Detecting text generated by large language models (LLMs) is of great recent interest.

In this paper, we present a comprehensive study of the performance of average-link in metric spaces, regarding several natural criteria that capture separability and cohesion, and aremore interpretable than Dasgupta'scost function and itsvariants.

Our main result is a matching upper and lower bound for the secretary ranking problem.

In the most general setting, a coreset compresses the data set in such a way that for any set of previously specified candidate queries, the cost of evaluating the query and the cost of the coreset are similar,up to an arbitrarysmalldistortion. A popular subject in coreset literature is the Euclideank-means problem.

Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 8166 Messina, Italy Complex and even chaotic dynamics, though prevalent in many natural and engineered systems, has been largely avoided in the design of electromechanical systems due to concerns about wear and controlability. Here, we demonstrate that complex dynamics might be particularly advantageous in soft robotics, offering new functionalities beyond motion not easily achievable with traditional actuation methods. We designed and realized resilient magnetic soft actuators capable of operating in a tunable dynamic regime for tens of thousands cycles without fatigue. We experimentally demonstrated the application of these actuators for true random number generation and stochastic computing. These findings show that exploring the complex dynamics in soft robotics would extend the application scenarios in soft computing, human-robot interaction and collaborative robots as we demonstrate with biomimetic blinking and randomized voice modulation. A large number of mechanical systems, including simple ones such as the double pendulum, exhibit dynamics characterized by deterministic periodic and chaotic responses depending on the excitation frequency f and amplitude A of the applied force [1]. Mechanical systems with a tendency to chaotisation demonstrate multiple resonances and various transitions to chaos [2]. Today, the concept of complexity and, especially, deterministic chaos that refers to systems without stochastic fluctuations jet losing stability of phase space trajectories is explored for a variety of directions [3] even including biological systems [4] or optics [5]. In particular, chaos is a fundamental aspect of electromechanical systems and is broadly explored in motion planning for mobile rigid robots, fluid mixing, and improving energy harvesting, as well as in mechanisms used in washing machines, dishwashers, and air conditioners [6]. Although the analysis of traditional robotics and mechanisms has revealed inherent chaotic dynamics [7], chaos can also be intentionally generated through nonlinear feedback [6] to achieve specific functionalities. In contrast to rigid mechanisms, soft actuators can facilitate transition into complex dynamics without the need for dedicated feedback algorithms. Mechanically soft actuators do not possess any rigid components in their embodiment rendering them ideally suited to explore complex and even chaotic dynamics which is typically observed at higher frequencies (Supplementary Tables 1 and 2). The inherent nonlinear oscillations emerging in soft actuators for specific parameter values [8, 9] can be applied for secure, biomimetic, and soft computing applications.

Quality-Diversity algorithms have transformed optimization by prioritizing the discovery of diverse, high-performing solutions over a single optimal result. However, traditional Quality-Diversity methods, such as MAP-Elites, rely heavily on predefined behavior descriptors and complete prior knowledge of the task to define the behavior space grid, limiting their flexibility and applicability. In this work, we introduce Vector Quantized-Elites (VQ-Elites), a novel Quality-Diversity algorithm that autonomously constructs a structured behavior space grid using unsupervised learning, eliminating the need for prior task-specific knowledge. At the core of VQ-Elites is the integration of Vector Quantized Variational Autoencoders, which enables the dynamic learning of behavior descriptors and the generation of a structured, rather than unstructured, behavior space grid -- a significant advancement over existing unsupervised Quality-Diversity approaches. This design establishes VQ-Elites as a flexible, robust, and task-agnostic optimization framework. To further enhance the performance of unsupervised Quality-Diversity algorithms, we introduce behavior space bounding and cooperation mechanisms, which significantly improve convergence and performance, as well as the Effective Diversity Ratio and Coverage Diversity Score, two novel metrics that quantify the actual diversity in the unsupervised setting. We validate VQ-Elites on robotic arm pose-reaching, mobile robot space-covering, and MiniGrid exploration tasks. The results demonstrate its ability to efficiently generate diverse, high-quality solutions, emphasizing its adaptability, scalability, robustness to hyperparameters, and potential to extend Quality-Diversity optimization to complex, previously inaccessible domains.