This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz equation. By utilizing a weak Laplacian operator defined on a space of discontinuous functions, the proposed framework facilitates the seamless treatment of complex boundary conditions and internal interfaces. We emphasize the geometric flexibility of the LS-WG scheme on general polygonal and polyhedral partitions. Furthermore, we prove the uniqueness of the numerical solution and derive optimal-order error estimates with respect to a specifically designed discrete energy norm. Extensive numerical experiments validate the theoretical convergence rates and demonstrate the algorithm's robustness and efficiency over traditional Galerkin approaches.
Retrieval-Augmented Generation enhances large language models by incorporating external knowledge, but deploying it in sensitive scenarios risks privacy leakage via malicious prompts. To address this, we propose a multi-agent framework that sanitizes retrieved content through semantic rewriting. By employing three specialized agents for privacy extraction, semantic analysis, and reconstruction, our approach collaboratively removes sensitive identifiers while preserving the semantic core. We evaluate the framework on the ChatDoctor and Wiki-PII datasets across six large language models. Experimental results demonstrate a significant reduction in privacy leakage under targeted attacks. For instance, we reduced targeted information exposure in LLaMA-3-8B from 144 instances in the baseline to just 1. Furthermore, we maintain strong contextual fidelity with a BLEU-1 score of 0.122, outperforming the existing SAGE method's 0.117. Finally, the framework operates as an asynchronous preprocessing module, introducing no additional latency to online inference, as all rewriting is executed as a one-time offline preprocessing step. To promote reproducibility, the source code of this work is publicly available at https://github.com/foursoils/Privacy-Preserving-RAG.
Personal network size is a versatile and fundamental structural network measure, capturing the total number of personal connections or specific subgroups within an individual’s social environment. In standard sociological methods, such as surveys, personal network size is often indirectly inferred from name generators, which are used to list alters from the respondents’ personal networks. Implicitly, a higher count of named alters is assumed to indicate a larger personal network. We explicitly test this common assumptionand address this imprecise association between network size and number of listed alters by comparing the results from two very distinct approaches to measuring personal network size: alter counts derived from name generators and size estimates obtained from the network scale-up method (NSUM). Using survey data from over 300 participants in Spain, we compute these two independent network measures for the same respondents and assess the strength, significance and robustness of their association, including potential question-order effects on personal network size. Our analyses conclude that the alter counts from name generators primarily reflect participants’ response behaviour and task constraints rather than the underlying personal network size. Finally, our findings highlight critical limitations in the use of free name generators as proxies for personal network size.
Pineapple (Ananas comosus L.) is classified as a nonclimacteric tropical fruit that exhibits significant internal browning (IB), which severely affects its postharvest quality. In this study, we identified the transcription factor AcWRKY65 as a key regulator of IB susceptibility. Molecular characterization revealed that nuclear-localized AcWRKY65 functions as a transcriptional activator, directly binding to the promoters of browning-linked genes (laccase, AcLAC; polyphenol oxidase, AcPPO; citrate synthase, AcCS; and abscisic acid receptor, AcPYL5) and thereby enhancing their expression. Overexpression of AcWRKY65 enhanced pineapple tissue disc and callus browning, while heterologous overexpression in tomato fruit accelerated ripening processes. These results elucidate the role of AcWRKY65 in co-regulating enzymatic browning processes and oxidative stress response pathways, offering critical insights into the molecular mechanisms underlying IB and proposing AcWRKY65 as a promising molecular target to improve postharvest pineapple quality.
We examine the potential of ChatGPT and other large language models in predicting stock market returns using news headlines. We use ChatGPT to assess whether each headline is good, bad, or neutral for firms' stock prices. We document a significantly positive correlation between ChatGPT scores and subsequent daily stock returns. We find that ChatGPT outperforms traditional sentiment analysis methods. More basic models such as GPT-1, GPT-2, and BERT cannot accurately forecast returns, indicating return predictability is an emerging capacity of complex language models. Long-short strategies based on ChatGPT-4 deliver the highest Sharpe ratio. Furthermore, we find predictability in both small and large stocks, suggesting market underreaction to company news. Predictability is stronger among smaller stocks and stocks with bad news, consistent with limits-to-arbitrage also playing an important role. Finally, we propose a new method to evaluate and understand the models' reasoning capabilities. Overall, our results suggest that incorporating advanced language models into the investment decision-making process can yield more accurate predictions and enhance the performance of quantitative trading strategies.
