Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate early-warning tasks. This study proposes a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling. Through systematic comparison, six methods including diffusion maps (DM) are selected to construct low-dimensional representations. Based on these, a data-driven stochastic differential equation model is established to robustly estimate the probability evolution scoring function of the system. Building on this, a new Score Function (SF) indicator is defined by incorporating Schrödinger bridge theory to quantify the likelihood of significant state transitions in the system. Experiments demonstrate that this indicator exhibits higher sensitivity and robustness in epilepsy prediction, enables earlier identification of critical points, and clearly captures dynamic features across various stages before and after seizure onset. This work provides a systematic theoretical framework and practical methodology for extracting early-warning signals from high-dimensional data.

This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms.

In this article, we present a framework for designing neural networks that remain consistent with the underlying principles of agent-based models. We begin by highlighting the limitations of standard neural differential equations in modeling complex systems, where physical invariants (like energy) are often absent but other constraints (like mass conservation, information locality, bounded rationality) must be enforced. To address this, we introduce Agent-Based-Model informed Neural Networks (ABM-NNs), which leverage restricted graph neural networks and hierarchical decomposition to learn interpretable, structure-preserving dynamics. We validate the framework across three case studies of increasing complexity: (i) a Generalized Lotka-Volterra system, where we recover ground-truth parameters from short trajectories in presence of interventions; (ii) a graph-based SIR contagion model, where our method outperforms state-of-the-art graph learning baselines (GCN, GraphSAGE, Graph Transformer) in out-of-sample forecasting and noise robustness; and (iii) a real-world macroeconomic model of the ten largest economies, where we learn coupled GDP dynamics from empirical data and demonstrate counterfactual analysis for policy interventions.

Representing and reasoning about objects, relations and physics is a "core" domain of human common

Agent-based modeling (ABM) is a principal approach for studying complex systems. By decomposing a system into simpler, interacting agents, agent-based modeling (ABM) allows researchers to observe the emergence of complex phenomena. High-performance array computing libraries like JAX can help scale such computational models to a large number of agents by using automatic vectorization and just-in-time (JIT) compilation. One of the caveats of using JAX to achieve such scaling is that the shapes of arrays used in the computational model should remain immutable throughout the simulation. In the context of agent-based modeling (ABM), this can pose constraints on certain agent manipulation operations that require flexible data structures. A subset of which is represented by the ability to update a dynamically selected number of agents by applying distinct changes to them during a simulation. To this effect, we introduce ABMax, an ABM framework based on JAX that implements multiple just-in-time (JIT) compilable algorithms to provide this functionality. On the canonical predation model benchmark, ABMax achieves runtime performance comparable to state-of-the-art implementations. Further, we show that this functionality can also be vectorized, making it possible to run many similar agent-based models in parallel. We also present two examples in the form of a traffic-flow model and a financial market model to show the use case of ABMax

The diversity of patterns that emerge from complex systems motivates their use for scientific or artistic purposes. When exploring these systems, the challenges faced are the size of the parameter space and the strongly non-linear mapping between parameters and emerging patterns. In addition, artists and scientists who explore complex systems do so with an expectation of particular patterns. Taking these expectations into account adds a new set of challenges, which the exploration process must address. We provide design choices and their implementation to address these challenges; enabling the maximization of the diversity of patterns discovered in the user's region of interest -- which we call the constrained diversity -- in a sample-efficient manner. The region of interest is expressed in the form of explicit constraints. These constraints are formulated by the user in a system-agnostic way, and their addition enables interactive system exploration leading to constrained diversity, while maintaining global diversity.

Describing and comparing complex systems requires principled, theoretically grounded tools. Built around the phenomenon of type turbulence, allotaxonographs provide map-and-list visual comparisons of pairs of heavy-tailed distributions. Allotaxonographs are designed to accommodate a wide range of instruments including rank- and probability-turbulence divergences, Jenson-Shannon divergence, and generalized entropy divergences. Here, we describe a suite of programmatic tools for rendering allotaxonographs for rank-turbulence divergence in Matlab, Javascript, and Python, all of which have different use cases.

Guiding biological systems toward desired states, such as morphogenetic outcomes, remains a fundamental challenge with far-reaching implications for medicine and synthetic biology. While large language models (LLMs) have enabled natural language as an interface for interpretable control in AI systems, their use as mediators for steering biological or cellular dynamics remains largely unexplored. In this work, we present a functional pipeline that translates natural language prompts into spatial vector fields capable of directing simulated cellular collectives. Our approach combines a large language model with an evolvable neural controller (Prompt-to-Intervention, or P2I), optimized via evolutionary strategies to generate behaviors such as clustering or scattering in a simulated 2D environment. We demonstrate that even with constrained vocabulary and simplified cell models, evolved P2I networks can successfully align cellular dynamics with user-defined goals expressed in plain language. This work offers a complete loop from language input to simulated bioelectric-like intervention to behavioral output, providing a foundation for future systems capable of natural language-driven cellular control.

In [1] a novel global feature importance method for regression has been introduced for explainable artificial intelligence (XAI) [2], based on recent results which generalize the traditional dyadic description of networks of variables to the higher-order setting [3, 4]. Notably, an increasing attention is being devoted to the emergent properties of complex systems, with a prominent role in this literature played by partial information decomposition (PID) [5] and its subsequent developments [6], exploiting information-theoretic tools to reveal high-order dependencies among groups of three or more random variables and describe their synergistic or redundant nature [7-11]. Within this framework, redundancy refers to information retrievable from multiple sources, while synergy refers to statistical relationships existing within the whole system that cannot be observed in its individual parts. The approach described in [1], named Hi-Fi (high-order interactions for feature importance), is rooted on a well known metric of feature importance named Leave-One-Out Covariates (LOCO) [12], i.e. the reduction of the prediction error when the feature under consideration is added to the set of all the features used for regression, and proposes an adaptive version of LOCO which provides three scores for each feature: the unique pure standalone (two-body) influence of the feature on the target, and the contributions stemming from synergistic and redundant interactions with other features. It is worth mentioning that the decomposition of feature importance in [1] clearly depends also on the choice of the hypothesis space for regression, hence it should be assumed that a proper model for data has been selected.

It has been dubbed'Britain's most confusing junction', thanks to its complex system of mini–roundabouts. But while many drivers struggle to navigate their way around Swindon's Magic Roundabout, the junction proved to be light work for a self–driving car. To put its Full Self Driving (FSD) mode to the test, Tesla sent a Model 3 through the complex intersection. Footage shows the car expertly navigating the roundabout – not just once, but three times – as cars continuously join from seemingly every direction. Fans have flocked to X to discuss the feat, with one calling it'superb'.