Threshold behaviour of a stochastic SIR model

In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.     

On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.     

基于机场货运预测的GM(1,1)建模过程问题分析

运用灰色系统GM(1,1)模型进行预测时,模拟精度和预测精度是关注的焦点.对原始数据构造缓冲算子和进行完整的前期检验,运用等维灰数递补的动态建模方法,针对误差建立残差修正模型,都可以提高预测的可信度.通过归纳建模各阶段可能出现的典型问题以及解决方法,以期对建立优化模型有所帮助.最后建立GM(1,1)模型预测天津滨海机场货邮吞吐量.     

The fractional chromatic number, the Hall ratio, and the lexicographic product

Let χ_f denote the fractional chromatic number and ρ the Hall ratio, and let the lexicographic product of G and H be denoted GlexH. Main results: (i) ρ(GlexH)≤χ_f(G)ρ(H); (ii) if ρ(G)=χ_f(G) then ρ(GlexH)=ρ(G)ρ(H) for all H; (iii) χ_f−ρ is unbounded. In addition, the question of how big χ_f/ρ can be is discussed.     

SWEIA艾滋病毒传染模型及应用

人类免疫缺陷病毒(HIV)是一种严重威胁生命的病毒,感染艾滋病毒患者一般经历四个阶段:i)艾滋病毒阴性的窗口期(W);ii)阳性的无症状潜伏期(E);iii)有症状期(Ⅰ);以及iv)移除阶段(A).为深入研究艾滋病传播过程,建立SWEIA艾滋病毒传染模型,定义基本再生数,分析无病与地方病平衡点的存在性和局部稳定性,根据2004至2015年中国艾滋病患者数据,采用遗传算法对SWEIA模型中参数进行估计.通过对基本再生数敏感性分析以及模型数值随参数不同而产生的变化,揭示艾滋病窗口期的接触率是影响艾滋病流行的主要原因之一.     

多值不确定型直觉模糊识别决策方法

基于模糊环境给出多值不确定型直觉模糊集的概念,定义了集合的交、并、包含等基本运算性质。通过刻画集合间的相似程度,提出八个新的相似度公式。最后将相似度应用于识别决策,说明公式的实用性和有效性。     

Four distinctive 1-D lanthanide carboxylate coordination polymers: Synthesis,crystal structures and spectral properties

Four novel lanthanide coordination polymers [Pr(mal)(OH)(bipy) · 2H₂O]_n (1), {[Dy¹(SBA)₃(H₂O)₂][Dy²(SBA)₃(H₂O)₂] · 4H₂O}_n (2), {[Tb(OHnic)(Onic)(H₂O)₅ · (OHnicH)] · H₂O}_n (3) and {[Sm(OHnic)(Onic)(H₂O)₅ · (OHnicH)] · H₂O}_n (4) (Hmal = maleic acid, HSBA = 4-sulfobenzoic acid, OHnicH = 6-hydroxynicotinic acid and bipy = 2,2′-bipyridine) have been synthesized and determined by single crystal X-ray diffraction. Complex 1 is a 1-D helical chain with seven-coordinated praseodymium centers. Complex 2 forms 1-D chain-like molecular structure containing two crystallographically unique dysprosium centers, the Dy¹ center is seven-coordinated while Dy² is eight-coordinated. The isomorphous complexes 3 and 4 exhibit an unprecedented 1-D chain-like polymeric structure through hydroxyl oxygen atoms of bridging Onic²⁻ anions linking up the neighboring central ions, and there exist three types of 6-OHnicH ligands in the structural unit which is rare for lanthanide carboxylate complexes. The photophysical properties of these complexes were studied using ultraviolet absorption spectra, fluorescence excitation and emission spectra.     

Selection of Wavelength Range and Number of Factors to be Used in the PLS Treatment of Spectrophotometric Data

Abstract

A procedure for selection of wavelength range and number of factors to be used in partial least square calibration that involves the calculation of prediction residual sum of squares (PRESS) in different conditions is proposed. The best model takes into account the minimum PRESS value that does not show significant differences with respect to the corresponding model with fewer factors. The ability of the proposed method to minimize errors in partial least squares (PLS) prediction is demonstrated by applying it to the resolution of phenytoine (DPH) and phenobarbital (PB) binary mixtures with errors less than 2.8%; the results are compared with those obtained using another wavelength selection procedure. The ensuing method, which was validated by high performance liquid chromatography (HPLC), also gives good results with real samples (pharmaceutical preparations).