Jonathan Brown

Gurpreet Tandi, Josue Gonzalez-Hendrix, Jonathan Brown

The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic system can describe said conjecture. In this work, we construct explicit Turing machines that search for a solution to Brocard's problem greater than 7 and a Fermat prime beyond the 4th which halt if and only if such a solution exists.

Debdeep Mukherjee, Eduardo Di Santi, Clément Lefebvre et al.

Track circuits are critical for railway operations, acting as the main signalling sub-system to locate trains. Continuous Variable Current Modulation (CVCM) is one such technology. Like any field-deployed, safety-critical asset, it can fail, triggering cascading disruptions. Many failures originate as subtle anomalies that evolve over time, often not visually apparent in monitored signals. Conventional approaches, which rely on clear signal changes, struggle to detect them early. Early identification of failure types is essential to improve maintenance planning, minimising downtime and revenue loss. Leveraging deep neural networks, we propose a predictive maintenance framework that classifies anomalies well before they escalate into failures. Validated on 10 CVCM failure cases across different installations, the method is ISO-17359 compliant and outperforms conventional techniques, achieving 99.31% overall accuracy with detection within 1% of anomaly onset. Through conformal prediction, we provide uncertainty estimates, reaching 99% confidence with consistent coverage across classes. Given CVCMs global deployment, the approach is scalable and adaptable to other track circuits and railway systems, enhancing operational reliability.

Eduardo Di Santi, Ruixiang Ci, Clément Lefebvre et al.

The Point Machine (PM) is a critical piece of railway equipment that switches train routes by diverting tracks through a switchblade. As with any critical safety equipment, a failure will halt operations leading to service disruptions; therefore, pre-emptive maintenance may avoid unnecessary interruptions by detecting anomalies before they become failures. Previous work relies on several inputs and crafting custom features by segmenting the signal. This not only adds additional requirements for data collection and processing, but it is also specific to the PM technology, the installed locations and operational conditions limiting scalability. Based on the available maintenance records, the main failure causes for PM are obstacles, friction, power source issues and misalignment. Those failures affect the energy consumption pattern of PMs, altering the usual (or healthy) shape of the power signal during the PM movement. In contrast to the current state-of-the-art, our method requires only one input. We apply a deep learning model to the power signal pattern to classify if the PM is nominal or associated with any failure type, achieving >99.99\% precision, <0.01\% false positives and negligible false negatives. Our methodology is generic and technology-agnostic, proven to be scalable on several electromechanical PM types deployed in both real-world and test bench environments. Finally, by using conformal prediction the maintainer gets a clear indication of the certainty of the system outputs, adding a confidence layer to operations and making the method compliant with the ISO-17359 standard.