LpL^p integrability of functions with Fourier support on a smooth space curve

We prove that if $f\in L^p(\mathbb{R}^k)$ with $p<(k^2+k+2)/2$ satisfies that $\widehat{f}$ is supported on a small perturbation of the moment curve in $\mathbb{R}^k$, then $f$ is identically zero. This improves the more general result of Agranovsky and Narayanan, and the exponents are sharp in all dimensions. In the process, we develop a mechanism that should lead to further progress on related problems

Image reconstruction through a multimode fiber with a simple neural network architecture

Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.Comment: 17 pages, 10 figure

AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models

Evaluating the general abilities of foundation models to tackle human-level tasks is a vital aspect of their development and application in the pursuit of Artificial General Intelligence (AGI). Traditional benchmarks, which rely on artificial datasets, may not accurately represent human-level capabilities. In this paper, we introduce AGIEval, a novel benchmark specifically designed to assess foundation model in the context of human-centric standardized exams, such as college entrance exams, law school admission tests, math competitions, and lawyer qualification tests. We evaluate several state-of-the-art foundation models, including GPT-4, ChatGPT, and Text-Davinci-003, using this benchmark. Impressively, GPT-4 surpasses average human performance on SAT, LSAT, and math competitions, attaining a 95% accuracy rate on the SAT Math test and a 92.5% accuracy on the English test of the Chinese national college entrance exam. This demonstrates the extraordinary performance of contemporary foundation models. In contrast, we also find that GPT-4 is less proficient in tasks that require complex reasoning or specific domain knowledge. Our comprehensive analyses of model capabilities (understanding, knowledge, reasoning, and calculation) reveal these models' strengths and limitations, providing valuable insights into future directions for enhancing their general capabilities. By concentrating on tasks pertinent to human cognition and decision-making, our benchmark delivers a more meaningful and robust evaluation of foundation models' performance in real-world scenarios. The data, code, and all model outputs are released in https://github.com/microsoft/AGIEval.Comment: 19 page

Danhong Injection (a Traditional Chinese Patent Medicine) for Acute Myocardial Infarction: A Systematic Review and Meta-Analysis

Objective. We aimed to systematically assess the efficacy and safety of Danhong injection (DHI) for acute myocardial infarction (AMI) patients. Methods. We searched several electrical databases and hand searched several Chinese medical journals. Randomized controlled trials (RCTs) comparing DHI plus conventional western medicine with conventional western medicine plus placebo and RCTs comparing DHI plus conventional western medicine with conventional western medicine were retrieved. Study screening, data extraction, quality assessment, and data analysis were conducted in accordance with the Cochrane standards. Results. 13 RCTs enrolling 979 patients were included. Danhong injection could significantly reduce the risk of mortality, recurrent angina, arrhythmia, and heart failure. In addition, DHI was associated with improvement of left ventricular ejection fraction (LVEF) and reperfusion. No significant difference of DHI was found on recurrent acute myocardial infarction. However, the safety of DHI remained unknown for limited data. Conclusion. DHI might be a potentially efficacious treatment for AMI patients. Nevertheless, the safety of DHI remained uncertain for limited information. Due to the fact that the overall quality of all included studies is generally low, more high quality RCTs are expected to validate the efficacy and safety of DHI for AMI patients

Interactions Between Emodin and Efflux Transporters on Rat Enterocyte by a Validated Ussing Chamber Technique

Emodin, a major active anthraquinone, frequently interacts with other drugs. As changes of efflux transporters on intestine are one of the essential reasons why the drugs interact with each other, a validated Ussing chamber technique was established to detect the interactions between emodin and efflux transporters, including P-glycoprotein (P-gp), multidrug-resistant associated protein 2 (MRP2), and multidrug-resistant associated protein 3 (MRP3). Digoxin, pravastatin, and teniposide were selected as the test substrates of P-gp, MRP2, and MRP3. Verapamil, MK571, and benzbromarone were their special inhibitors. The results showed that verapamil, MK571, and benzbromarone could increase digoxin, pravastatin, and teniposide absorption, and decrease their Er values, respectively. Verapamil (220 μM) could significantly increase emodin absorption at 9.25 μM. In the presence of MK571 (186 μM), the Papp values of emodin from M-S were significantly increased and the efflux ratio decreased. With the treatment of emodin (185, 370, and 740 μM), digoxin absorption was significantly decreased while teniposide increased. These results indicated that emodin might be the substrate of P-gp and MRP2. Besides, it might be a P-gp inducer and MRP3 inhibitor on enterocyte, which are reported for the first time. These results will be helpful to explain the drug–drug interaction mechanisms between emodin and other drugs and provide basic data for clinical combination therapy