Impact of bias in predicted height on tree volume estimation: A case-study of intrinsic nonlinearity

Bias originating from intrinsic nonlinearity in nonlinear models is caused by excess curvature in the solution locus of parameter estimates derived from least squares procedures. Bias due to intrinsic nonlinearity varies according to sample size as well as model specification. This paper analyses consequences of fractionising data into smaller sub-samples. Based on measurements of stem diameter and total tree height from the first Danish national forest inventory, it is demonstrated how data splitting at random may cause the intrinsic nonlinear curvature to exceed the critical F-value. Application of a Taylor-series expansion shows that, for all practical purposes, the bias in predictions of individual tree volume (based on stem diameter and tree height) is negligible. To minimize residual variance, intrinsic curvature and, in turn, prediction bias, it is recommended that data be stratified according to site conditions, stand characteristics or other relevant criteria. Finally, the preferred model should exhibit close-to-linear behaviour.     

均匀设计法处理含硫废水的研究

对钠盐型和铵盐型含硫工业废水进行脱硫处理,采用均匀设计法设计试验,得到定量描述试验内在规律的多元非线性回归方程.用该回归方程计算的预测值与试验结果一致.对影响脱硫效果和脱硫效率的影响因素--絮凝剂投加量、pH以及废水含硫量进行了考察.利用回归方程,对反应体系进行了模拟优化处理.研究表明,在试验条件下,用聚合氯化铝作为絮凝剂、pH=7的条件下,采用两段工艺,可以使脱硫后废水含硫量降至40 mg/L以下,满足下游污水处理装置对含硫量的要求.     

Forecasting of dissolved oxygen in the Guanting reservoir using an optimized NGBM (1,1) model

An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guanting reservoir inlet and outlet (China). The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What's more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.     

Forecasting of dissolved oxygen in the Guanting reservoir using an optimized NGBM (1,1) model

An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guanting reservoir inlet and outlet (China). The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What's more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.     

Investigation of some nonlinear singular model ecosystems and new concerned mathematical problems

The work is devoted to the investigation of nonlinear singular ecological models with initial functional conditions and determination of solutions of problems, which are connected with these models. It is also considered some of its applications in field of ecological modelling under formulation and investigation of the so-called keeping and protection problems. We shall investigate nonlinear models that are described with the help of partial differential equation of first and second orders. Solutions of linear and some singular nonlinear problems with functional initial conditions are obtained in the form depending from initial parameters.     

Complex dynamics of the population with a simple age structure

The effects of the following modes of density-dependent control of population growth: density-dependent birth rate, adult survival rate, juvenile survival rate are compared based on the mathematical model of population dynamics. It is shown that the most efficient mechanisms limiting population size are decreasing with the growth of the adult population birth rate and/or the decreasing survival rate of the offspring with the increase in their number. However, these same mechanisms are responsible for oscillations of the population size and its chaotic change. The density-dependence of the adult survival rate is not efficient in constraining the population growth, but it can substantially limit the magnitude of oscillations of the population size.     

Fitness Landscapes and the Precautionary Principle: The Geometry of Environmental Risk

The Precautionary Principle is a legal mechanism for managing the environmental risk arising from incomplete scientific knowledge of a proposal's impacts. The Precautionary Principle is applied to actions that carry with them the potential for serious or irreversible environmental change. The model proposed in this paper draws on methods used in a range of disciplines for modeling (potentially highly nonlinear) interactions between multiple parts of a complex system. These methods have been drawn together under the common mathematical umbrella of Fitness Landscape Theory. It is argued that the model, called “Environmental Impact Fitness Landscapes,” allows statements about the sensitivity of the gross effect from a set of impacts to be made when the number of impacts in the set, and/or their degree of interaction, is varied. It is argued that this can be achieved through identification of “meta” or “emergent” properties of the set itself, without reference to the specific causal chains determining behavior in specific instances. While such properties are very general, they may at least allow for the parameterization of the effects of sets of impacts where interactions are highly uncertain and empirical data severely limited, i.e., situations that would typically invoke the Precautionary Principle.     

复杂地基重力坝深层抗滑稳定非线性有限元分析

重力坝的深层抗滑稳定是保证大坝安全的一个重要条件。针对《混凝土重力坝设计规范》(DL5 10 8—1999)中关于复杂地基重力坝的稳定性需进行有限元分析的新规定,笔者结合某重力坝稳定问题实例,用非线性有限元方法进行了分析计算,并与刚体极限平衡法及结构可靠度分析方法的成果进行了对比。对有限元法的适用性,岩体侧面阻滑力的影响及抗滑稳定安全度的表达方法等问题进行了探讨     

Effects of lipids on the sorption of hydrophobic organic compounds on geosorbents: a case study using phenanthrene

The impact of the lipid fraction of natural geosorbents on the sorption of a polycyclic aromatic hydrocarbon was assessed using several experiments. In the first set of experiments phenanthrene was sorbed on a coastal sediment as well as on its humin and humic acid fractions before and after lipid extraction. Before lipid extraction, sorption shows dominantly partitioning characteristics. However, the extraction of lipids from sediment and humin drastically increases, by up to one order of magnitude, their sorption affinity for phenanthrene at low sorbate concentrations, resulting in increased isotherm nonlinearity. This effect is less pronounced for humic acids. One mechanism proposed for the increasing sorption is that lipids, despite their very low relative abundance in the sediments, can compete with phenanthrene for specific high affinity sorption sites (e.g., matrix pores and adsorption sites). This competition is not surprising considering the similar hydrophobic nature of lipids and phenanthrene. Lipids, or any non-polar molecules, could also act like plasticizers by swelling rigid domains and disrupting high affinity sites. In both cases, the removal of lipids (and extraction solvents) makes those sites available for phenanthrene. These provide alternative explanations to the previously proposed “solvent conditioning effect” believed to occur when geosorbents are treated with non-polar solvents modifying the matrix structure, an effect yet to be proven at molecular scale. To further investigate the impact of lipids on sorption, other independent experiments were performed. In a second experiment, re-addition of lipids to the extracted sediment restored the sorption isotherm linearity observed in the native material supporting the absence of irreversible extraction artifacts. However, high addition of lipids (i.e., after saturation of high affinity sites) seems to also enlarge the low affinity partitioning domain. These results are consistent with dual-mode, hole-filling, sorption models involving diffusion. In the final set of experiments, solid-state ¹⁹F-NMR using F-labeled lipids sorbed onto the sediments confirmed that lipids may be in different domains (mobile or rigid) that interact or not with phenanthrene. The possible effects of lipid removal on sorption have been overlooked and should be considered when geosorbents are pretreated.     

Bisolute Equilibrium Studies for the Sorption of Basic Dyes on a GAC from Almond Shells: A Nonlinear Approach

Aqueous phase adsorption of three textile dyes onto a granular activated carbon produced from acid activation of almond shells is presented. Primarily, the sorption of three basic dyes, methylene blue, rhodamine b, and malachite green oxalate were studied. Four models, the Freundlich, the Langmuir, the Redlich-Peterson, and the Toth isotherms were compared for their quality of fit to the single-solute sorption data. Next, sorption of the three likely binary systems was examined. Four bi-solute models, the extended Langmuir with and without an interaction term, the extended Redlich-Peterson with an interaction term, and the empirical extended Freundlich model were used to predict sorption in the binary systems. Nonlinearly determined constants of the corresponding single-solute isotherms were used in the binary models to compare with experimental binary sorption data. For the single-solute system, the three-parameter models of the Redlich-Peterson and the Toth isotherms outperformed the Langmuir and Freundlich models. The empirical extended Freundlich model produced the closest comparison to the binary data in each system. In general, the nonlinear method provided a simple and computationally effective technique of producing optimal fitting parameters for the bi-solute sorption models.