A Single Compartment Quantal Response Model with a Renewal Type Input Process and IID Releases

We deal with a single compartment quantal response model, where unlike the previous models, which do not have any input after the administration of a single dose Z(0)=z at time t=0, we allow inputs of doses after time t=0. More precisely, the system uses the (s, S) input policy as in inventory models, and has IID releases. Also when the amount of dose in the subject reaches 0, there is a probability p to stop having input thereafter. Among other results, the probability that the subject never responds and the expressions for some quantities of interest are obtained.     

A Generalized Logistic Model for Quantal Response Bioassay

In bioassay, where different levels of the stimulus may represent different doses of a drug, the binary response is the death or survival of an individual receiving a specified dose. In such applications, it is common to model the probability of a positive response P at the stimulus level x by P = F(x′β), where F is a cumulative distribution function and β is a vector of unknown parameters which characterize the response function. The two most popular models used for modelling binary response bioassay involve the probit model [BLISS (1935), FINNEY (1978)], and the logistic model [BERKSON (1944), BROWN (1982)]. However, these models have some limitations. The use of the probit model involves the inverse of the standard normal distribution function, making it rather intractable. The logistic model has a simple form and a closed expression for the inverse distribution function, however, neither the logistic nor the probit can provide a good fit to response functions which are not symmetric or are symmetric but have a steeper or gentler incline in the central probability region. In this paper we introduce a more realistic model for the analysis of quantal response bioassay. The proposed model, which we refer to it as the generalized logistic model, is a family of response curves indexed by shape parameters m₁ and m₂. This family is rich enough to include the probit and logistic models as well as many others as special cases or limiting distributions. In particular, we consider the generalized logistic three parameter model where we assume that m₁ = m, m is a positive real number, and m₂ = 1. We apply this model to various sets of data, comparing the fit results to those obtained previously by other dose-response curves such as the logistic and probit, and showing that the fit can be improved by using the generalized logistic.     

A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

多重二元响应Probit模型的渐近有效估计

针对多重二元响应Probit模型提出了两步估计方法,第一步由边际似然得到参数√n相合的估计,第二步通过一步迭代得到渐近有效估计,由于只需一步迭代,因此在利用模拟方法计算信息阵时,可以增加模拟的次数,从而减少模拟所产生的扰动对估计的影响．     

A Model with Three Compartments and Nonnegative Transfers

We consider a periodic model with three compartments, which can be considered as a simplified model for the dynamics of follicles. We give necessary and sufficient conditions for the solvability in nonnegative inputs, transfers and outputs, and we determine the minimal solution. If the problem is not solvable according to measurement errors of the given data, we recover suitable values by the method of least-squares, solving a quadratic optimization problem.     

Box-Behnken响应面法优化金线莲颗粒成型工艺

以填充剂种类、辅料配比、原料用量、干燥温度和黏合剂用量为考察因素,以颗粒合格率、溶化性、吸湿性和感官评价的总评归一值(OD)作为评价指标,采用单因素实验并结合响应面优化设计优选金线莲颗粒剂最佳成型工艺。结果表明,最佳成型工艺为辅料乳糖:糊精=3:1,原料药比例7.01%、干燥温度50 ℃,按此方案进行试验,预测颗粒成型率87.18%,吸湿率8.22%,溶化时间34.95 s,感官评价81分。采用响应面法优化金线莲颗粒的成型工艺结果可靠,可为金线莲颗粒剂的工业化生产提供依据。     

Microbial Metabolism as an Evolutionary Response: The Cybernetic Approach to Modeling

ABSTRACT:?

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions.

The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.

IMTECH communication no.001/2001     

响应面法优化土茯苓多糖除蛋白工艺

为了优化土茯苓(Smilax glabra Roxb.)多糖溶液除蛋白的工艺,采用Sevage试剂法除蛋白,在单因素实验的基础上,以多糖保留率和蛋白清除率为指标,使用响应面法对Sevage试剂法除蛋白工艺进行优化。结果显示,Sevage试剂法去除土茯苓多糖的最佳工艺为采用Sevage试剂:供试液=1:3、振摇强度8挡、振摇时间10 min、除蛋白次数5次,蛋白清除率为97.39%,多糖保留率为74.13%。优化后的除蛋白工艺重复性好,与理论值误差较小,可用于土茯苓多糖除蛋白。     

响应面优化酶解—微波辅助提取桑叶多糖的工艺研究

采用响应面优化酶解——微波辅助法从桑叶中提取桑叶多糖的提取工艺。在单因素试验的基础上通过采用Box-Behnken方法,研究液固比、提取时间、提取温度对桑叶多糖提取率的影响。结果显示,拟合方程显著,最终确定桑叶多糖的最优提取条件为：酶含量2%、酶解pH6、酶解温度50℃、酶解时间20 min、液固比15 mL·g^-1、提取时间13 min、提取温度76℃,该条件下桑叶多糖的实际提取率为15.23%,与理论模拟值15.12%接近,建立的模型真实可靠。该方法用于提取桑叶中的多糖类成分,工艺简单、成本低,具有有较高的应用价值。     

A Bayesian Estimator of the Optimum for a Single Factor Quadratic Response Model

Estimation of the location and magnitude of the optimum has long been considered an important problem in response surface methodology. In the industrial context, prior information accumulated by the subject matter specialist bears special significance. In this paper we use the Bayesian approach to estimating the optimum in a single factor quadratic regression model. Following the Bayesian general linear model development by Broemeling the normal/gamma conjugate prior is used. Explicit formulas for the generalized maximum likehood estimates of the characteristic parameters are obtained from the joint posterior distribution.     

一类具有Crowley-Martin型的恒化器模型的定性分析

研究了恒化器中一类具有Crowley—Martin型功能反应函数的单种微生物培养系统,应用微分方程定性理论,得到微生物培养失败和成功的充分条件．最后给出本文的一个应用．     

A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors

Biophysics - The course of an infection was modeled as a controlled nonlinear process. Understanding the substantial differences observed in the trajectory of the disease caused by the new...     

Mechanical Response of Single Plant Cells to Cell Poking： A Numerical Simulation Model

Cell poking is an experimental technique that is widely used to study the mechanical properties of plant cells. A full understanding of the mechanical responses of plant cells to poking force Is helpful for experimental work. The aim of this study was to numerically investigate the stress distribution of the cell wall, cell turgor, and deformation of plant cells in response to applied poking force. Furthermore, the locations damaged during poking were analyzed. The model simulates cell poking, with the cell treated as a spherical, homogeneous, isotropic elastic membrane, filled with incompressible, highly viscous liquid. Equilibrium equations for the contact region and the non-contact regions were determined by using membrane theory. The boundary conditions and continuity conditions for the solution of the problem were found. The forcedeformation curve, turgor pressure and tension of the cell wall under cell poking conditions were obtained. The tension of the cell wall circumference was larger than that of the meridian. In general, maximal stress occurred at the equator around. When cell deformation increased to a certain level, the tension at the poker tip exceeded that of the equator. Breakage of the cell wall may start from the equator or the poker tip, depending on the deformation. A nonlinear model is suitable for estimating turgor, stress, and stiffness, and numerical simulation is a powerful method for determining plant cell mechanical properties.     

A Two-Level Regression Model for Growth Curves with Correlated Outcomes

We propose a mixed-effect linear model, as a particular case of the two-level regression model, for analyzing repeated measures made at completely irregular time points. The model allows for subject-level covariates, so as to study the trend and the variability of the individual growth curves. Application of this model is illustrated on a published data set.     

具免疫时滞的HIV感染模型动力学性质分析

讨论了一类具免疫时滞的HIV感染模型.分析了未感染平衡点的全局渐近稳定性,给出了感染无免疫平衡点及感染免疫平衡点局部渐近稳定的充分条件.数值模拟结果表明,当易感细胞生成率的取值使得基本再生数满足平衡存在的条件且低于某一临界值时,时滞对平衡点的稳定性没有影响;若大于该临界值,随着时滞增大,稳定性开关发生,平衡点不稳定,出现一系列Hopf分支,最终表现为周期波动模式.     

A Numerical Model of Radiation Distribution Under an Individual Tree

A numerical model was developed to model the radiation distribution under an individual tree crown with different tree geometric parameters, different geographical locations and different topographical parameterrs and different transmissivity of the tree crown. The model was encoded into C and FORTRAN functions and could be utilized in agroforestry ecosystem modeling. The analysis showed that when the tree crown was more or less a conical shape with fixed tree height and crown radius, an increase in crown volume could even increase the average radiation under the tree.     

一类功能性反应模型在常数收获下的动态特性

具有功能性反应的捕食与被捕食模型具有非常复杂的动态性质．特别是在常数收获下,该模型呈现了各种各样、纷杂多变的动态特性。其中包括正平衡点及其稳定性的变化、各种分叉的产生以及周期解和极限环的出现．本文重点研究了常数收获项对一类功能性反应模型的动态性能的影响,得到了该收获模型存在稳定正平衡点、产生分叉以及在Hopf分叉附近产生周期解和极限环的若干充分条件．