Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

Summary. The paper develops methods for the design of experiments for mechanistic models when the response must be transformed to achieve symmetry and constant variance. The power transformation that is used is partially justified by a rule in analytical chemistry. Because of the nature of the relationship between the response and the mechanistic model, it is necessary to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples are given of optimum designs, not only for single-response models, but also for experiments in which multivariate responses are measured and for experiments in which the model is defined by a set of differential equations which cannot be solved analytically. The extension to designs for checking models is discussed.     

Incorporating Time‐Dose‐Response into Legionella Outbreak Models

A novel method was used to incorporate in vivo host–pathogen dynamics into a new robust outbreak model for legionellosis. Dose‐response and time‐dose‐response (TDR) models were generated for Legionella longbeachae exposure to mice via the intratracheal route using a maximum likelihood estimation approach. The best‐fit TDR model was then incorporated into two L. pneumophila outbreak models: an outbreak that occurred at a spa in Japan, and one that occurred in a Melbourne aquarium. The best‐fit TDR from the murine dosing study was the beta‐Poisson with exponential‐reciprocal dependency model, which had a minimized deviance of 32.9. This model was tested against other incubation distributions in the Japan outbreak, and performed consistently well, with reported deviances ranging from 32 to 35. In the case of the Melbourne outbreak, the exponential model with exponential dependency was tested against non‐time‐dependent distributions to explore the performance of the time‐dependent model with the lowest number of parameters. This model reported low minimized deviances around 8 for the Weibull, gamma, and lognormal exposure distribution cases. This work shows that the incorporation of a time factor into outbreak distributions provides models with acceptable fits that can provide insight into the in vivo dynamics of the host‐pathogen system.     

T-optimum designs for discrimination between two multiresponse dynamic models

Summary.  The paper is concerned with a problem of finding an optimum experimental design for discriminating between two rival multiresponse models. The criterion of optimality that we use is based on the sum of squares of deviations between the models and picks up the design points for which the divergence is maximum. An important part of our criterion is an additional vector of experimental conditions, which may affect the design. We give the necessary conditions for the design and the additional parameters of the experiment to be optimum, we present the algorithm for the numerical optimization procedure and we show the relevance of these methods to dynamic systems, especially to chemical kinetic models.     

新型复合吸附干燥剂的吸附动力学特性研究

研制的一种由粗孔球形硅胶和氯化钙组成的新型复合吸附干燥剂SiO2.xH2O.yCaC l2与常用的干燥剂相比具有更好的吸水除湿性能.采用理论分析与实验验证的方法分析了新型复合吸附剂的吸附动力学特性及其影响因素,并建立了传质数学模型.研究结果表明,外扩散过程是传质的主要阻力,增大风速、减小吸附剂颗粒直径是减少传质阻力的有效措施.     

回旋管复合腔的綫性理諭

本文利用线性动力学理论和扰动方法,详细研究了回旋管复合腔的注波互作用和电子注的预群聚作用。推出了电子注与波的互作用功率、频偏和起振电流等公式,并进行了详细的讨论和分析。     

关于动力学理論中的扰动方法

本文讨论了动力学理论中求解Vlasov-Maxwell方程的扰动方法,证明了第一次线性化后的高阶分布函数对研究电磁波与带电粒子之间的互作用没有影响,并给出了第二次线性化后的Vlasov-Maxwell方程的一般求解方法.     

论化学热力学和化学动力学的矛盾及其统一

以平衡常数的理论计算,化学反应与温度的关系,以胶体的稳定性为例,分析了化学热力学和化学动力学之间的一些矛盾和产生矛盾的原因,揭示了化学热力学和化学动力学对立统一的关系。     

MnCO_3非等温热分解反应动力学的研究

本文采用程序升温热分解色谱技术,首次研究MnCO_3在动态条件下热分解速率随温度等条件变化的规律,提出了测定动力学参数的方法。实验表明,MnCO_3在不同条件下的分解速率有较大差异,在氮气流中其分解温度范围为310~400℃,最大分解速率的温度为370℃左右,在空气流中则相应偏低10℃左右,测出表观活化能E_a为177KJ/mol,频率因子k_0为1.69×10~(-2)S~(-1),反应级数近似为1。     

Differential Evolution Markov Chain with snooker updater and fewer chains

Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t ₃ distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.     

Impact of Microbial Ecology of Meat and Poultry Products on Predictions from Exposure Assessment Scenarios for Refrigerated Storage

A novel extension of traditional growth models for exposure assessment of food-borne microbial pathogens was developed to address the complex interactions of competing microbial populations in foods. Scenarios were designed for baseline refrigeration and mild abuse of servings of chicken broiler and ground beef Our approach employed high-quality data for microbiology of foods at production, refrigerated storage temperatures, and growth kinetics of microbial populations in culture media. Simple parallel models were developed for exponential growth of multiple pathogens and the abundant and ubiquitous nonpathogenic indigenous microbiota. Monte Carlo simulations were run for unconstrained growth and growth with the density-dependent constraint based on the "Jameson effect," inhibition of pathogen growth when the indigenous microbiota reached 10(9) counts per serving. The modes for unconstrained growth of the indigenous microbiota were 10(8), 10(10), and 10(11) counts per serving for chicken broilers, and 10(7), 10(9) and 10(11) counts per serving for ground beef at respective sites for backroom, meat case, and home refrigeration. Contamination rates and likelihoods of reaching temperatures supporting growth of the pathogens in the baseline refrigeration scenario were rare events. The unconstrained exponential growth models appeared to overestimate L. monocytogenes growth maxima for the baseline refrigeration scenario by 1500-7233% (10(6)-10(7) counts/serving) when the inhibitory effects of the indigenous microbiota are ignored. The extreme tails of the distributions for the constrained models appeared to overestimate growth maxima 110% (10(4)-10(5) counts/serving) for Salmonella spp. and 108% (6 x 10(3) counts/serving) for E. coli O157:H7 relative to the extremes of the unconstrained models. The approach of incorporating parallel models for pathogens and the indigenous microbiota into exposure assessment modeling motivates the design of validation studies to test the modeling assumptions, consistent with the analytical-deliberative process of risk analysis.