Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing

We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A unified framework is established for the continuous dependence estimates, fractional BV regularity estimates, and well-posedness for stochastic entropy solutions of the nonlinear stochastic degenerate parabolic-hyperbolic equation. In particular, we establish the well-posedness of the nonlinear stochastic equation in $L^p \cap N^{\kappa,1}$ for $p\in (1,\infty)$ and the $\kappa$--Nikolskii space $N^{\kappa,1}$ with $\kappa>0$, and the $L^1$ continuous dependence of the stochastic entropy solutions not only on the initial data, but also on the degenerate diffusion matrix function, the flux function, and the multiplicative noise function involving in the nonlinear equation.Comment: 30 page

Guideline Learning for In-context Information Extraction

Large language models (LLMs) can perform a new task by merely conditioning on task instructions and a few input-output examples, without optimizing any parameters. This is called In-Context Learning (ICL). In-context Information Extraction (IE) has recently garnered attention in the research community. However, the performance of In-context IE generally lags behind the state-of-the-art supervised expert models. We highlight a key reason for this shortfall: underspecified task description. The limited-length context struggles to thoroughly express the intricate IE task instructions and various edge cases, leading to misalignment in task comprehension with humans. In this paper, we propose a Guideline Learning (GL) framework for In-context IE which reflectively learns and follows guidelines. During the learning phrase, GL automatically synthesizes a set of guidelines based on a few error cases, and during inference, GL retrieves helpful guidelines for better ICL. Moreover, we propose a self-consistency-based active learning method to enhance the efficiency of GL. Experiments on event extraction and relation extraction show that GL can significantly improve the performance of in-context IE.Comment: EMNLP 2023 main conferenc

Anhuienoside C ameliorates atherosclerosis in rats via regulation of the NFκB/eNOS/NO signaling pathway

Purpose: To investigate the protective effect of anhuienoside C (AC) against high cholesterol dietinduced atherosclerosis in a rat model. Methods: Atherosclerosis was induced in rats by administration of high fat diet for 8 weeks, and AC (20 and 40 mg/kg) was administered orally. The effect of AC was determined by assessing serum lipid profiles and mediators of inflammation, as well as oxidative stress parameters in aortic tissue using enzyme-linked immunosorbent assay (ELISA). Western blot assay and reverse transcription polymerase chain reaction (RT-PCR) were used for the evaluation of protein expressions. Results: Serum levels of total cholesterol (TC), triglycerides (TGs), high density lipoprotein (HDL), low density lipoprotein (LDLP), and IL-1β, IL-18, TNF-α and NF-κB were significantly reduced in AC-treated group, relative to atherosclerotic rats (p < 0.01). Moreover, parameters of oxidative stress were attenuated in the aortic tissues of AC-treated group, when compared with atherosclerotic rats. There was significant increase in eNOS expression, and marked decrease in the expressions of MAPK and NF-kB protein in the aortic tissue homogenate of AC treated group, relative to atherosclerotic group (p <0.01). Treatment with AC attenuated the mRNA expressions of ICAM-1, VCAM-1 and MCP-1 in aortic tissue of the atherosclerotic rats. Conclusion: These results reveal that AC prevents atherosclerosis in rats by modulating the NFκB/eNOS/NO signaling pathway, and thus, can thus potentially be developed as anti-atherosclerotic agent. Keywords: Anhuienoside C, Atherosclerosis, Inflammation, Oxidative stress, Cholestero