Effect of thickness variations of lithium niobate on insulator waveguide on the frequency spectrum of spontaneous parametric down-conversion

We study the effect of waveguide thickness variations on the frequency spectrum of spontaneous parametric down-conversion in the periodically-poled lithium niobate on insulator (LNOI) waveguide. We analyze several variation models and our simulation results show that thickness variations in several nanometers can induce distinct effects on the central peak of the spectrum, such as narrowing, broadening, and splitting. We also prove that the effects of positive and negative variations can be canceled and thus lead to a variation-robust feature and an ultra-broad bandwidth. Our study may promote the development of on-chip photon sources in the LNOI platform, as well as opens up a way to engineer photon frequency state.     

Limit theorems for a class of critical superprocesses with stable branching

We consider a critical superprocess $\{X;{\mathbf{P}}_{\mu }\}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index ${\gamma }_0>1$. We first show that, under some conditions, ${\mathbf{P}}_{\mu }(\left|X_t\right|\ne 0)$ converges to 0 as $t\to \infty$ and is regularly varying with index ${({\gamma }_0-1)}^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of $\{X_t\left(f\right);{\mathbf{P}}_{\mu }\left(\cdot \right|6X_{t}6\ne 0)\}$, after appropriate rescaling, converges weakly to a positive random variable ${\mathbf{z}}^{({\gamma }_0-1)}$ with Laplace transform $E\left[e^{-u{\mathbf{z}}^{({\gamma }_0-1)}}\right]=1-{(1+u^{-({\gamma }_0-1)})}^{-1∕({\gamma }_0-1)}.$     

Analysis of variations in the contents of steroidal saponins in Fructus Tribuli during stir-frying treatment

Just as natural saponins transform into aglycones, secondary glycosides and their derivatives using biotransformation technology, steroidal saponins may also undergo similar transformation after stir-frying. The purpose of this study was to elucidate the variations and the reasons for these variations in the contents of steroidal saponins in Fructus Tribuli (FT) during a stir-frying treatment. Stir-fried FT was processed in different time–temperature conditions. An UHPLC–MS/MS method was established and fully validated for quantitative analysis. In addition, the simulation processing products of tribuluside A, terrestroside B, terrestrosin K, terrestrosin D and 25R-tribulosin were determined by qualitative analysis using UHPLC–Q-TOF–MS. The established UHPLC–MS/MS method provides a rapid, flexible, and reliable method for the quality assessment of FT. The present study revealed that furostanol saponins with a C22-OH group could transform into corresponding furostanol saponins with a C-20–C-22 double bond (FSDB) via dehydroxylation. Additionally, FSDB could be successively converted into its secondary glycosides via a deglycosylation reaction. The transformation of spirostanol saponins into corresponding aglycones via deglycosylation led to a decrease in spirostanol saponins and an increase in aglycones. The results of this research provided scientific evidence of variation and structural transformation among steroidal saponins. These findings might be helpful for elucidating the processing mechanism of FT.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

Vector‐borne diseases, such as leishmaniasis, dengue, malaria, and yellow fever, transmitted by microparasites show periodic fluctuations in their prevalence. The novelty of this research is to assess the relationship between the vector feeding preference for an infectious host and the annual seasonal transmission through a vector‐host mathematical model. For the first time, numerical simulations illustrate that by increasing the vector feeding preference value in the transmission dynamics, periodic fluctuations accentuate and the endemic equilibrium average increases in vector and host populations. Moreover, increasing the vector feeding preference value, the amplitude strengthens for the infectious host and vector populations. This periodic behavior shows a similar pattern with the Peruvian incidence data from 2000 to 2016 for Andean cutaneous leishmaniasis provided by the Ministry of Health of Peru (MINSA). In addition, using the Floquet theory, the time average method and the linear operator method provides for the first time that the basic reproduction number for a nonautonomous system depends explicitly on the vector feeding preference for the infectious host. The nonautonomous model system shows that is a threshold parameter for the local stability of the disease‐free periodic solution. Therefore, the vector feeding preference is an important factor that should be considered and attended to for future research. Public and veterinary health in Peru and other countries should consider the vector feeding preference for specific host to vector control.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits

In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters and (with ). When , then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when . On the contrary, if , the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at . Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.     

片段化森林中檵木幼苗种内叶经济性状变异及其驱动因子

在异质性生境中，种内功能性状变异有助于植物对环境的适应，进而影响种群更新、群落构建和生态系统过程。探讨了种内叶经济性状的变异及受生境异质性的塑造情况。以千岛湖片段化生境中的常见种檵木（Loropetalum chinense）的幼苗为研究对象，测定了200株檵木幼苗个体水平的7个叶经济性状（比叶面积SLA、叶全碳量C、叶全氮量N等）及其对应的生境因子（郁闭度、土壤全碳量、土壤全氮量等），采用相关性检验、主成分分析和线性混合效应模型等方法探讨片段化森林中檵木幼苗的种内叶经济性状变异及生境异质性对该变异的驱动作用。结果显示：（1） 在7个叶经济性状所构成的21对相关性分析中，有12对显著相关。经主成分分析降维后，主成分1（PC1）占性状总变异的43.02%，主要与比叶面积、叶绿素浓度、叶全氮量呈正相关，与叶干物质质量分数和叶碳氮比呈负相关，体现了檵木的种内叶经济谱，可反映叶片的最大光合效率。（2）片段化对生境条件和叶经济性状均有影响。岛屿森林群落的郁闭度显著低于大陆。相对于大陆，岛屿中的檵木幼苗趋向于更小的PC1值（缓慢投资-收益策略）；大岛边缘较大岛内部偏向于更小的PC1值。（3）生境因子中，郁闭度对PC1具有显著正效应。研究表明，片段化生境中的檵木在幼苗阶段存在叶经济谱，生境片段化可通过影响生境条件进而改变檵木幼苗的叶经济性状。随着生境片段化程度的加剧，檵木幼苗的叶经济性状逐渐向缓慢投资-收益策略靠拢。     

Tutorial review on validation of liquid chromatography–mass spectrometry methods: Part II

This is the part II of a tutorial review intending to give an overview of the state of the art of method validation in liquid chromatography mass spectrometry (LC–MS) and discuss specific issues that arise with MS (and MS–MS) detection in LC (as opposed to the “conventional” detectors). The Part II starts with briefly introducing the main quantitation methods and then addresses the performance related to quantification: linearity of signal, sensitivity, precision, trueness, accuracy, stability and measurement uncertainty. The last section is devoted to practical considerations in validation. With every performance characteristic its essence and terminology are addressed, the current status of treating it is reviewed and recommendations are given, how to handle it, specifically in the case of LC–MS methods.