Persistent entropy (PE) is an information-theoretic summary statistic of persistence barcodes that has been widely used to detect regime changes in complex systems. Despite its empirical success, a general theoretical understanding of when and why persistent entropy reliably detects phase transitions has remained limited, particularly in stochastic and data-driven settings. In this work, we establish a general, model-independent theorem providing sufficient conditions under which persistent entropy provably separates two phases. We show that persistent entropy exhibits an asymptotically non-vanishing gap across phases. The result relies only on continuity of persistent entropy along the convergent diagram sequence, or under mild regularization, and is therefore broadly applicable across data modalities, filtrations, and homological degrees. To connect asymptotic theory with finite-time computations, we introduce an operational framework based on topological stabilization, defining a topological transition time by stabilizing a chosen topological statistic over sliding windows, and a probability-based estimator of critical parameters within a finite observation horizon. We validate the framework on the Kuramoto synchronization transition, the Vicsek order-to-disorder transition in collective motion, and neural network training dynamics across multiple datasets and architectures. Across all experiments, stabilization of persistent entropy and collapse of variability across realizations provide robust numerical signatures consistent with the theoretical mechanism.

Multi-agent systems often operate under feedback, adaptation, and non-stationarity, yet many simulation studies retain static decision rules and fixed control parameters. This paper introduces a general adaptive multi-agent learning framework that integrates: (i) four dynamic regimes distinguishing static versus adaptive agents and fixed versus adaptive system parameters; (ii) information-theoretic diagnostics (entropy rate, statistical complexity, and predictive information) to assess predictability and structure; (iii) structural causal models for explicit intervention semantics; (iv) procedures for generating agent-level priors from aggregate or sample data; and (v) unsupervised methods for identifying emergent behavioral regimes. The framework offers a domain-neutral architecture for analyzing how learning agents and adaptive controls jointly shape system trajectories, enabling systematic comparison of stability, performance, and interpretability across non-equilibrium, oscillatory, or drifting dynamics. Mathematical definitions, computational operators, and an experimental design template are provided, yielding a structured methodology for developing explainable and contestable multi-agent decision processes.

The neural generation and control of speech utterances is a complex process that is still not fully understood. However, several neurobiologically inspired models have been proposed that describe the hierarchical control concept of utterance generation (e.g., Hickok and Poeppel (2012); Bohland et al. (2010); Kröger et al. (2020); Parrell et al. (2018)). This process begins with the neural activation of the cognitive-linguistic representation of an utterance, followed by a higher-level premotor representation, leading to neuromuscular activation patterns, and finally to the articulatory-acoustic realization of the utterance (cf.

Abstract-- Controller performance in quadrotor trajectory tracking depends heavily on parameter tuning, yet standard approaches often rely on fixed, manually tuned parameters that sacrifice task-specific performance. We present Trajectory-A ware Controller Optimization (T ACO), a framework that adapts controller parameters online based on the upcoming reference trajectory and current quadrotor state. T ACO employs a learned predictive model and a lightweight optimization scheme to optimize controller gains in real time with respect to a broad class of trajectories, and can also be used to adapt trajectories to improve dynamic feasibility while respecting smoothness constraints. T o enable large-scale training, we also introduce a parallelized quadrotor simulator supporting fast data collection on diverse trajectories. Experiments on a variety of trajectory types show that T ACO outperforms conventional, static parameter tuning while operating orders of magnitude faster than black-box optimization baselines, enabling practical real-time deployment on a physical quadrotor . Furthermore, we show that adapting trajectories using T ACO significantly reduces the tracking error obtained by the quadrotor .

Robotic performance emerges from the coupling of body and controller, yet it remains unclear when morphology-control co-design is necessary. We present a unified framework that embeds morphology and control parameters within a single neural network, enabling end-to-end joint optimization. Through case studies in static-obstacle-constrained reaching, we evaluate trajectory error, success rate, and collision probability. The results show that co-design provides clear benefits when morphology is poorly matched to the task, such as near obstacles or workspace boundaries, where structural adaptation simplifies control. Conversely, when the baseline morphology already affords sufficient capability, control-only optimization often matches or exceeds co-design. By clarifying when control is enough and when it is not, this work advances the understanding of embodied intelligence and offers practical guidance for embodiment-aware robot design.

A monoped's jump height and energy consumption depend on both, its mechanical design and control strategy. Existing co-design frameworks typically optimize for either maximum height or minimum energy, neglecting their trade-off. They also often omit gearbox parameter optimization and use oversimplified actuator mass models, producing designs difficult to replicate in practice. In this work, we introduce a novel three-stage co-design optimization framework that jointly maximizes jump height while minimizing mechanical energy consumption of a monoped. The proposed method explicitly incorporates realistic actuator mass models and optimizes mechanical design (including gearbox) and control parameters within a unified framework. The resulting design outputs are then used to automatically generate a parameterized CAD model suitable for direct fabrication, significantly reducing manual design iterations. Our experimental evaluations demonstrate a 50 percent reduction in mechanical energy consumption compared to the baseline design, while achieving a jump height of 0.8m. Video presentation is available at http://y2u.be/XW8IFRCcPgM

Regarding "plots are noisy and don't really support well the claim that the algorithm recovers the true Check the sharp jump in Figure 2 which is expected based on Theorem 3. Similarly, Figure 3 shows that Markov blanket can be recovered with sufficient number of observational data. NP-hard [Chickering, 1996, Learning Bayesian Networks Is NP-Complete]. Rank-2 is only used for clarity. Reviewer 2 has asked to present a case where Assumption 4 is violated. Assume that every variable can take 4 values.

In automated planning, control parameters extend standard action representations through the introduction of continuous numeric decision variables. Existing state-of-the-art approaches have primarily handled control parameters as embedded constraints alongside other temporal and numeric restrictions, and thus have implicitly treated them as additional constraints rather than as decision points in the search space. In this paper, we propose an efficient alternative that explicitly handles control parameters as true decision points within a systematic search scheme. We develop a best-first, heuristic search algorithm that operates over infinite decision spaces defined by control parameters and prove a notion of completeness in the limit under certain conditions. Our algorithm leverages the concept of delayed partial expansion, where a state is not fully expanded but instead incrementally expands a subset of its successors. Our results demonstrate that this novel search algorithm is a competitive alternative to existing approaches for solving planning problems involving control parameters.