Rather,theyare generated by latent variables, such as confounders and mediators, which may themselvesbecausallyrelated.

Aircraft collision avoidance systems is critical to modern aviation. These systems are designed to predict potential collisions between aircraft and recommend appropriate avoidance actions. Creating effective collision avoidance systems requires solutions to a variety of technical challenges related to surveillance, decision making, and validation. These challenges have sparked significant research and development efforts over the past several decades that have resulted in a variety of proposed solutions. This article provides an overview of these challenges and solutions with an emphasis on those that have been put through a rigorous validation process and accepted by regulatory bodies. The challenges posed by the collision avoidance problem are often present in other domains, and aircraft collision avoidance systems can serve as case studies that provide valuable insights for a wide range of safety-critical systems.

Stellarators are inherently steady-state plasma confinement devices, which is among the key reasons behind their renaissance as promising candidates for fusion power plants. Ideal MHD equilibria are a central part in optimising the complex, three-dimensional plasma shapes which are a necessary condition for steady-state operation of such devices. The equilibrium magnetic field is required not only in optimisation but also plays a role in future real-time control algorithms and simulation frameworks (Schissel et al. 2025). Solving the three-dimensional MHD equations requires numerical approaches, because no analytical solutions throughout the full volume of ideal MHD equilibria with nested magnetic topology exists yet (Bruno & Laurence 1996). Recent work advanced analytical models for Fourier components of the equilibrium magnetic field in a subset of reactor-relevant magnetic fields and analytical expansions close to the magnetic axis are used extensively in research (Nikulsin et al. 2024; Sengupta et al. 2024). These analytical solutions and the following numerical solvers assume nested magnetic topology, or inte-grability throughout the volume, and computation of chaotic regions or magnetic islands takes considerably more effort (Hudson et al. 2012). Accuracy of numerical PDE solutions is inherently connected to the representation which defines gradients, and commonly used ideal MHD equilibrium solvers with nested magnetic field topology can be differentiated accordingly: A widely used finite-difference solver employed in the design of currently operating stellarator devices is VMEC (Hirshman & Whitson 1983), another pseudo spectral solver is DESC (Dudt & Kolemen 2020) and a third example is GVEC (Hindenlang et al. 2025), that abstracts the notion of basis functions, which enabled computation of plasmas with figure-8 shape (Plunk et al. 2025). Email address for correspondence: timo.thun@ipp.mpg.de

Algorithm 1: The proposed Persistence Interaction Detection (PID) algorithmInput: A trained feed-forward neural network, target layer l, norm p. Output: ranked list of interaction candidates {I Our PID framework is presented in Algorithm 1. PID in all experiments of this paper (i.e., set η as 0). In this subsection, we will prove Theorem 1 and evaluate it empirically. We have the following corollary: Corollary 1. |b Combining them together finishes the proof. It is trivial to show that Corollary 1 can be extended to the death time, i.e., we also have After proving Corollary 1, we return to prove the theorem. In this section, first, we show how to extend PID to CNNs.

Recovering the past from present observations is an intriguing challenge with potential applications in forensics and scene analysis. Thermal imaging, operating in the infrared range, provides access to otherwise invisible information. Since humans are typically warmer (37 C -98.6 F) than their surroundings, interactions such as sitting, touching, or leaning leave residual heat traces. These fading imprints serve as passive temporal codes, allowing for the inference of recent events that exceed the capabilities of RGB cameras. This work proposes a time-reversed reconstruction framework that uses paired RGB and thermal images to recover scene states from a few seconds earlier. The proposed approach couples Visual-Language Models (VLMs) with a constrained diffusion process, where one VLM generates scene descriptions and another guides image reconstruction, ensuring semantic and structural consistency. The method is evaluated in three controlled scenarios, demonstrating the feasibility of reconstructing plausible past frames up to 120 seconds earlier, providing a first step toward time-reversed imaging from thermal traces.

In this study, we focus on the automatic evaluation of long and detailed image captions generated by multimodal Large Language Models (MLLMs). Most existing automatic evaluation metrics for image captioning are primarily designed for short captions and are not suitable for evaluating long captions. Moreover, recent LLM-as-a-Judge approaches suffer from slow inference due to their reliance on autoregressive inference and early fusion of visual information. To address these limitations, we propose VELA, an automatic evaluation metric for long captions developed within a novel LLM-Hybrid-as-a-Judge framework. Furthermore, we propose LongCap-Arena, a benchmark specifically designed for evaluating metrics for long captions. This benchmark comprises 7,805 images, the corresponding human-provided long reference captions and long candidate captions, and 32,246 human judgments from three distinct perspectives: Descriptiveness, Relevance, and Fluency. We demonstrated that VELA outperformed existing metrics and achieved superhuman performance on LongCap-Arena.

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.

As large language models (LLMs) become increasingly embedded in products used by millions, their outputs may influence individual beliefs and, cumulatively, shape public opinion. If the behavior of LLMs can be intentionally steered toward specific ideological positions, such as political or religious views, then those who control these systems could gain disproportionate influence over public discourse. Although it remains an open question whether LLMs can reliably be guided toward coherent ideological stances and whether such steering can be effectively prevented, a crucial first step is to develop methods for detecting when such steering attempts occur. In this work, we adapt a previously proposed statistical method to the new context of ideological bias auditing. Our approach carries over the model-agnostic design of the original framework, which does not require access to the internals of the language model. Instead, it identifies potential ideological steering by analyzing distributional shifts in model outputs across prompts that are thematically related to a chosen topic. This design makes the method particularly suitable for auditing proprietary black-box systems. We validate our approach through a series of experiments, demonstrating its practical applicability and its potential to support independent post hoc audits of LLM behavior.

High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of large-scale benchmarks, existing LLM-generated datasets often suffer from limited reliability, diversity, and scalability. To address these challenges, we introduce PuzzleClone, a formal framework for synthesizing verifiable data at scale using Satisfiability Modulo Theories (SMT). Our approach features three key innovations: (1) encoding seed puzzles into structured logical specifications, (2) generating scalable variants through systematic variable and constraint randomization, and (3) ensuring validity via a reproduction mechanism. Applying PuzzleClone, we construct a curated benchmark comprising over 83K diverse and programmatically validated puzzles. The generated puzzles span a wide spectrum of difficulty and formats, posing significant challenges to current state-of-the-art models. We conduct post training (SFT and RL) on PuzzleClone datasets. Experimental results show that training on PuzzleClone yields substantial improvements not only on PuzzleClone testset but also on logic and mathematical benchmarks. Post training raises PuzzleClone average from 14.4 to 56.2 and delivers consistent improvements across 7 logic and mathematical benchmarks up to 12.5 absolute percentage points (AMC2023 from 52.5 to 65.0). Our code and data are available at https://github.com/HiThink-Research/PuzzleClone.