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I introduce the Twin prime detector formula D(p), a closed-form expression involving ratios of Gamma function products that evaluates to 1 if and only if (p,p+2) is a twin prime pair. By applying the Gauss Multiplication Formula to simplify the MAF to 〖(2π)〗^((p+2 -(σ(p)+σ(p+2))/2)), I establish an exact equivalence between the twin prime condition and the vanishing of an arithmetic exponent involving the sum-of-divisors function σ. Building on this characterisation, I construct a GMF-weighted Dirichlet series L(s) whose […]

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Background: Knee osteoarthritis (OA) frequently exhibits discordance between structural damage observed in imaging and patient-reported symptoms such as pain. This mismatch complicates clinical interpretation and patient stratification and remains insufficiently modeled in existing decision-support systems. Methods: We propose a discordance-aware multimodal framework that combines machine learning prediction models with a tool-grounded multi-agent reasoning system. Using baseline data from the FNIH Osteoarthritis Biomarkers Consortium (600 knees), we trained multimodal models to predict two progression tasks: (i) joint-space-loss-only progression versus […]

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The health status of rolling bearings is critical to the normal operation of rotating machinery. To effectively extract vibration signal features and accurately identify different fault types, a novel method based on enhanced composite multi-scale slope entropy (ECMSE) and a honey badger algorithm-optimized kernel extreme learning machine (HBA-KELM) is proposed. Specifically, ECMSE integrates high-order differences into the composite multi-scale framework to capture high-frequency information while preserving low-frequency characteristics, thereby enhancing the discriminability of time-series representations. Meanwhile, an average […]

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As large language model agents advance beyond software engineering (SWE) tasks toward machine learning engineering (MLE), verifying agent behavior becomes orders of magnitude more expensive: while SWE tasks can be verified via fast-executing unit tests, MLE verification requires running full ML pipelines — data preprocessing, model training, and metric evaluation — on large datasets at each rollout step, rendering trajectory-wise on-policy reinforcement learning (RL) prohibitively slow. Existing approaches retreat to supervised fine-tuning (SFT) or offline proxy rewards, sacrificing […]

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Large Language Models (LLMs) have shown strong performance across a wide range of natural language processing tasks; however, their effectiveness is highly dependent on prompt design, structure, and embedded reasoning signals. Conventional prompt engineering methods largely rely on heuristic trial-and-error processes, which limits scalability, reproducibility, and generalization across tasks. DSPy, a declarative framework for optimizing text-processing pipelines, offers an alternative approach by enabling automated, modular, and learnable prompt construction for LLM-based systems.This paper presents a systematic study of […]

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Tabular foundation models (TFMs) such as TabPFN (Tabular Prior-Data Fitted Network) are designed to generalize across heterogeneous tabular datasets through in-context learning (ICL). They perform prediction in a single forward pass conditioned on labeled examples without dataset-specific parameter updates. This paradigm is particularly attractive in industrial domains (e.g., finance and healthcare) where tabular prediction is pervasive. Retraining a bespoke model for each new table can be costly or infeasible in these settings, while data quality issues such as […]

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Tabular foundation models (TFMs) such as TabPFN (Tabular Prior-Data Fitted Network) are designed to generalize across heterogeneous tabular datasets through in-context learning (ICL). They perform prediction in a single forward pass conditioned on labeled examples without dataset-specific parameter updates. This paradigm is particularly attractive in industrial domains (e.g., finance and healthcare) where tabular prediction is pervasive. Retraining a bespoke model for each new table can be costly or infeasible in these settings, while data quality issues such as […]

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Objective: Algorithmic fairness is essential for equitable and trustworthy machine learning in healthcare. Most fairness tools emphasize single-axis demographic comparisons and may miss compounded disparities affecting intersectional populations. This study introduces Fairlogue, a toolkit designed to operationalize intersectional fairness assessment in observational and counterfactual contexts within clinical settings. Methods: Fairlogue is a Python-based toolkit composed of three components: 1) an observational framework extending demographic parity, equalized odds, and equal opportunity difference to intersectional populations; 2) a counterfactual framework […]

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Training interpretable concept-based policies requires practitioners to manually select which human-understandable concepts an agent should reason with when making sequential decisions. This selection demands domain expertise, is time-consuming and costly, scales poorly with the number of candidates, and provides no performance guarantees. To overcome this limitation, we propose the first algorithms for principled automatic concept selection in sequential decision-making. Our key insight is that concept selection can be viewed through the lens of state abstraction: intuitively, a concept […]

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