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In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while the other part of the boundary is subject to a Dirichlet boundary condition. We show that, as the crescent-shaped area collapses into a segment under suitable conditions, the boundary value problem obeys uniform Schauder estimates and induces an asymptotic estimate.

In recent years, the United States has witnessed a significant surge in the popularity of vaping or e-cigarette use, leading to a notable rise in cases of e-cigarette and vaping use-associated lung injury (EVALI) that caused hospitalizations and fatalities during the EVALI outbreak in 2019, highlighting the urgency to comprehend vaping behaviors and develop effective strategies for cessation. Due to the ubiquity of social media platforms, over 4.7 billion users worldwide use them for connectivity, communications, news, and entertainment with a significant portion of the discourse related to health, thereby establishing social media data as an invaluable organic data resource for public health research. In this study, we extracted a sample dataset from one vaping sub-community on Reddit to analyze users' quit-vaping intentions. Leveraging OpenAI's latest large language model GPT-4 for sentence-level quit vaping intention detection, this study compares the outcomes of this model against layman and clinical expert annotations. Using different prompting strategies such as zero-shot, one-shot, few-shot and chain-of-thought prompting, we developed 8 prompts with varying levels of detail to explain the task to GPT-4 and also evaluated the performance of the strategies against each other. These preliminary findings emphasize the potential of GPT-4 in social media data analysis, especially in identifying users' subtle intentions that may elude human detection., Comment: Accepted for the AI Applications in Public Health and Social Services workshop at the 22nd International Conference on Artificial Intelligence in Medicine (AIME 2024)

The widespread adoption of social media platforms globally not only enhances users' connectivity and communication but also emerges as a vital channel for the dissemination of health-related information, thereby establishing social media data as an invaluable organic data resource for public health research. The surge in popularity of vaping or e-cigarette use in the United States and other countries has caused an outbreak of e-cigarette and vaping use-associated lung injury (EVALI), leading to hospitalizations and fatalities in 2019, highlighting the urgency to comprehend vaping behaviors and develop effective strategies for cession. In this study, we extracted a sample dataset from one vaping sub-community on Reddit to analyze users' quit vaping intentions. Leveraging large language models including both the latest GPT-4 and traditional BERT-based language models for sentence-level quit-vaping intention prediction tasks, this study compares the outcomes of these models against human annotations. Notably, when compared to human evaluators, GPT-4 model demonstrates superior consistency in adhering to annotation guidelines and processes, showcasing advanced capabilities to detect nuanced user quit-vaping intentions that human evaluators might overlook. These preliminary findings emphasize the potential of GPT-4 in enhancing the accuracy and reliability of social media data analysis, especially in identifying subtle users' intentions that may elude human detection.

In this paper, we prove some supercongruences concerning truncated hypergeometric series. For example, we show that for any prime $p>3$ and positive integer $r$, $$ \sum_{k=0}^{p^r-1}(3k+1)\frac{(\frac12)_k^3}{(1)_k^3}4^k\equiv p^r+\frac76p^{r+3}B_{p-3}\pmod{p^{r+4}} $$ and $$ \sum_{k=0}^{(p^r-1)/2}(4k+1)\frac{(\frac12)_k^4}{(1)_k^4}\equiv p^r+\frac76p^{r+3}B_{p-3}\pmod{p^{r+4}}, $$ where $(x)_k=x(x+1)\cdots(x+k-1)$ is the Pochhammer symbol and $B_0,B_1,B_2,\ldots$ are Bernoulli numbers. These two congruences confirm conjectures of Sun [Sci. China Math. 54 (2011), 2509--2535] and Guo [Adv. Appl. Math. 120 (2020), Art. 102078], respectively., Comment: 18 pages. This is a preliminary version