Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations

This paper is devoted to a new numerical approach for the possibility of (ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of (ω,Lδ)-periodic Lipschitz shadowing orbits and expression of shadowing distance are established. The numerical implementation approaches to the shadowing distance by the random Romberg algorithm are presented, and the convergence of this method is also proved to be mean-square. This ensures the feasibility of the numerical method. The practical use of these theorems and the associated algorithms is demonstrated in the numerical computations of the (ω,Lδ)-periodic Lipschitz shadowing orbits of the stochastic logistic equation

Uniqueness of Limit Cycles for a Class of Cubic Systems with Two Invariant Straight Lines

A class of cubic systems with two invariant straight lines dx/dt=y(1-x2),  dy/dt=-x+δy+nx2+mxy+ly2+bxy2. is studied. It is obtained that the focal quantities of O(0,0) are, W0=δ; if W0=0, then W1=m(n+l); if W0=W1=0, then W2=−nm(b+1); if W0=W1=W2=0, then O is a center, and it has been proved that the above mentioned cubic system has at most one limit cycle surrounding weak focal O(0,0). This paper also aims to solve the remaining issues in the work of Zheng and Xie (2009)

Stability Results for a Class of Differential Equation and Application in Medicine

A Chemostat system incorporating hepatocellular carcinomas is discussed. The model generalizes the classical Chemostat model, and it assumes that the Chemostat is an increasing function of the concentration. The asymptotic behavior of solutions is determined. Sufficient conditions for the local and global asymptotic stability of equilibrium and numerical simulation are obtained, which is used to select the disease control tactics

Genetic variants in the calcium signaling pathway genes are associated with cutaneous melanoma-specific survival

Remodeling or deregulation of the calcium signaling pathway is a relevant hallmark of cancer including cutaneous melanoma (CM). In this study, using data from a published genome-wide association study (GWAS) from The University of Texas M.D. Anderson Cancer Center, we assessed the role of 41,377 common single-nucleotide polymorphisms (SNPs) of 167 calcium signaling pathway genes in CM survival. We used another GWAS from Harvard University as the validation dataset. In the single-locus analysis, 1830 SNPs were found to be significantly associated with CM-specific survival (CMSS; P ≤ 0.050 and false-positive report probability ≤ 0.2), of which 9 SNPs were validated in the Harvard study (P ≤ 0.050). Among these, three independent SNPs (i.e. PDE1A rs6750552 T>C, ITPR1 rs6785564 A>G and RYR3 rs2596191 C>A) had a predictive role in CMSS, with a meta-analysis-derived hazards ratio of 1.52 (95% confidence interval = 1.19–1.94, P = 7.21 × 10−4), 0.49 (0.33–0.73, 3.94 × 10−4) and 0.67 (0.53–0.86, 0.0017), respectively. Patients with an increasing number of protective genotypes had remarkably improved CMSS. Additional expression quantitative trait loci analysis showed that these genotypes were also significantly associated with mRNA expression levels of the genes. Taken together, these results may help us to identify prospective biomarkers in the calcium signaling pathway for CM prognosis

Chinese Expert Consensus on Critical Care Ultrasound Applications at COVID-19 Pandemic

The spread of new coronavirus (SARS-Cov-2) follows a different pattern than previous respiratory viruses, posing a serious public health risk worldwide. World Health Organization (WHO) named the disease as COVID-19 and declared it a pandemic. COVID-19 is characterized by highly contagious nature, rapid transmission, swift clinical course, profound worldwide impact, and high mortality among critically ill patients. Chest X-ray, computerized tomography (CT), and ultrasound are commonly used imaging modalities. Among them, ultrasound, due to its portability and non-invasiveness, can be easily moved to the bedside for examination at any time. In addition, with use of 4G or 5G networks, remote ultrasound consultation can also be performed, which allows ultrasound to be used in isolated medial areas. Besides, the contact surface of ultrasound probe with patients is small and easy to be disinfected. Therefore, ultrasound has gotten lots of positive feedbacks from the frontline healthcare workers, and it has played an indispensable role in the course of COVID-19 diagnosis and follow up

Postoperative survival of pulmonary invasive mucinous adenocarcinoma versus non-mucinous invasive adenocarcinoma

Abstract Purpose In 2015, the World Health Organization renamed mucinous bronchioloalveolar adenocarcinoma as pulmonary invasive mucinous adenocarcinoma (IMA). Due to its low incidence and unclear prognosis with surgical treatment, previous studies have presented opposing survival outcomes. We aimed to investigate the differences in surgical prognosis and prognosis-related risk factors by comparing IMA with non-mucinous invasive adenocarcinoma (NMA). Methods A total of 20,914 patients diagnosed with IMA or NMA from 2000 to 2014 were screened from the Surveillance, Epidemiology, and End Results database. The screened patients were subjected to propensity score matching (PSM) in a 1:4 ratio to explore the survival differences between patients with IMA and NMA and the factors influencing prognosis. Results For all patients, IMA was prevalent in the lower lobes of the lungs (p < 0.0001), well-differentiated histologically (p < 0.0001), less likely to have lymph node metastases (94.4% vs. 72.0%, p < 0.0001) and at an earlier pathological stage (p = 0.0001). After PSM, the IMA cohort consisted of 303 patients, and the NMA cohort consisted of 1212 patients. Kaplan‒Meier survival analysis showed no difference in overall survival (OS) between patients in the IMA cohort and those in the NMA cohort (p = 0.7). Cox proportional hazards analysis showed that differences in tumor pathological type did not influence OS between the two cohorts (p = 0.65). Age (HR: 1.98, 95% CI 1.7–2.31, p < 0.0001), gender (HR: 0.64, 95% CI 0.55–0.75, p < 0.0001), and radiation treatment (HR: 2.49, 95% CI 1.84–3.37, p < 0.0001) were independent predictors of patient OS. Conclusion There was no significant difference in OS between patients with IMA and those with NMA after surgical treatment. Age, sex, and radiation treatment can independently predict OS

Dynamical analysis in explicit continuous iteration algorithm and its applications

Abstract This article is devoted to the dynamical analysis of an explicit continuous iteration algorithm, describing its construction, relationship with the explicit trapezoid method, and error analysis. A theorem demonstrating the equality of these methods is also established. The accuracy of the theoretical results and universality of the explicit continuous iteration algorithm are proved by numerical experiments

Role of skip N2 lymph node metastasis for patients with the stage III-N2 lung adenocarcinoma: a propensity score matching analysis

Abstract Purpose Recent studies have indicated some differences in the prognosis of patients with stage III-N2 lung adenocarcinoma, and the prognosis of patients with skip N2 lymph node metastasis (SKN2) is good. This study grouped patients with stage III-N2 lung adenocarcinoma by propensity score matching (PSM) to evaluate the impact of SKN2 on the prognosis of these patients. Methods The clinical data for patients who underwent radical lobectomy and had a postoperative pathological diagnosis of stage III-N2 lung adenocarcinoma at our centre from 2016 to 2018 were collected, and PSM was performed at a ratio of 1:1. Results A total of 456 patients were enrolled in this study. After PSM, 112 patients were included in the SKN2 group, and 112 patients were included in the non-SKN2 group. When comparing the SKN2 group with the non-SKN2 group, the 3-year OS rate was (71.4% vs. 12.5%, p < 0.001), and the 3-year DFS rate was (35.7% vs. 5.4%, p < 0.001). It is further divided into four groups:single-station SKN2 (N2a1),Multi-station SKN2 (N2a2),single-station non-SKN2 (N2b1) and Multi-station non-SKN2 (N2b2).The 3-year OS and DFS rates of skip lymph node metastasis were better than those of non-skip lymph node metastasis(OS:N2a1 vs. N2b1 68.4% vs. 23.5%,p < 0.001;N2a2 vs. N2b2 73.0% vs. 7.7%,p < 0.001)(DFS:N2a1 vs. N2b1 68.4% vs. 5.9%,p < 0.001;N2a2 vs. N2b2 62.2% vs. 5.1%,p < 0.001), regardless of the number of N2 station(OS:N2a1 vs. N2a2 68.4% vs. 73.0%,p = 0.584;N2b1 vs. N2b2 23.5% vs. 7.7%,p = 0.051). On multivariate analysis, sex (p = 0.008) ,Vascular tumour thrombus(p = 0.047),size(p = 0.002)and SKN2 (p < 0.001) were independent predictors of OS. Conclusion For patients with stage III-N2 lung adenocarcinoma, the prognosis of SKN2 patients is better than non-SKN2 patients’, and SKN2 may be used as an important factor in the N2 subgroup classification in future TNM staging

The Application of Magnetic Nanoparticles for Sentinel Lymph Node Detection in Clinically Node-Negative Breast Cancer Patients: A Systemic Review and Meta-Analysis

Superparamagnetic iron oxide (SPIO), an alternative mapping agent, can be used to identify sentinel lymph nodes in patients with clinically node-negative breast cancer. However, its performance in comparison with the standard method, using a radioisotope (technetium-99 m, Tc) alone or in combination with blue dye, remains controversial. Hence, a systematic review and meta-analysis were conducted to evaluate the diagnostic accuracy of SPIO and its clinical impact in the management of breast cancer. The PubMed, Embase, and Cochrane databases were comprehensively searched from inception to 1 May 2022. Cohort studies regarding the comparison of SPIO with standard methods for sentinel lymph node identification were included. A total of 19 prospective cohort studies, which collectively included 2298 clinically node-negative breast cancer patients undergoing sentinel lymph node identification through both the standard method and SPIO, were identified. The detection rate for sentinel lymph nodes (RR, 1.06; 95% CI, 1.05–1.08; p < 0.001) was considerably higher in the SPIO cohorts than in the standard method cohorts, although this difference was not significant in detected patients, patients with positive sentinel lymph nodes, or positive sentinel lymph nodes. Compared with the standard method, the SPIO method could be considered as an alternative standard of care for sentinel lymph node detection in patients with clinically node-negative breast cancer

Effect of Folic Acid Supplementation on Renal Phenotype and Epigenotype in Early Weanling Intrauterine Growth Retarded Rats

Background/Aims: The objective of this study was to examine the responses of p53 promoter methylation involved in kidney structure and function of early weaning intrauterine growth retarded (IUGR) rats to dietary folic acid supplementation. Method: Sprague-Dawley rats were fed isocaloric diets containing either 21% protein diet (normal feed) or 10% protein diet throughout pregnancy and normal feed during lactation. After weaning, Offspring were then fed onto normal feed and normal feed supplemented with 5 mg folic acid/kg feed for a month, this produced 4 dietary groups (maternal diet/ weanling diet): Con, Folic, IUGR and IUGR+Folic. Renal function, renal structure, p53 promoter methylation and protein expression of offspring rats were measured at postnatal 2 months and 3 months. Results: Glomerular volume, blood urea nitrogen, 24 hours urine protein were significantly elevated in IUGR rats compared with Con rats but were decreased by dietary folic acid supplementation. p53 protein expression in IUGR rats were significantly higher than that in Con rats, and p53 promoter methylation status in IUGR rats was reduced significantly compared with Con rats. However, the changes in p53 gene expression and DNA methylation status of IUGR rats were reversed by dietary folic acid supplementation. Conclusions: Our study showed for the first time that folic acid supplementation during early period of life could reverse the abnormality in renal p53 methylation status and protein expression, glomerular volume and renal function of IUGR rats offspring