Sharp bounds for a class of integral operators in weighted-type spaces on Heisenberg group

In this paper, we will use the conclusions and methods in \cite{1} to obtain the sharp bounds for a class of integral operators with the nonnegative kernels in weighted-type spaces on Heisenberg group. As promotions, the sharp bounds of Hardy operator , Hardy Littlewood-P\'{o}lya operator and Hilbert operator are also obtained

DPM-OT: A New Diffusion Probabilistic Model Based on Optimal Transport

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OTComment: iccv2023 accepte

Sharp bound for m-linear nn-dimensional Hardy-Littlewood-Polya operator in Morrey space on Heisenberg group

In this paper, we obtained the sharp bounds for $m$-linear $n$-dimensional Hardy-Littlewood-P\'{o}lya operator and Hilbert operator in two power weighted Morrey space on Heisenberg group.Comment: arXiv admin note: text overlap with arXiv:2304.0875

Investigation of therapeutic effect of Longchai Formula Granule on chronic hepatitis B patients: A double-blind, controlled and randomized clinical trial

Objective: To objectively evaluate the clinical efficacy of Longchai Formula Granule (LCFG) on chronic hepatitis B (CHB). Methods: According to GCP, 100 CHB patients who meet enter criterion were encoded and divided randomly into the test group (50 cases) and the control group (50 cases). The patients in test group were treated with LCFG and matrine capsule simulation agent, the patients in control group was treated with matrine capsule and LCFG simulation agent. Both groups have 12-week treatment period. The changes of Chinese medicine symptoms, ALT, AST, graduation of liver function, HBeAg, HBsAg, HBVDNA in CHB patients were observed and compared. Results: After unblinding, statistical data showed that there were 82 effective actual CHB cases composed of 40 CHB patients in test group (10 cases dropout) and 42 CHB patients in control group (8 cases dropout). The total efficient of Chinese symptoms improvement and ALT in test group is better than the control group (P0.05). As a whole, it shows a tendency that the change of these values in test group induced by LCFG is better than these values in control group induced by matrine capsule. Conclusions: In summary, LCFG is effective for CHB patients and has no significant difference with matrine cpasules. However, LCFG is better than matrine capsule in the improvement of symptomatology and liver function

Bibliometric Analysis Reveals the Progress of PM_2.5 in Health Research, Especially in Cancer Research

PM2.5 has an aerodynamic diameter of less than or equal to 2.5 microns due to its inherent physical and chemical properties so that it can enter the alveoli through the respiratory tract for blood gas exchange. Numerous studies have shown that PM2.5 is a serious air pollutant that poses a wide range of health risks, especially for cancer. Bibliometric methods were employed to have comprehensively analyzed the research of PM2.5 in cancer for about a decade in Web of Science to identify hotspots and trends using VOSviewer, CiteSpace, and R. The field has undergone overall growth in the past decade. As research on PM2.5 in health deepens, cancer related to it expanded beyond the respiratory system to the digestive system, urinary system, female gonadal axis, breast cancer and other cancers. Another observation is that research on PM2.5 in cancer has progressed in the mechanisms of deterioration, such as the role of matrix metalloproteinases in cancer. In addition, research on the risks of PM2.5 in combination with polycyclic aromatic hydrocarbons and heavy metals has also emerged. Results showed that there are relatively more studies on PM2.5 in high-latitude countries, which may be due to different national conditions, such as climate and coal combustion. Our research has combed through the progress of PM2.5 in cancer research and provided a supplement for developing pollution prevention ideas with different national conditions in this field