Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Parameter estimation techniques for interaction and redistribution models: a predator-prey example

Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

Aspects of the mineral nutrition of some native British plants — inter-site variation

Fifteen common native British plants were each sampled at a range of sites in Great Britain and green tissues analysed for several inorganic nutrients. Sampling criteria are discussed. The inter-site variation of each element within a species is assessed as a frequency distribution of raw data. Sample values of parameters including arithmetic mean, variance (coefficient of variation), skewness and kurtosis are presented. Their stability is assessed from nitrogen in sub-samples of Pteridium. This suggested sample sizes were adequate but some distributions had sufficient kurtosis to affect the variance. These parameters showed distinctions between macro- and micro-elements and between species. Some mean values sharply distinguished between species and may help to assess current theories of strategy and adaptation but a wider range of species is needed to clarify trends. Coefficients of variation are discussed and were relatively low for a nation-wide survey after allowing for sampling constraints. Coefficients of skewness and kurtosis showed two-thirds of the sample distributions were non-normal. Ecological aspects of the distributions are discussed and are relevant to studies along environmental gradients. Published hypotheses linking positive skewness to stress in the field are considered and two other postulates discussed. Distribution bounds such as those confining 95% of the values are discussed in relation to possible critical levels of nutrients.Nomenclature follows Clapham et al. (1981), Excursion flora of the British Isles. 3rd ed. University Press, Cambridge, except Chamaenerion.     

Thermodynamical model for insertion and aggregate binding of caffeine to the homopolymer poly(riboadenylate) and model choice by data analysis

This paper describes the model used to estimate the parameters of caffeine-poly(riboadenylate) (poly(A)) interactions from corresponding 1H-NMR measurements. The model of insertion and aggregate binding describes the non-cooperative insertion of a molecule C into an interspace between two monomers of a homopolymer in competition with aggregate binding. It contains two binding constants, K1 for insertion and K2 for the interaction of monomeric A units of the polymer with C molecules in bound aggregates, and two cooperativity parameters, Kcc for stacking of C molecules within aggregates and tau which is thought to be due to conformational adaptation of the polymer to those bound aggregates which cover more than one A unit. In contrast to other models, the size of a binding site (within the aggregates) is less than one monomeric unit, with n denoting the maximum number of C molecules per A unit in bound aggregates. The model is developed for general n by means of the method of sequence-generating functions. For n = 2 and n = 3, the correctness of the model treatment was checked by the matrix method. The model is applicable to the binding of aggregates to homopolymers, which are flexible enough to fit their structure to the aggregates.     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

用人工神经网络方法估计Ligistic方程参数

本文提出Logistic方程参数优化估计的人工神经网络方法,并选取一组标样进行具体尝试。结果表明,用这种方法估计Logistic方程参数效果极好。     

利用各世代的小区平均数估计遗传参数的加权最小二乘法

本文提出了在随机区组设计下利用六个世代的小区平均数估计加性-显性-二基因互作模型的各参数、检验该模型的加权最小二乘法的基本步骤。     

BME-1生物医用电子微分器

本文介绍了一个用国产高输入阻抗运算放大器制成的生物医用电子微分器。电路由同步输入、延时、三角波发生器、微分单元和滤波单元组成。微分时间常数20μs—50ms;校正电压变化率±0.1v/s—±200v/s;延时20μs—10s。微分器可为外来正脉冲触发,也可手动触发,它已用于微分心肌细胞动作电位、心腔压力等多种生物讯号。     

Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages

Weighted averaging regression and calibration form a simple, yet powerful method for reconstructing environmental variables from species assemblages. Based on the concepts of niche-space partitioning and ecological optima of species (indicator values), it performs well with noisy, species-rich data that cover a long ecological gradient (>3 SD units). Partial least squares regression is a linear method for multivariate calibration that is popular in chemometrics as a robust alternative to principal component regression. It successively selects linear components so as to maximize predictive power. In this paper the ideas of the two methods are combined. It is shown that the weighted averaging method is a form of partial least squares regression applied to transformed data that uses the first PLS-component only. The new combined method, ast squares, consists of using further components, namely as many as are useful in terms of predictive power. The further components utilize the residual structure in the species data to improve the species parameters (optima) in the final weighted averaging predictor. Simulations show that the new method can give 70% reduction in prediction error in data sets with low noise, but only a small reduction in noisy data sets. In three real data sets of diatom assemblages collected for the reconstruction of acidity and salinity, the reduction in prediction error was zero, 19% and 32%.