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Large language models (LLMs) have achieved impressive performance but face high computational costs and latency, limiting their deployment in resource-constrained settings. In contrast, small-scale LLMs (SLMs) are more efficient yet struggle to capture evolving real-world knowledge. Retrieval-augmented generation (RAG) helps by integrating external knowledge, but imperfect retrieval can introduce distracting noise that misleads SLMs. We propose {\name}, a robust RAG framework for SLMs via Margin-aware Preference Optimization. {\name} employs multi-turn prompting for detailed reasoning, rejection sampling for high-quality explanations, and contrastive preference selection to refine responses by maximizing the likelihood gap between preferred and non-preferred outputs. 

Inclusive electron scattering cross sections off a hydrogen target at a beam energy of 10.6 GeV have been measured with data collected from the CLAS12 spectrometer at Jefferson Laboratory. These first absolute cross sections from CLAS12 cover a wide kinematic area in invariant mass $W$of the final state hadrons from the pion threshold up to 2.5 GeV for each bin in virtual photon four-momentum transfer squared $Q^2$from 2.55 to $10.4{\mathrm{GeV}}^2$owing to the large scattering angle acceptance of the CLAS12 detector. Comparison of the cross sections with the resonant contributions computed from the CLAS results on the nucleon resonance electroexcitation amplitudes has demonstrated a promising opportunity to extend the information on their $Q^2$evolution up to 10 ${\mathrm{GeV}}^2$. Together these results from CLAS and CLAS12 offer good prospects for probing the nucleon parton distributions at large fractional parton momenta $x$for $W<2.5$GeV, while covering the range of distances where the transition from the strongly coupled to the perturbative regimes is expected. 

The relationships between crop yields and meteorology are naturally non-stationary because of spatiotemporal heterogeneity. Many studies have examined spatial heterogeneity in the regression model, but only limited research has attempted to account for both spatial autocorrelation and temporal variation. In this article, we develop a novel spatiotemporally varying coefficient (STVC) model to understand non-stationary relationships between crop yields and meteorological variables. We compare the proposed model with variant models specialized for time or spatial, namely spatial varying coefficient (SVC) model and temporal varying coefficient (TVC) model. This study was conducted using the county-level corn yield and meteorological data, including seasonal Growing Degree Days (GDD), Killing Degree Days (KDD), Vapor Pressure Deficit (VPD), and precipitation (PCPN), from 1981 to 2018 in three Corn Belt states, including Illinois, Indiana, and Iowa. Allowing model coefficients varying in both temporal and spatial dimensions gives the best performance of STVC in simulating the corn yield responses toward various meteorological conditions. The STVC reduced the root-mean-square error to 10.64 Bu/Ac (0.72 Mg/ha) from 15.68 Bu/Ac (1.06 Mg/ha) for TVC and 16.48 Bu/Ac (1.11 Mg/ha) for SVC. Meanwhile, the STVC resulted in a higher R2 of 0.81 compared to 0.56 for SVC and 0.64 for TVC. The STVC showed better performance in handling spatial dependence of corn production, which tends to cluster estimation residuals when counties are close, with the lowest Moran’s I of 0.10. Considering the spatiotemporal non-stationarity, the proposed model significantly improves the power of the meteorological data in explaining the variations of corn yields. 

We establish the consistency of K-medoids in the context of metric spaces. We start by proving that K-medoids is asymptotically equivalent to K-means restricted to the support of the underlying distribution under general conditions, including a wide selection of loss functions. This asymptotic equivalence, in turn, enables us to apply the work of Pärna (1986) on the consistency of K-means. This general approach applies also to non-metric settings where only an ordering of the dissimilarities is available. We consider two types of ordinal information: one where all quadruple comparisons are available; and one where only triple comparisons are available. We provide some numerical experiments to illustrate our theory.