Some seemingly simple sequences of multiplication and addition grow so quickly that they question the very foundations of mathematics. Did you hear the one about the man who invented chess and got himself executed? Legend has it that a man called Sessa, who lived in India long ago, developed the rules for the game and presented them to a king. The king was delighted and offered the man his pick of reward. Sessa asked for a supposedly humble quantity of rice.

One of the most bitterly contested proofs in modern mathematics may be on the verge of being untangled. Two projects, both aiming to use a computer program to cast new light on the controversy, are now up and running - with one having operated in secret for more than two years already. The developments are a positive sign that the row might find a solution, say mathematicians. The saga began in 2012 when Shinichi Mochizuki at Kyoto University, Japan, claimed to have proved a famous idea called the ABC conjecture, posting a 500-page proof online. The conjecture is simple to state, concerning prime numbers involved in solutions to the equation a + b = c and how these numbers relate to each other.

Gödel's seminal work directly contradicted one of the great minds of mathematics and limited the field forever Kurt Gödel, the man who ruined mathematics, was one of the most important thinkers of the 20th century. He was born in 1906, smack-bang in the middle of the greatest crisis that maths has ever known. Just a few decades later, he would help resolve this turmoil, but in doing so doom mathematicians to a smaller world than the one that came before. Mathematics, as an intellectual framework, is incredibly powerful. The entire point is taking one set of logical ideas and using them to build another, making maths the closest thing we have to a cognitive perpetual-motion machine - there is always a new mathematical idea lurking across the horizon, and we just need to assemble the steps to get there.

This paper presents a logic programming-based framework for policy-aware autonomous agents that can reason about potential penalties for non-compliance and act accordingly. While prior work has primarily focused on ensuring compliance, our approach considers scenarios where deviating from policies may be necessary to achieve high-stakes goals. Additionally, modeling non-compliant behavior can assist policymakers by simulating realistic human decision-making. Our framework extends Gelfond and Lobo's Authorization and Obligation Policy Language (AOPL) to incorporate penalties and integrates Answer Set Programming (ASP) for reasoning. Compared to previous approaches, our method ensures well-formed policies, accounts for policy priorities, and enhances explainability by explicitly identifying rule violations and their consequences. Building on the work of Harders and Inclezan, we introduce penalty-based reasoning to distinguish between non-compliant plans, prioritizing those with minimal repercussions. To support this, we develop an automated translation from the extended AOPL into ASP and refine ASP-based planning algorithms to account for incurred penalties. Experiments in two domains demonstrate that our framework generates higher-quality plans that avoid harmful actions while, in some cases, also improving computational efficiency. These findings underscore its potential for enhancing autonomous decision-making and informing policy refinement.

Learning-based planners are sensitive to the long-tailed distribution of driving data. Common maneuvers dominate datasets, while dangerous or rare scenarios are sparse. This imbalance can bias models toward the frequent cases and degrade performance on critical scenarios. To tackle this problem, we compare balancing strategies for sampling training data and find reweighting by trajectory pattern an effective approach. We then present FlowDrive, a flow-matching trajectory planner that learns a conditional rectified flow to map noise directly to trajectory distributions with few flow-matching steps. We further introduce moderated, in-the-loop guidance that injects small perturbation between flow steps to systematically increase trajectory diversity while remaining scene-consistent. On nuPlan and the interaction-focused interPlan benchmarks, FlowDrive achieves state-of-the-art results among learning-based planners and approaches methods with rule-based refinements. After adding moderated guidance and light post-processing (FlowDrive*), it achieves overall state-of-the-art performance across nearly all benchmark splits.

Ensuring safety in autonomous driving requires a seamless integration of perception and decision making under uncertain conditions. Although computer vision (CV) models such as YOLO achieve high accuracy in detecting traffic signs and obstacles, their performance degrades in drift scenarios caused by weather variations or unseen objects. This work presents a simulated autonomous driving system that combines a context aware CV model with adaptive control using the ADORE framework. The CARLA simulator was integrated with ADORE via the ROS bridge, allowing real-time communication between perception, decision, and control modules. A simulated test case was designed in both clear and drift weather conditions to demonstrate the robust detection performance of the perception model while ADORE successfully adapted vehicle behavior to speed limits and obstacles with low response latency. The findings highlight the potential of coupling deep learning-based perception with rule-based adaptive decision making to improve automotive safety critical system.

This paper presents a methodology to process large-scale naturalistic driving studies (NDS) to describe the driving behavior for five vehicle metrics, including speed, speeding, lane keeping, following distance, and headway, contextualized by roadway characteristics, vehicle classes, and driver demographics. Such descriptions of normative driving behaviors can aid in the development of vehicle safety and intelligent transportation systems. The methodology is demonstrated using data from the Second Strategic Highway Research Program (SHRP 2) NDS, which includes over 34 million miles of driving across more than 3,400 drivers. Summaries of each driving metric were generated using vehicle, GPS, and forward radar data. Additionally, interactive online analytics tools were developed to visualize and compare driving behavior across groups through dynamic data selection and grouping. For example, among drivers on 65-mph roads for the SHRP 2 NDS, females aged 16-19 exceeded the speed limit by 7.5 to 15 mph slightly more often than their male counterparts, and younger drivers maintained headways under 1.5 seconds more frequently than older drivers. This work supports better vehicle systems and safer infrastructure by quantifying normative driving behaviors and offers a methodology for analyzing NDS datasets for cross group comparisons.

The main transportation safety regulator in the US is requesting information from Tesla after videos showed the company's self-driving Robotaxis exceeding the speed limit or veering into the wrong lane. The company launched the service in Austin, Texas, over the weekend. Tesla heavily promoted the initial, limited rollout of its Robotaxis, which included pro-Tesla influencers using the paid ride service and showing off footage of their trips. Instead of positive promotion, though, those videos appear to have drawn scrutiny from the National Highway Transit Safety Administration (NHTSA), as the cars struggled to comply with traffic laws. "NHTSA is aware of the referenced incidents and is in contact with the manufacturer to gather additional information," the agency said in a statement.

Machine Learning (ML) models are increasingly integrated into safety-critical systems, such as autonomous vehicle platooning, to enable real-time decision-making. However, their inherent imperfection introduces a new class of failure: reasoning failures often triggered by distributional shifts between operational and training data. Traditional safety assessment methods, which rely on design artefacts or code, are ill-suited for ML components that learn behaviour from data. SafeML was recently proposed to dynamically detect such shifts and assign confidence levels to the reasoning of ML-based components. Building on this, we introduce a probabilistic safety assurance framework that integrates SafeML with Bayesian Networks (BNs) to model ML failures as part of a broader causal safety analysis. This allows for dynamic safety evaluation and system adaptation under uncertainty. We demonstrate the approach on an simulated automotive platooning system with traffic sign recognition.

The Traffic Assignment Problem is a fundamental, yet computationally expensive, task in transportation modeling, especially for large-scale networks. Traditional methods require iterative simulations to reach equilibrium, making real-time or large-scale scenario analysis challenging. In this paper, we propose a learning-based approach using Message-Passing Neural Networks as a metamodel to approximate the equilibrium flow of the Stochastic User Equilibrium assignment. Our model is designed to mimic the algorithmic structure used in conventional traffic simulators allowing it to better capture the underlying process rather than just the data. We benchmark it against other conventional deep learning techniques and evaluate the model's robustness by testing its ability to predict traffic flows on input data outside the domain on which it was trained. This approach offers a promising solution for accelerating out-of-distribution scenario assessments, reducing computational costs in large-scale transportation planning, and enabling real-time decision-making.