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Background This study aims to construct a reliable diagnostic model for coronary artery disease (CAD) patients and explore its potential mechanism by consensus molecular subtypes of ferroptosis-related genes. Methods GSE12288 and GSE20680 were downloaded from Gene Expression Omnibus database. CAD patients were divided into different molecular subtypes according to the expression level of ferroptosis-related genes. Then, the distribution of differentially expressed genes, functional annotations and immune infiltration cells between the two subtypes were compared. Finally, a prognostic model of ferroptosis-related genes in CAD was constructed and verified. Results Two different molecular subtypes of CAD were obtained according to the expression level of ferroptosis-related genes. Then, a total of 1944 differentially expressed genes (DEGs) were found, among which, 236 genes were up-regulated and 1708 genes were down-regulated. In addition, 43 DEGs were ferroptosis-related genes. Functional enrichment analysis showed that these DEGs between two subtypes of CAD were mainly enriched in immune-related pathways and processes, such as T cell receptor, mTOR, NOD-like receptor and Toll-like receptor signaling pathways. We also found that 21 immune cells were significantly changed between two subtypes of CAD. The LASSO method was performed to identify and construct the 16 ferroptosis-related genes-based diagnostic signature. Diagnostic efficiency of diagnostic signature measured by AUC in the training set and validation cohort was 0.971 and 0.899, respectively. Conclusions This study contributes to a more comprehensive understanding of the mechanism of ferroptosis-related genes in CAD.

Titanium (Ti) has been extensively used in medical devices owing to their low density, high strength, excellent corrosion resistance, and biocompatibility. However, thrombus formation and bacterial infections are still challenges for their application in specific clinical cases. Hence, we have developed a simple, efficient, and stable strategy that endow Ti with anticoagulant and antibacterial properties through chemical bonding and electrostatic bonding. A large number of hydroxyl groups were produced on the surface of Ti by annealing at 500 °C. Then, heparin was immobilized on annealed surface with chemical bonding and chitosan was captured in an electrostatically bound manner by simply soaking in solution. The results indicated that the surface-functionalized Ti exhibited excellent anticoagulant properties by a reduction in platelet adhesion and prolonged blood clotting time. Furthermore, the modified Ti also showed antibacterial properties against both Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus).

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with finite-dimensional deterministic and stochastic inputs. Such methods construct an optimal index set that corresponds to the sharp estimates of the polynomial coefficients. Our analysis, furthermore, represents a novel approach for estimating best M-term approximation errors by means of coefficient bounds, without the use of the standard Stechkin inequality. In particular, the framework we propose for analyzing asymptotic truncation errors is based on an extension of the underlying multi-index set into a continuous domain, and then an approximation of the cardinality (number of integer multi-indices) by its Lebesgue measure. Several types of isotropic and anisotropic (weighted) multi-index sets are explored, and rigorous proofs reveal sharp asymptotic error estimates in which we achieve sub-exponential convergence rates [of the form $$M \text {exp}({-(\kappa M)^{1/N}})$$ , with $$\kappa $$ a constant depending on the shape and size of multi-index sets] with respect to the total number of degrees of freedom. Through several theoretical examples, we explicitly derive the constant $$\kappa $$ and use the resulting sharp bounds to illustrate the effectiveness of Legendre over Taylor approximations, as well as compare our rates of convergence with current published results. Computational evidence complements the theory and shows the advantage of our generalized framework compared to previously developed estimates

Background It is becoming increasingly clear that cancers can rarely be ascribed to just one or a few genomic variations. Genes generally do not function alone, but in groups that function as “networks”. This study aimed to develop a competing endogenous RNA (ceRNA) network to elucidate the role of long non-coding RNA H19 in colorectal cancer. Methods Large-scale RNA-seq data was obtained from The Cancer Genome Atlas database. Differentially expressed RNAs were identified by bioinformatics analysis, and a competing endogenous RNA network was constructed. Functional enrichment analysis and correlation analysis between competing endogenous RNAs and clinical features were performed to reveal their roles in the tumorigenesis of colorectal cancer. To verify the conclusions derived from bioinformatics analysis, we investigated the effect of lncRNA H19 knockdown in human colorectal cancer cell lines HT-29 and HCT116. Results The present study successfully identify various cancer-specific lncRNAs and pseudogenes in CRC. The lncRNA/pseudogene–miRNA–mRNA ceRNA network was constructed using 10 lncRNAs, 5 pseudogenes, 122 mRNAs and 39 miRNAs. In the ceRNA network of CRC, H19 up-regulates various cancer-related mRNA by competitively sponging various miRNA, and participates in PI3K–Akt signaling pathway in this manner. Cox regression and correlation analysis showed that H19 and some other competing endogenous RNAs in the network are associated with poor prognosis and clinical parameters such as tumor grade and metastasis. Knockdown of H19 reduces the protein level of MET, ZEB1, and COL1A1 in vitro. Conclusions H19 regulates PI3K–Akt signal pathway through a competing endogenous RNA network and predicts poor prognosis in colorectal cancer. The pseudogene RPLP0P2 may be an important oncogene like H19 and needs to be studied further. Electronic supplementary material The online version of this article (10.1186/s12935-019-0866-2) contains supplementary material, which is available to authorized users.

We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [17, 25] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.

Traditional nuclear magnetic resonance (NMR) spectroscopy relies on the versatile chemical information conveyed by spectra. To complement conventional NMR, Laplace NMR explores diffusion and relaxation phenomena to reveal details on molecular motions. Under a broad concept of ultrafast multidimensional Laplace NMR, here we introduce an ultrafast diffusion-relaxation correlation experiment enhancing the resolution and information content of corresponding 1D experiments as well as reducing the experiment time by one to two orders of magnitude or more as compared with its conventional 2D counterpart. We demonstrate that the method allows one to distinguish identical molecules in different physical environments and provides chemical resolution missing in NMR spectra. Although the sensitivity of the new method is reduced due to spatial encoding, the single-scan approach enables one to use hyperpolarized substances to boost the sensitivity by several orders of magnitude, significantly enhancing the overall sensitivity of multidimensional Laplace NMR., Laplace NMR provides complementary information to traditional NMR, such as details of molecular motion. Here, the authors report a correlation experiment capable of providing information on the physical environment of molecules while enhancing the chemical resolution and greatly reducing the experiment times.