolved, but deteriorates as observations become more widely separated. Losing information about node states can compromise performance more than losing information about edges. Overall, the results show how inference from incomplete observations depends on network structure, temporal sampling, and the information retained in the observations.
Characterizing the complexity of cardiac arrhythmias is essential for distinguishing different dynamical regimes, comparing rhythms across physiological and pathological conditions, and identifying transitions to life-threatening states such as fibrillation. In this work, we develop a comprehensive pipeline to quantify, for the first time, the degree of chaotic dynamics in mathematical cardiac models by calculating the largest Lyapunov exponent (LE) across a wide range of different dynamical regimes and parameter sets. This analysis was enabled by high-performance graphics processing unit-based 2D simulations implemented in WebGL, allowing fast systematic exploration of long-duration spatiotemporal dynamics across large parameter spaces. We show that both temporal and spatial LE (λT and λS) estimators can be effectively used with action potential duration (APD) data, even without full access to state variables. Specifically, a spatiotemporal algorithm and Wolf’s algorithm are used to quantify LEs from APD data obtained from simulations exhibiting a broad range of complex reentrant spatiotemporal dynamics. Across different dynamical regimes and parameter variations, λT and λS generally track changes in chaotic complexity, while differences between them reflect distinct sensitivities to how the underlying instability is expressed in the spatiotemporal dynamics. We also identify the minimum data length and spatial density necessary to achieve robust and accurate LE estimation. In particular, the estimation of λS requires shorter recordings and fewer APD measurements and remains robust at lower spatial and temporal resolution, substantially reducing the data requirements compared with λT. Our results suggest that these APD-based methods can be applied not only to simulation data but also to clinical or experimental data, where access to complete state variables and long, high-resolution recordings is inherently limited. The ability of λS to track changes in chaotic complexity with substantially reduced data requirements, together with the complementary information obtained when both estimators are available, makes this framework particularly promising for quantifying chaotic dynamics in experimentally and clinically observed cardiac arrhythmias.
Inferring interaction structure from steady-state observations is a central inverse problem when transient trajectories are unavailable. Here, we formulate this problem as simultaneous compatibility of a single interaction operator with equilibrium constraints generated by heterogeneous perturbations. We introduce a variational physics-informed ansatz that represents the unknown operator as a trainable object and minimizes the resulting steady-state residuals across experiments. In the affine-interaction setting, the stacked equilibrium equations yield explicit finite-sample identifiability conditions: unique recovery is controlled by the rank of the compatibility matrix after elimination of experiment-wise gauge freedom. Synthetic benchmarks on pairwise, directed, weighted, empirical-topology, and selected higher-order systems illustrate this identifiability picture and show how additional heterogeneous steady states improve structural discrimination under the stated assumptions. The results clarify a concrete steady-state reconstruction regime in which equilibrium observations alone can determine hidden interaction operators when the governing dynamics are known and node-level equilibria are fully observed.
Complex system dynamics and structures can often be evaluated through their reconstructions from available fragmented samples, which may be relatively short, with paleoclimatic and other geophysical time series obtained from proxies such as tree-ring data, as well as DNA and protein structures obtained from short reads among prominent examples. Although existing reconstruction methods focus on capturing short-term dynamics, they largely overlook long-term evolution, failing to account for the persistent long-range correlations inherent in these systems. To address this gap, we propose a generalized approach that unifies Kalman-based filtering with Kasdin’s method for the generation of colored noise. We validate its performance using both simulated time series and fragmented tree-ring width records drawn from a dendrochronological archive. The advantage of the proposed technique is that it does not require any detailed knowledge of the data properties beyond the Hurst exponent at the time of application. As a single free parameter, the Hurst exponent remains stable and representative for a given class of records, offering a powerful and accessible tool for an adequate reconstruction of the long-term behavior of complex systems.
Considering agents tend to interact preferentially with others adopting similar behaviors, this paper investigates the impact of similarity-based interaction mechanism on learning dynamics and evolution of strategies. We propose a novel evolution model for reactive strategies in which agents interact with similar partners within some threshold, forming a dynamically structural population. By combining exploitation and exploration, we analyze the evolution dynamics of cooperation under the influence of various payoff parameters and similarity thresholds. The results show that similarity-based interactions can efficiently protect cooperative strategies and promote their persistence. Robustness analysis further demonstrates that similarity-driven interactions sustain high cooperation across different population sizes and that moderate random exploration enhances cooperative evolution.
