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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 (Pinteraction=0·029) and BHMT rs3733890 (Pinteraction=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, I2=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.
The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality.
Quantum Schur–Weyl theory refers to a three-level duality relation. At Level I, it investigates a certain double centralizer property, the quantum Schur– Weyl reciprocity, associated with some bimodules of quantum gln and the Hecke algebra (of type A)—the tensor spaces of the natural representation of quantum gln (see , , ). This is the quantum version of the well-known Schur–Weyl reciprocity which was beautifully used in H. Weyl's influential book . The key ingredient of the reciprocity is a class of important finite dimensional endomorphism algebras, the quantum Schur algebras or q-Schur algebras, whose classical version was introduced by I. Schur over a hundred years ago (see , ). At Level II, it establishes a certain Morita equivalence between quantum Schur algebras and Hecke algebras. Thus, quantum Schur algebras are used to bridge representations of quantum gln and Hecke algebras. More precisely, they link polynomial representations of quantum gln with representations of Hecke algebras via the Morita equivalence. The third level of this duality relation is motivated by two simple questions associated with the structure of (associative) algebras. If an algebra is defined by generators and relations, the realization problem is to reconstruct the algebra as a vector space with hopefully explicit multiplication formulas on elements of a basis; while, if an algebra is defined in terms of a vector space such as an endomorphism algebra, it is natural to seek their generators and defining relations.