arXiv subjects

Jonathan Brown

Publications and source records attributed to Jonathan Brown.

14 recordsLinked to original sources

arXiv2026

Measuring Decidability as Related to Busy Beaver Numbers

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.

cs.CC↗

arXiv2025

CVCM Track Circuits Pre-emptive Failure Diagnostics for Predictive Maintenance Using Deep Neural Networks

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.

cs.AI↗

arXiv2025

Scalable, Technology-Agnostic Diagnosis and Predictive Maintenance for Point Machine using Deep Learning

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.

eess.SP↗

arXiv2019

Graded C-algebras and twisted groupoid C-algebras

Let $C^*$-algebra that is acted upon by a compact abelian group. We show that if the fixed-point algebra of the action contains a Cartan subalgebra $D$ satisfying an appropriate regularity condition, then $A$ is the reduced $C^*$-algebra of a groupoid twist. We further show that the embedding $D \hookrightarrow A$ is uniquely determined by the twist. These results generalize Renault's results on Cartan subalgebras of $C^*$-algebras.

math.OA↗

arXiv2019

A controlled study of virtual reality in first-year magnetostatics

Stereoscopic virtual reality (VR) has experienced a resurgence due to flagship products such as the Oculus Rift, HTC Vive and smartphone-based VR solutions like Google Cardboard. This is causing the question to resurface: how can stereoscopic VR be useful in instruction, if at all, and what are the pedagogical best practices for its use? To address this, and to continue our work in this sphere, we performed a study of 289 introductory physics students who were sorted into three different treatment types: stereoscopic virtual reality, WebGL simulation, and static 2D images, each designed to provide information about magnetic fields and forces. Students were assessed using preliminary items designed to focus on heavily-3D systems. We report on assessment reliability, and on student performance. Overall, we find that students who used VR did not significantly outperform students using other treatment types. There were significant differences between sexes, as other studies have noted. Dependence on students' self-reported 3D videogame play was observed, in keeping with previous studies, but this dependence was not restricted to the VR treatment.

physics.ed-ph↗

arXiv2017

On the variety of 1-dimensional representations of finite $W$-algebras in low rank

Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$ and let $e \in \mathfrak g$ be nilpotent. We consider the finite $W$-algebra $U(\mathfrak g,e)$ associated to $e$ and the problem of determining the variety $\mathcal E(\mathfrak g,e)$ of 1-dimensional representations of $U(\mathfrak g,e)$. For $\mathfrak g$ of low rank, we report on computer calculations that have been used to determine the structure of $\mathcal E(\mathfrak g,e)$, and the action of the component group $\Gamma_e$ of the centralizer of $e$ on $\mathcal E(\mathfrak g,e)$. As a consequence, we provide two examples where the nilpotent orbit of $e$ is induced, but there is a 1-dimensional $\Gamma_e$-stable $U(\mathfrak g,e)$-module which is not induced via Losev's parabolic induction functor. In turn this gives examples where there is a "non-induced" multiplicity free primitive ideal of $U(\mathfrak g)$.

math.RT↗

arXiv2016

Cartan Subalgebras of Topological Graph Algebras and k-Graph C*-algebras

In this paper, two sufficient and necessary conditions are given. The first one characterizes when the boundary path groupoid of a topological graph without singular vertices has closed interior of its isotropy group bundle, and the second one characterizes when the path groupoid of a row-finite k-graph without sources has closed interior of its isotropy group bundle. It follows that the associated topological graph algebra and the associated k-graph C*-algebra have Cartan subalgebras due to a result of Brown-Nagy-Reznikoff-Sims-Williams.

math.OA↗

arXiv2014

Purely infinite $C^*$-algebras associated to \'etale groupoids

Let $G$ be a Hausdorff, \'etale groupoid that is minimal and topologically principal. We show that $C^*_r(G)$ is purely infinite simple if and only if all the nonzero positive elements of $C_0(G^0)$ are infinite in $C_r^*(G)$. If $G$ is a Hausdorff, ample groupoid, then we show that $C^*_r(G)$ is purely infinite simple if and only if every nonzero projection in $C_0(G^0)$ is infinite in $C^*_r(G)$. We then show how this result applies to $k$-graph $C^*$-algebras. Finally, we investigate strongly purely infinite groupoid $C^*$-algebras.

math.OA↗

arXiv2013

The Rokhlin property for endomorphisms and strongly self-absorbing C*-algebras

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing C*-algebra, and use this result to deduce that the same result holds for crossed products by endomorphisms in the sense of Stacey. This generalizes earlier results of the second named author and W. Winter.

math.OA↗

arXiv2012

Representation theory of type B and C standard Levi W-algebras

We classify the finite dimensional irreducible representations with integral central character of finite $W$-algebras $U(\mathfrak g,e)$ associated to standard Levi nilpotent orbits in classical Lie algebras of types B and C. This classification is given explicitly in terms of the highest weight theory for finite $W$-algebras.

math.RT↗

arXiv2012

Principal W-algebras for GL(m|n)

We consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb C)$. Our main result gives an explicit description of $W_{m|n}$ as a certain truncation of a shifted version of the Yangian $Y(\mathfrak{gl}_{1|1})$. We also show that $W_{m|n}$ admits a triangular decomposition and construct its irreducible representations.

math.RT↗

arXiv2010

Representation theory of rectangular finite $W$-algebras

We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is a nilpotent element with Jordan blocks all the same size.

math.RT↗

arXiv2008

Twisted Yangians and finite W-algebras

We construct an explicit set of generators for the finite W-algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such finite W-algebras are quotients of twisted Yangians.

math.QA↗

arXiv2006

Elementary invariants for centralizers of nilpotent matrices

We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the Lie algebra gl_N(C). In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova (math.RT/0610049).

math.RA↗