Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.Symbols C ₁ activity of pacing enzyme pool for glucose fermentation (dimensionless) - C ₂ activity of pacing enzyme pool for glucose oxidation (dimensionless) - C ₃ activity of pacing enzyme pool for ethanol oxidation (dimensionless) - E ethanol concentration (g/l) - G glucose concentration (g/l) - k _a regulation constant for (g glucose/g cell h^–1) - k _b regulation constant for (dimensionless) - k _c regulation constant for (g glucose/g cell h^–1) - k _d regulation constant for (dimensionless) - K _m1 saturation constant for glucose fermentation (g/l) - K _m2 saturation constant for glucose oxidation (g/l) - K _m3 saturation constant for ethanol oxidation (g/l) - L ( t) time lag function (dimensionless) - p probability of plasmid loss of plasmid-bearing cells (dimensionless) - P recombinant protein concentration (mg/g cell) - q _G total glucose flux culture time (g glucose/g cell h) - t culture time (h) - t _lag lag time (h) - X total cell concentration (g/l) - X ⁺ plasmid-bearing cell concentration (g/l) - Y ^F _{X / G} cell yield for glucose fermentation pathway (g cell/g glucose) - Y ^O _{X / G} cell yield for glucose oxidation pathway (g cell/g glucose) - Y _{X / E} cell yield for ethanol oxidation pathway (g cell/g ethanol) - Y _{E / X} ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell) - ₂ glucoamylase yield for glucose oxidation (units/g cell) - ₃ glucoamylase yield for ethanol oxidation (units/g cell) - µ₁ specific growth rate for glucose fermentation (h^–1) - µ₂ specific growth rate for glucose oxidation (h^–1) - µ₃ specific growth rate for ethanol oxidation (h^–1) - µ_1max maximum specific growth rate for glucose fermentation (h^–1) - µ_2max maximum specific growth rate for glucose oxidation (h^–1) - µ_3max maximum specific growth rate for ethanol oxidation (h^–1)     

Hypothesis testing in semiparametric additive mixed models

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.     

A simple SIS epidemic model with a backward bifurcation

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.     

Calibration for nonlinear mixed effects models: an application to the withdrawal time prediction

We propose calibration methods for nonlinear mixed effects models. Using an estimator whose asymptotic properties are known, four different statistics are used to perform the calibration. Simulations are carried out to compare the performance of these statistics. Finally, the milk discard time prediction of an antibiotic, which has motivated this study, is performed on real data.     

Applications of likelihood asymptotics for nonlinear regression in herbicide bioassays

Dose-response models are intensively used in herbicide bioassays. Despite recent advancements in the development of new herbicides, statistical analyses are commonly based on asymptotic approximations that are sometimes poor. This paper presents the use of recent results in higher order asymptotics for likelihood-based inference in nonlinear regression. The methods presented provide accurate approximation for the distribution of test statistics and for prediction limits. Analyses of the fit and measures of detection limits of the bioassays are considered, and the potential of the methods is illustrated by examples with real data.     

不同盐浓度的混合盐对羊草苗的胁迫效应

用５０～３５０ｍｍｏｌ／Ｌ含有不同比例的ＮａＣｌ、Ｎａ２ＳＯ４、ＮａＨＣＯ３和Ｎａ２ＣＯ３等４种盐成分的３０种混合盐对羊草（Ａｎｅｕｒｏｌｅｐｉｄｉｕｍｃｈｉｎｅｎｓｅ（Ｔｒｉｎ．）Ｋｉｔａｇ．）苗进行盐碱混合胁迫处理。结果表明：相对生长率、Ｋ和Ｎａ含量、脯氨酸积累量及叶片电解质外渗率等胁变反应均随盐浓度增大以及碱性盐比例增高而加剧。而且碱性盐所造成的高ｐＨ的致胁变效应与盐浓度关系极大,浓度低时作用较小,随浓度增大其作用加剧。在含有碱性盐的混合盐胁迫中,包含有盐胁迫和碱胁迫两种作用。以总盐浓度代表盐胁强,缓冲量代表碱胁强。在碱胁强较弱时胁变主要受盐浓度影响,随碱胁强增大缓冲量变为影响胁变的主导因素     

Access to 7β-analogs of codeine with mixed μ/δ agonist activity via 6,7-α-epoxide opening

(?)-Codeine 1 was converted into previously unknown 7β-methyl-7,8-dihydrocodeine/morphine derivatives such as 13 via classical diaxial opening of α-epoxide 3. Several analogs exhibited dual μ/δ-agonist activity.     

混合喂养法建立成年营养性肥胖大鼠模型

目的:尝试用混合喂养法建立一种与临床相仿的成年营养性肥胖大鼠模型。方法:55只8周龄SD大鼠随机分为对照组10只(普通饲料喂养)和实验组45只(混合喂养),喂养2周后实验组剔除肥胖抵抗大鼠。每周记录大鼠体重,喂养9周后观察两组大鼠体重、体长、Lee's指数、空腹血糖(FBG)、血脂、葡萄糖耐量水平和肝脏组织病理改变。结果:喂养第9周末,实验组大鼠和对照组大鼠体重分别为(645.6±34.8)g和(483.3±31.5)g,Lee's指数分别为(326.3±24.2)和(302.7±19.8),组间比较有显著差异(P0.05)。实验组血清甘油三酯(TG)、总胆固醇(TC)及低密度脂蛋白胆固醇(LDL-C)、FPG、糖负荷后30、60、120分钟血糖均明显高于对照组,差异有统计学意义。HE染色病理结果显示实验组大鼠肝脏均出现脂肪样变,而对照组未见明显变性。结论:本研究所应用的混合喂养法可以稳定成功地建立伴有葡萄糖耐量减低和高脂血症的成年营养性肥胖大鼠模型。