Smooth local solutions to weingarten equations and σk\sigma_k-equations

In this paper, we study the existence of smooth local solutions to Weingarten equations and $\sigma_k$-equations. We will prove that, for $2 \leq k \leq n$, the Weingarten equations and the $\sigma_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately

Stability Based Generalization Bounds for Exponential Family Langevin Dynamics

Recent years have seen advances in generalization bounds for noisy stochastic algorithms, especially stochastic gradient Langevin dynamics (SGLD) based on stability (Mou et al., 2018; Li et al., 2020) and information theoretic approaches (Xu and Raginsky, 2017; Negrea et al., 2019; Steinke and Zakynthinou, 2020). In this paper, we unify and substantially generalize stability based generalization bounds and make three technical contributions. First, we bound the generalization error in terms of expected (not uniform) stability which arguably leads to quantitatively sharper bounds. Second, as our main contribution, we introduce Exponential Family Langevin Dynamics (EFLD), a substantial generalization of SGLD, which includes noisy versions of Sign-SGD and quantized SGD as special cases. We establish data-dependent expected stability based generalization bounds for any EFLD algorithm with a O(1/n) sample dependence and dependence on gradient discrepancy rather than the norm of gradients, yielding significantly sharper bounds. Third, we establish optimization guarantees for special cases of EFLD. Further, empirical results on benchmarks illustrate that our bounds are non-vacuous, quantitatively sharper than existing bounds, and behave correctly under noisy labels

Exosomes derived from MSC as drug system in osteoarthritis therapy

Osteoarthritis (OA) is the most common degenerative disease of the joint with irreversible cartilage damage as the main pathological feature. With the development of regenerative medicine, mesenchymal stem cells (MSCs) have been found to have strong therapeutic potential. However, intraarticular MSCs injection therapy is limited by economic costs and ethics. Exosomes derived from MSC (MSC-Exos), as the important intercellular communication mode of MSCs, contain nucleic acid, proteins, lipids, microRNAs, and other biologically active substances. With excellent editability and specificity, MSC-Exos function as a targeted delivery system for OA treatment, modulating immunity, inhibiting apoptosis, and promoting regeneration. This article reviews the mechanism of action of MSC-Exos in the treatment of osteoarthritis, the current research status of the preparation of MSC-Exos and its application of drug delivery in OA therapy

Titanate nanotube-promoted chemical fixation of carbon dioxide to cyclic carbonate: a combined experimental and computational study

Titanate nanotubes (TNT) were found to be air-and water-tolerant, efficient, and recyclable Lewis acid catalysts towards the cycloaddition of carbon dioxide (CO2) to propylene oxide (PO) for the synthesis of cyclic propylene carbonate (PC). Using TNT as the catalyst and potassium iodide, tetrabutylammonium bromide or tetraphenylphosphonium bromide as the co-catalyst, PO was readily converted to PC with a yield of up to >99.9% and a PC selectivity of 100% under relatively mild conditions. Experimental research revealed that the TNT catalyst with the highest exposure of active sites, including surface hydroxyl groups and Lewis acid sites, proved to be the most active for the cycloaddition reaction. Our theoretical evaluation based on density functional theory calculations further indicated that the high Lewis acidity of TNT strongly reduces the energy barrier for the ring-opening step through the polarization of the C-O bond of PO, which allows a subsequent nucleophilic attack easily. Both experimental and computational studies demonstrated that the synergetic effect between TNT and the co-catalyst plays an important role in PC formation. The TNT catalyst is richer in surface Lewis acid sites, shows a large surface area and mesoporous structure, and has a heterogeneous and recyclable nature, which makes TNT an excellent, interesting and ideal catalyst for chemical fixation of CO2

Association of the blood levels of specific volatile organic compounds with nonfatal cardio-cerebrovascular events in US adults

Abstract Background Cardio-cerebrovascular diseases constitute a major global public health burden. Volatile organic compounds (VOCs) exposure has become progressively severe, endangering human health and becoming one of the main concerns in environmental pollution. The associations of VOCs exposure with nonfatal cardio-cerebrovascular events have not been identified in observational study with a large sample size, so we aim to examine the association in US adult population. Methods Adults aged > 18 years with complete data regarding selected blood levels of VOCs (including benzene, ethylbenzene, o-xylene, and m-/p-xylene) and nonfatal cardio-cerebrovascular events were included in the analysis (n = 3,968, National Health and Nutrition Examination Survey, NHANES, 2013–2018 survey cycle). Participants were classified into low- and high-exposure based on whether above selected VOCs low limit detect concentration or median value. Weighted multivariate logistic analyses and subgroup analyses were used to detect the association between selected VOCs exposure and nonfatal cardio-cerebrovascular events in US adults. Results Weighted multivariate logistic analyses showed that the high-VOCs exposure group had an increased risk of nonfatal cardio-cerebrovascular events compared with the low-VOCs exposure group; the adjusted odds ratios (OR) and 95% confidence intervals (CI) of nonfatal cardio-cerebrovascular events for the high-VOCs exposure group were 1.41 (0.91, 2.19), 1.37 (0.96, 1.95), 1.32 (0.96, 1.82), and 1.17 (0.82, 1.67) for benzene, ethylbenzene, o-xylene, and m-/p-xylene, respectively, which was not significant assuming statistical significance at a 0.05 significance level (95% CI) for a two-tailed test. Lastly, we found high-VOCs exposure was associated with increased incidence of nonfatal cardio-cerebrovascular events in both daily smokers an non-daily smokers (p-interaction > 0.01), but the association was not statistically significant in non-daily smokers. Conclusions This study found that VOCs (benzene, ethylbenzene, o-xylene, and m-/p-xylene) exposure was associated with increased incidence of nonfatal cardio-cerebrovascular events in US adults, and the results need to be confirmed by larger cohort studies

Diaphragmatic Surgery and Related Complications In Primary Cytoreduction for Advanced Ovarian, Tubal, and Peritoneal Carcinoma

Abstract Background To evaluate the procedures and complications of diaphragm peritonectomy (DP) and diaphragm full-thickness resection (DFTR) during primary cytoreduction for advanced stage epithelial ovarian cancer. Methods All the patients with epithelial ovarian carcinoma who underwent diaphragm procedures at our institution between January 2009 and August 2015 were identified. Clinicopathological data were retrospectively collected from the patients’ medical records. Postoperative morbidities were assessed according to the Memorial Sloan-Kettering Cancer Center (MSKCC) grading system. Results A total of 150 patients were included in the study. The majority of the patients had ovarian cancer (96%), stage IIIC disease (76%) and serous histology (89.3%). DP and DFTR were performed in 124 (82.7%) and 26 (17.3%) patients, respectively. A total of 142 upper abdominal procedures in addition to the diaphragmatic surgery were performed in 77 (51.3%) patients. No macroscopic residual disease was observed in 35.3% of the patients, while 84% of the total patient cohort had residual disease ≤1 cm. The overall incidence of at least one major morbidity (MSKCC grades 3–5) was 18.0%, whereas pleural effusions (33.3%), pneumonia (15.3%) and pneumothorax (7.3%) were the most commonly reported morbidities. The rate of postoperative pleural drainage was 14.6% in total, while half the patients in the DFTR group received drainage intraoperatively (11.5%) and postoperatively (38.5%). The incidence of postoperative pleural effusion was associated with stage IV disease (hazard ratio [HR], 17.2; 95% confidence interval [CI]: 4.5–66.7; P < 0.001), DFTR (HR, 4.9; 95% CI: 1.2–19.9; P = 0.028) and a long surgery time (HR, 15.4; 95% CI: 4.3–55.5; P < 0.001). Conclusions Execution of DP and DFTR as part of an extensive upper abdominal procedure resulted in an acceptable morbidity rate. Pleural effusion, pneumonia and pneumothorax were the most common pulmonary morbidities. The pleural drainage rate was not high enough to justify prophylactic chest tube placement for all the patients. However, patients who underwent DFTR merited special consideration for intraoperative prophylactic drainage