To assess the relationship between the neutrophil-to-lymphocyte ratio (NLR) and related parameters to the severity of coronavirus disease 2019 (COVID-19) symptoms. Clinical data from 38 COVID-19 patients who were diagnosed, treated and discharged from the Qishan Hospital in Yantai over the period from January to February 2020 were analysed. NLR and procalcitonin (PCT) were determined in the first and fourth weeks after their admission, along with the clinical characteristics and laboratory test results of these patients. Based on results as obtained on the first and fourth weeks after admission, five indices consisting of NLR, white blood cells, neutrophils, lymphocytes (LY) and monocytes (MON) were selected to generate receiver operating characteristic curves, while optimal cutoff values, sensitivities and specificities were obtained according to the Yuden index. Statistically significant differences in neutrophils, LY and the NLR were present in the severe vs. moderate COVID-19 group from the first to the fourth week of their hospitalisation. The cut-off value of NLR for predicting the severity of COVID-19 was 4.425, with a sensitivity of 0.855 and a specificity of 0.979. A statistically significant positive correlation was present between PCT and NLR in the severe group as determined within the first week of admission. NLR can serve as a predictor of COVID-19 disease severity as patients' progress from the first to the fourth week of their hospitalisation. The statistically significant positive correlation between levels of NLR and PCT in severe patients indicated that increases in NLR were accompanied with gradual increases in PCT.

Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.

To eliminate the toxic effect of chemotherapy drug of lobaplatin (LBP) on body tissue in liver cancer therapy, this work prepared a nanodrug carrier based on polyethylene glycol-modified carbon nanotubes (PEG–CNTs) and then constructed a targeted drug delivery system (LBP–PEG–CNTs) by loading LBP on PEG–CNTs. Fluorescein isothiocyanate (FITC) was used to label PEG–CNTs to observe the cellular uptake of PEG–CNTs. In addition, the inhibitions of LBP–PEG–CNTs on HepG2 cells were investigated. The results show that the FITC-labeled PEG–CNTs have good cell penetrability; meanwhile, LBP–PEG–CNTs have good stability, pH-controlled release property, and high inhibition rate on HepG2 cells. To be specific, 80% of LBP is released under physiological conditions of liver cancer cells at pH 5.0, and LBP–PEG–CNTs show a high inhibition rate of 77.86% on HepG2 cells, demonstrating that they have targeted, pH-controlled release and inhibition properties on HepG2 cells.

This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain. Two classes of artificial boundary conditions (ABCs) are designed, namely, nonlocal analog Dirichlet-to-Neumann-type ABCs (global in time) and high-order Padé approximate ABCs (local in time). These ABCs reformulate the original problem into an initial-boundary-value (IBV) problem on a bounded domain. For the global ABCs, we adopt a fast evolution to enhance computational efficiency and reduce memory storage. High order fully discrete schemes, both second-order in time and space, are given to discretize two reduced problems. Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.

Choline and betaine are essential nutrients involved in one-carbon metabolism and have been hypothesised to affect breast cancer risk. Functional polymorphisms in genes encoding choline-related one-carbon metabolism enzymes, including phosphatidylethanolamine N-methyltransferase (PEMT), choline dehydrogenase (CHDH) and betaine-homocysteine methyltransferase (BHMT), have important roles in choline metabolism and may thus interact with dietary choline and betaine intake to modify breast cancer risk. This study aimed to investigate the interactive effect of polymorphisms in PEMT, BHMT and CHDH genes with choline/betaine intake on breast cancer risk among Chinese women. This hospital-based case–control study consecutively recruited 570 cases with histologically confirmed breast cancer and 576 age-matched (5-year interval) controls. Choline and betaine intakes were assessed by a validated FFQ, and genotyping was conducted for PEMT rs7946, CHDH rs9001 and BHMT rs3733890. OR and 95 % CI were estimated using unconditional logistic regression. Compared with the highest quartile of choline intake, the lowest intake quartile showed a significant increased risk of breast cancer. The SNP PEMT rs7946, CHDH rs9001 and BHMT rs3733890 had no overall association with breast cancer, but a significant risk reduction was observed among postmenopausal women with AA genotype of BHMT rs3733890 (OR 0·49; 95 % CI 0·25, 0·98). Significant interactions were observed between choline intake and SNP PEMT rs7946 (P interaction=0·029) and BHMT rs3733890 (P interaction=0·006) in relation to breast cancer risk. Our results suggest that SNP PEMT rs7946 and BHMT rs3733890 may interact with choline intake on breast cancer risk.

Findings from observational studies have suggested a possible relation between Ca and breast cancer risk. However, the results of these studies are inconclusive, and the dose–response relationship between Ca intake and risk of breast cancer remains to be determined. A meta-analysis of prospective studies was conducted to address these issues. PubMed and Embase databases were searched for relevant studies concerning the association between Ca intake and breast cancer up to March 2016. The summary relative risks (RR) with 95 % CI were calculated with a random-effects model. The final analysis included eleven prospective cohort studies involving 26 606 cases and 872 895 participants. The overall RR of breast cancer for high v. low intake of Ca was 0·92 (95 % CI 0·85, 0·99), with moderate heterogeneity (P=0·026, I 2=44·2 %). In the subgroup analysis, the inverse association appeared stronger for premenopausal breast cancer (RR 0·75; 95 % CI 0·59, 0·96) than for postmenopausal breast cancer (RR 0·94; 95 % CI 0·87, 1·01). Dose–response analysis revealed that each 300 mg/d increase in Ca intake was associated with 2 % (RR 0·98; 95 % CI 0·96, 0·99), 8 % (RR 0·92; 95 % CI 0·87, 0·98) and 2 % (RR 0·98; 95 % CI 0·97, 0·99) reduction in the risk of total, premenopausal and postmenopausal breast cancer, respectively. Our findings suggest an inverse dose–response association between Ca intake and risk of breast cancer.

We investigate the critical nuclei morphology in phase transformation by combining two effective ingredients, with the first being the phase field modeling of the relevant energetics which has been a popular approach for phase transitions and the second being shrinking dimer dynamics and its variants for computing saddle points and transition states. In particular, the newly formulated generalized shrinking dimer dynamics is proposed by adopting the Cahn-Hilliard dynamics for the generalized gradient system. As illustrations, a couple of typical cases are considered, including a generic system modeling heterogeneous nucleation and a specific material system modeling the precipitate nucleation in FeCr alloys. While the standard shrinking dimer dynamics can be applied to study the non-conserved case of generic heterogeneous nucleation directly, the generalized shrinking dimer dynamics is efficient to compute precipitate nucleation in FeCr alloys due to the conservation of concentration. Numerical simulations are provided to demonstrate both the complex morphology associated with nucleation events and the effectiveness of generalized shrinking dimer dynamics based on phase field models.

In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on some non-local Poincaré-type inequalities and the compactness of the associated non-local operators. It also offers careful characterizations of the associated solution spaces, such as compact embedding, separability and completeness. In the limit of vanishing non-locality, the convergence of the peridynamic system to the classical Navier equations of elasticity with Poisson ratio ¼ is demonstrated.

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework. Utilizing an adaptive finite element implementation with effective gradient recovery techniques, we discuss how the Euler number can be accurately computed directly from the nu-merically solved phase field functions or order parameters. Numerical examples and applications to the topological analysis of point clouds are also presented.