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Christopher Stokes

Publications and source records attributed to Christopher Stokes.

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From Benchmark Performance to Tool Deployment: Human-in-the-Loop Anomaly Detection

Automated anomaly detection methods often report strong performance on curated academic benchmarks, but their behavior under real-world industrial conditions is less clear. In this work, we evaluate 19 unsupervised anomaly detection models on the BowTie dataset, a challenging manufacturing dataset with reflective surfaces, subtle defects, and profile-specific variation. In contrast to benchmark results, we observe that model performance is less stable than typically reported on standard benchmarks such as MVTec AD, highly sensitive to preprocessing, and inconsistent across conditions, with no single approach emerging as uniformly robust; a consensus audit further indicates that nominal-data quality affects deployment. Motivated by these findings, we developed and initially deployed a unified human-in-the-loop framework for manufactured-part inspection that combines image annotation, AI-assisted defect detection, and an integrated validation engine, replacing a prior manual visual inspection and documentation workflow. The system supports heatmap-guided defect review, SAM-refined candidate regions for inspector acceptance, rejection, or boundary adjustment, mask evaluation where annotations exist, and review history for inspector consistency and onboarding. Together, the results highlight the gap between benchmark performance and deployment reality, and provide a practical framework for addressing it.

cs.LG

On Gauss factorials and their connection to the cyclotomic $\lambda$-invariants of imaginary quadratic fields

In this paper we establish a connection between the Gauss factorials and Iwasawa's cyclotomic $\lambda$-invariant for an imaginary quadratic field $K$. As a result, we will explain a corespondance between the 1-exceptional primes of Cosgrave and Dilcher for $m = 3$ and $m = 4$, and the primes for which the $\lambda$-invariants for $K = \mathbb{Q}(\sqrt{-3})$ and $K = \mathbb{Q}(i)$ is greater than one, respectively. We refer to the latter primes as ``non-trivial'' for their respective fields. We will also see that similar correspondences are true for $K = \mathbb{Q}(\sqrt{-d})$ when $d = 2,5$ and $6$. As a corollary we find that primes $p$ of the form $p^2 = 3x^2 + 3x + 1$ are always non-trivial for $K = \mathbb{Q}(\sqrt{-3})$. Last, we show that the non-trivial primes $p$ for $K = \mathbb{Q}(i)$ and $K = \mathbb{Q}(\sqrt{-3})$ are characterized by modulo $p^2$ congruences involving Euler and Glaisher numbers respectively.

math.NT