A subset multicanonical Monte Carlo method for simulating rare failure events

Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in the entire domain of the input parameter in each iteration, the proposed subset MMC algorithm adaptively performs MMC simulations in a subset of the state space and thus improves the sampling efficiency. With numerical examples we demonstrate that the proposed method is significantly more efficient than both of the SS and the MMC methods. Moreover, the proposed algorithm can reconstruct the complete distribution function of the parameter of interest and thus can provide more information than just the failure probabilities of the systems

A spatial-temporal weight analysis and novel nonlinear weights of weighted essentially non-oscillatory schemes for hyperbolic conservation laws

In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variation diminishing Runge-Kutta method. The rationale for the improved performance of the finite volume WENO-M, WENO-Z and WENO-ZR schemes over WENO-JS in the first time step is that the nonlinear weights corresponding to large errors are adjusted to increase the accuracy of numerical solutions. Based on this analysis, we propose novel Z-type nonlinear weights of the finite volume WENO scheme for hyperbolic conservation laws. Instead of taking the difference of the smoothness indicators for the global smoothness indicator, we employ the logarithmic function with tuners to ensure that the numerical dissipation is reduced around discontinuities while the essentially non-oscillatory property is preserved. The proposed scheme does not necessitate substantial extra computational expenses. Numerical examples are presented to demonstrate the capability of the proposed WENO scheme in shock capturing

Explicit radial basis function Runge-Kutta methods

The aim of this paper is to design the explicit radial basis function (RBF) Runge-Kutta methods for the initial value problem. We construct the two-, three- and four-stage RBF Runge-Kutta methods based on the Gaussian RBF Euler method with the shape parameter, where the analysis of the local truncation error shows that the s-stage RBF Runge-Kutta method could formally achieve order s+1. The proof for the convergence of those RBF Runge-Kutta methods follows. We then plot the stability region of each RBF Runge-Kutta method proposed and compare with the one of the correspondent Runge-Kutta method. Numerical experiments are provided to exhibit the improved behavior of the RBF Runge-Kutta methods over the standard ones

A systematic review of maggot debridement therapy for chronically infected wounds and ulcers

SummaryObjectiveThis study aimed to systematically evaluate maggot debridement therapy (MDT) in the treatment of chronically infected wounds and ulcers.MethodsWe performed a meta-analysis referring to the PRISMA statement (Preferred Reporting Items for Systematic Reviews and Meta-Analyses). We searched for published articles in the following databases: PubMed, Web of Science, Embase, Wanfang (Chinese), and the China National Knowledge Infrastructure (CNKI). The latest search was updated on March 14, 2014. For dichotomous outcomes, the effects of MDT were expressed as the relative risk (RR) and 95% confidence interval (CI). For continuous outcomes with different measurement scales, we calculated the standardized mean difference (SMD). The pooled effects were estimated using a fixed effect model or random effect model based on the heterogeneity test. Subgroup analyses were performed according to the types of wounds or ulcers.ResultsMDT had a significantly increased positive effect on wound healing compared with conventional therapies, with a pooled RR of 1.80 (95% CI 1.24–2.60). The subgroup analysis revealed that the combined RRs were 1.79 (95% CI 0.95–3.38) for patients with diabetic foot ulcers (DFU) and 1.70 (95% CI 1.28–2.27) for patients with other types of ulcers. The time to healing of the ulcers was significantly shorter among patients treated with MDT, with a pooled SMD of −0.95 (95% CI −1.24, −0.65). For patients with DFU, the SMD was −0.79 (95% CI −1.18, −0.41), and for patients with other types of ulcers, the SMD was −1.16 (95% CI −1.63, −0.69).ConclusionMDT not only shortened the healing time but also improved the healing rate of chronic ulcers. Therefore, MDT may be a feasible alternative in the treatment of chronic ulcers

Crystal structure, thermal analyses, and acetate binding properties in Zinc(II) complex of a urea-functionalized pyridyl ligand

1302-1310A zinc(II) acetate complex with a urea-functionalized pyridyl ligand, [ZnL2(OAc)2]·2H2O (1) (L = N-(4-chlorophenyl)-N'-(4-pyridyl)urea), has been synthesized by the reaction of L with Zn(OAc)2·2H2O under water-containing condition. X-ray single-crystal diffraction analyses reveal that 2-D sheetlike network structure has been formed by the urea N−H×××Npyridyl interactions and C–H···O interactions in the free ligand L. Complex 1 features 3-D hydrogen bonded network formed by intermolecular N−H···O hydrogen bonds and O−H×××O hydrogen bonds involving urea groups, acetate anions and bridged water molecules. The hydrogen bonds play an important role in stabilizing the supramolecular structures. Thermal gravity analyses have been used to investigate the thermal stabilities of L and 1, and the apparent activation energy (Ea) of the decompositions have also been calculated, and the results indicate that the main decomposition of L needs higher apparent activation energy values Ea than that of 1. The acetate binding properties of L in solution have also been evaluated by Ultraviolet-Visible (UV-Vis) spectroscopy. CCDC: 1506202, L; 1506203, 1

Defect-induced helicity-dependent terahertz emission in Dirac semimetal PtTe2 thin films

Nonlinear transport enabled by symmetry breaking in quantum materials has aroused considerable interest in condensed matter physics and interdisciplinary electronics. However, the nonlinear optical response in centrosymmetric Dirac semimetals via the defect engineering has remained highly challenging. Here, we observe the helicity-dependent terahertz (THz) emission in Dirac semimetal PtTe2 thin films via circular photogalvanic effect (CPGE) under normal incidence. This is activated by artificially controllable out-of-plane Te-vacancy defect gradient, which is unambiguously evidenced by the electron ptychography. The defect gradient lowers the symmetry, which not only induces the band spin splitting, but also generates the giant Berry curvature dipole (BCD) responsible for the CPGE. Such BCD-induced helicity-dependent THz emission can be manipulated by the Te-vacancy defect concentration. Furthermore, temperature evolution of the THz emission features the minimum of the THz amplitude due to the carrier compensation. Our work provides a universal strategy for symmetry breaking in centrosymmetric Dirac materials for efficient nonlinear transport and facilitates the promising device applications in integrated optoelectronics and spintronics.Comment: 27 pages, 5 figure

Nutritional Risk, Health Outcomes, and Hospital Costs Among Chinese Immobile Older Inpatients: A National Study

Purpose: Evidence of the impact of nutritional risk on health outcomes and hospital costs among Chinese older inpatients is limited. Relatively few studies have investigated the association between clinical and cost outcomes and nutritional risk in immobile older inpatients, particularly those with neoplasms, injury, digestive, cardiac, and respiratory conditions. Methods: This China-wide prospective observational cohort study comprised 5,386 immobile older inpatients hospitalized at 25 hospitals. All patients were screened for nutritional risk using the Nutrition Risk Screening (NRS 2002). A descriptive analysis of baseline variables was followed by multivariate analysis (Cox proportional hazards models and generalized linear model) to compare the health and economic outcomes, namely, mortality, length of hospital stay (LoS), and hospital costs associated with a positive NRS 2002 result. Results: The prevalence of a positive NRS 2002 result was 65.3% (n = 3,517). The prevalence of “at-risk” patients (NRS 2002 scores of 3+) was highest in patients with cardiac conditions (31.5%) and lowest in patients with diseases of the respiratory system (6.9%). Controlling for sex, age, education, type of insurance, smoking status, the main diagnosed disease, and Charlson comorbidity index (CCI), the multivariate analysis showed that the NRS 2002 score = 3 [hazard ratio (HR): 1.376, 95% CI: 1.031–1.836] were associated with approximately a 1.5-fold higher likelihood of death. NRS 2002 scores = 4 (HR: 1.982, 95% CI: 1.491–2.633) and NRS scores ≥ 5 (HR: 1.982, 95% CI: 1.498–2.622) were associated with a 2-fold higher likelihood of death, compared with NRS 2002 scores <3. An NRS 2002 score of 3 (percentage change: 16.4, 95% CI: 9.6–23.6), score of 4 (32.4, 95% CI: 24–41.4), and scores of ≥ 5 (36.8, 95% CI 28.3–45.8) were associated with a significantly (16.4, 32.4, and 36.8%, respectively) higher likelihood of increased LoS compared with an NRS 2002 scores <3. The NRS 2002 score = 3 group (17.8, 95% CI: 8.6–27.7) was associated with a 17.8%, the NRS 2002 score = 4 group (31.1, 95% CI: 19.8–43.5) a 31.1%, and the NRS 2002 score ≥ 5 group (44.3, 95% CI: 32.3–57.4) a 44.3%, higher likelihood of increased hospital costs compared with a NRS 2002 scores <3 group. Specifically, the most notable mortality-specific comorbidity and LoS-specific comorbidity was injury, while the most notable cost-specific comorbidity was diseases of the digestive system. Conclusions: This study demonstrated the high burden of undernutrition at the time of hospital admission on the health and hospital cost outcomes for older immobile inpatients. These findings underscore the need for nutritional risk screening in all Chinese hospitalized patients, and improved diagnosis, treatment, and nutritional support to improve immobile patient outcomes and to reduce healthcare costs

New Poisson–Sch type inequalities and their applications in quantum calculus

Abstract The Poisson type inequalities, which were improved by Shu, Chen, and Vargas-De-Teón (J. Inequal. Appl. 2017:114, 2017), are generalized by using Poisson identities involving modified Poisson kernel functions with respect to a cone. New generalizations of improved Poisson–Sch type inequalities are obtained by using the generalized Montgomery identity associated with the Schrödinger operator. As applications in quantum calculus, we estimate the size of weighted Schrödingerean harmonic Bergman functions in the upper half space

On the consistency of the finite difference approximation with the Riemann-Liouville fractional derivative for 0<α<10 < \alpha < 1

Fractional differential equations have become an important modeling technique in describing various natural phenomena. A variety of numerical methods for solving fractional differential equations has been developed over the last decades. Among them, finite difference methods are most popular owing to relative easiness for implementation. In this paper, we show that the finite difference method with the Riemann-Liouville (RL) fractional derivative yields inconsistent and oscillatory numerical solutions to fractional differential equations of discontinuous problems for the fractional order alpha, 0 infinity and the method is consistent for smooth problems, the numerical solution can be oscillatory for any value of N. To illustrate the inconsistency and the oscillation phenomenon with the RL method, we also consider the finite difference methods with the Caputo and Grunwald-Letnikov fractional derivatives and compare the results with by with the RL method. We also show that the integral approach for the RL method can resolve the issues of the inconsistency and the oscillation phenomenon. Numerical results are presented to support the statements.11Nsciescopu

Fifth-order weighted essentially non-oscillatory schemes with new Z-type nonlinear weights for hyperbolic conservation laws

In this paper we propose new Z-type nonlinear weights of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the nonlinear weights, we take the pth root of the smoothness indicators and follow the form of Z-type nonlinear weights, leading to fifth order accuracy in smooth regions, even at the critical points, and sharper approximations around the discontinuities. We also prove that the proposed nonlinear weights converge to the linear weights as p→∞, implying the convergence of the resulting WENO numerical flux to the finite difference numerical flux. Numerical examples are presented by comparing with other WENO schemes, such as WENO-JS, WENO-M and WENO-Z, to demonstrate that the proposed WENO scheme performs better in shock capturing.11Nsciescopu