Cohomology classes, periods, and special values of Rankin-Selberg LL-functions

In this article, we give a cohomological interpretation of (a special case of) the integrals constructed by the second named author and Q. Zhang \cite{YanZhang2023} which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_n\times\mathrm{GL}_m$ and $\mathrm{GL}_n\times\mathrm{GL}_{n-m-1}$ for $m<n$. As an application, we prove an algebraicity result for the special values of certain $L$-functions. This work is a generalization of the algebraicity result of Raghuram for $\mathrm{GL}_n\times\mathrm{GL}_{n-1}$ \cite{Raghuram2010} in the special case $m=n-1$, and the results of Mahnkopf \cite{Mahnkopf1998, Mahnkopf2005} in the special case $m=n-2$.Comment: 21 page

Bridging deep learning force fields and electronic structures with a physics-informed approach

This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations, illustrated through twisted two-dimensional large-scale material systems. The deep potential molecular dynamics model is adopted as the backbone, and electronic structure simulation is integrated. Using Wannier functions as the basis, we categorize Wannier Hamiltonian elements based on physical principles to incorporate diverse information from a deep-learning force field model. This information-sharing mechanism streamlines the architecture of our multifunctional model, enhancing its efficiency and effectiveness. Utilizing Wannier functions as the basis lays the groundwork for predicting more physical quantities. This approach serves as a powerful tool to explore both the structural and electronic properties of large-scale systems characterized by low periodicities. By endowing an existing well-developed machine-learning force field with electronic structure simulation capabilities, the study marks a significant advancement in developing multimodal machine-learning-based computational methods that can achieve multiple functionalities traditionally exclusive to first-principles calculations

Free Vibration Analysis of Electromechanical Integrated Electromagnetic Harmonic Movable Teeth Drive System

In the electromagnetic harmonic movable tooth drive system, the flexible wheel generates elastic deformation under the action of electromagnetic force, meshing output torque of the movable tooth and the center wheel. In view that the vibration of the flexible wheel under the action of electromagnetic force has an impact on the meshing of the movable tooth, which affects the output torque, this paper uses the theory of thin-shell vibration to simplify the flexible wheel into a thin shell with one end fixed at one end, and establishes an equilibrium equation of the flexible wheel displacement. And the vibration differential equation of the flexible wheel is derived. The influence of different parameters on its dynamic characteristics is analyzed. The theoretical values of several natural frequencies are compared with the ANSYS simulation values to verify the correctness of the method

Effect of in vitro gastrointestinal digestion on the chemical composition and antioxidant properties of Ginkgo biloba leaves decoction and commercial capsules

In this study Ginkgo biloba leaves (GBL) decoction and commercial capsules were digested using an in vitro model. Thirty-six active compounds were identified and quantified by HPLC-ESI-MS analysis based on the MS/MS patterns (precursor ions and product ions) and retention times, in comparison with reference standards. Most compounds in GBL showed a significant decrease during intestinal digestion, with an exception of vanillic acid and biflavonoids. Bioaccessibility values of chemical compositions varied between decoction and capsules samples. Also, significant reductions of total flavonoids and total phenolic content was observed after in vitro digestion. Both, 2,2-diphenyl-1-picrylhydrazyl (DPPH) and 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonic acid (ABTS) scavenging capacity decreased after gastric digestion, but increased during intestinal digestion. Nevertheless, different behaviour was observed in reducing antioxidant power (FRAP) assay. Compared to the pH of digestion, the influence of digestive enzymes on the chemical composition and antioxidant activity of GBL was relatively minor. Overall, these results may help provide a valid foundation for further investigations on bioactive compounds and the pharmacodynamics of GBL

Learning To Teach Large Language Models Logical Reasoning

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work