Geometric optical optimization of the corneal lens of Notonecta glauca

The optimal shape of the corneal lens of the water bug backswimmer (Notonecta glauca) and the optimal shape and position of the thin transition layer between the distal and proximal units of its cornea are theoretically determined. Using a geometric optical method, first the shape of a geometric interface between the lens units is determined, which eliminates the longitudinal spherical aberration. This interface is investigated for differently formed thick lenses when the medium in contact with the entrance surface of the lens is water or air. The optimal transition layer for the amphibious backswimmer is that, the boundaries of which are the theoretical interfaces for water and air, and the refractive index varies continuously in it. The optimal shape of the corneal lens is determined, with the disadvantageous lenses, with respect to the possible minimal spherical aberration and amount of reflected light from the transition layer, being rejected. The optimal position of the transition layer in the cornea can be obtained from the minimization of the amount of diffracted light on the marginal connection of the layers. The optimal corneal lens for backswimmer has ellipsoid boundary surfaces; the optimal transition layer in it is thin bell-shaped, at the marginal connection of which there is no dimple, the maximum of the layer is on the margin of the cornea. The shape of the theoretically optimal corneal lens, the shape and position of the theoretically optimal transition layer agree well with those of Notonecta glauca. The question posed, the geometric optical method used and the results presented are of general importance, and not only with respect to vision in the bug Notonecta, but also in the fossil trilobites, or in the wave guide theories which have been employed in similar modelling problems, in design of system of lenses without spherical aberration, for example.     

Integrating optimal foraging and optimal oviposition theory in plant–insect research

The current approach for studying host selection by phytophagous insects is mainly based on optimal oviposition theory, i.e. the preference–performance hypothesis. Almost no attention has been given to optimal foraging theory. However, recent papers and additional evidence given in this work illustrate that also optimal foraging may shape host preference patterns of phytophagous insects. Therefore and because optimal foraging and optimal oviposition may oppose conflicting needs to phytophagous insects, we plea for an integration of optimal foraging and optimal oviposition in plant–insect research. We argue how this may improve our understanding of plant–insect interactions.     

The conservation and exploitation of vulnerable resources

The maximum principle of deterministic optimal control, which has proved to be a very useful tool in theoretical bioeconomics, is extended in this article to cover the optimal exploitation of a biological resource vulnerable to catastrophic collapse, the probability of which may depend in general on the state of the resource, the current control and time. A general formulation of the maximum principle for such stochastic problems is presented and a number of applications are outlined. These include: optimal harvesting of a fishery vulnerable to catastrophic collapse; optimal thinning of a forest vulnerable to fire; optimal expenditure and investment in forest fire protection and optimal consumption-pollution tradeoffs in an ecosystem vulnerable to pollution-related collapse. In addition an application of the method to a highly stylized behavioral ecology model is given.     

The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.     

密环菌胞外多糖的发酵条件研究

密环菌是天麻的共生菌,有研究证明,密环菌的菌丝及发酵液有与天麻相类似的药理作用,为此,我们进行密环菌深层发酵产胞外多糖条件的研究。研究结果表明：菌丝生长和多糖产生的最适初始pH为5．9左右;消泡剂用量在一定内增加,有利于菌丝的生长,但增加消泡剂用量会不利于多糖的产生;接种量大,菌丝得率高,但接种量为10％时的多糖得率最高;装液量试验表明,通气量大,有利于菌丝的生长和多糖的产生;机械搅拌对菌丝的生长和多糖的产生都不利;生长动态实验证明,密环菌可在6d内完成液体发酵;以豆粕粉作氮源时,菌丝得率最高,以麸皮作氮源时,多糖产量最高;红薯粉为密环菌菌丝生长和多糖产生的最适碳源。     

Multiple-year optimization of conservation effort and monitoring effort for a fluctuating population

We consider optimal conservation strategies for an endangered population. We assume that juvenile survival is affected by unpredictable environmental fluctuation and can be improved by costly conservation effort. The initial population size is not accurately known at the time that the conservation effort level is chosen, but the uncertainty of its estimate can be reduced by a costly monitoring effort. In a previous paper, we analysed the optimal management strategy that minimizes a weighted sum of extinction probability and economic costs when only a single year is considered. Here we examine the case in which the conservation period lasts for several years by dynamic programming with incompletely observed process states. We study the optimal levels of the conservation and the monitoring efforts, and their dependence on the length of the conservation period and other parameters. The main conclusions are: (1) The optimal conservation effort in the first year depends on the accuracy of the information on the population size in the first year, but is almost independent of the accuracy of the information in later years. (2) When the risk of population extinction is small, the optimal conservation effort increases with the uncertainty of the population size. In contrast when the population is endangered, the optimal conservation effort decreases with the uncertainty of the population size. (3) The optimal conservation and monitoring efforts both increase with the length of the conservation period, provided that the population is relatively safe. However, if the population is endangered, both types of effort become smaller when the conservation period increases.     

Bio-economics of a renewable resource in a seasonally varying environment

In this paper we study the bio-economics of a renewable resource with governing dynamics described by two distinct growth functions (viz., logistic and Gompertz growth functions) in a seasonally varying environment. Seasonality is introduced into the system by taking the involved ecological parameters to be periodic. In this work, we establish a procedure to obtain the optimal path and compute the optimal effort policy which maximizes the net revenue to the harvester for a fairly general optimal control problem and apply this procedure to the considered models to derive some important conclusions. These problems are solved on the infinite horizon. We find that, for both the models, the optimal harvest policy and the corresponding optimal path are periodic after a finite time. We also obtain optimal solution, a suboptimal harvesting policy and the corresponding suboptimal approach path to reach this optimal solution. The key results are illustrated using numerical simulations and we compare the revenues to the harvester along the optimal and suboptimal paths. The general procedure developed in this work, for obtaining the optimal effort policy and the optimal path, has wider applicability.     

Optimal production control of a service-oriented manufacturing system with customer balking behavior

The great challenge for service-oriented manufacturing (SOM) is how to cope with customer behavior while making decision on production planning and scheduling. In this paper, we consider a single-stage manufacturing system for SOM with impatient customers. In order to represent customer balking behavior caused by backlog, we employ a balking function, which is an arbitrary non-decreasing function of the backlog for characterizing the customer’s response to the backlog. The objective is to find the optimal production policy that minimizes the system cost. The problem is formulated as a Markov decision process. The optimal production policy is proved to be a base-stock policy. The effects of system parameters on the optimal base-stock level are analytically investigated, and the impact of customer balking behavior on the system is illustrated by numerical example in which linear balking function is employed. Numerical example shows that customer balking has a significant impact on the optimal control and the performance measures of the system under the optimal policy.     

Estimating optimal profiles of genetic alterations using constraint-based models

Metabolic engineering involves application of recombinant DNA methods to manipulate metabolic networks to improve cellular properties. It is critical that the genetic alterations be performed in an optimal manner to maximize profit. In addition to the product yield, productivity consideration is also critical, especially for the production of bulk chemicals such as 1,3-propanediol. In this work, we demonstrate that it is suboptimal from the standpoint of productivity to induce genetic alteration at the start of the production process. A bi-level optimization scheme is formulated to determine the optimal temporal flux profile for the manipulated reaction. In the first case study, an optimal flux in the reaction catalyzed by glycerol kinase is determined to maximize the glycerol production at the end of a 6-h batch cultivation of Escherichia coli under aerobic conditions. The final glycerol concentration is 30% higher for the optimal flux profile compared with having an active flux during the entire batch. The effect of the mass transfer coefficient on the optimal profile and the glycerol concentration is also determined. In the second case study, the anaerobic batch fermentation of the ldh(-) strain of Escherichia coli is considered. The optimal flux in the acetate pathway is determined to maximize the final ethanol concentration. The optimal flux results in higher ethanol concentration (11.92 mmol L(-1)) compared to strains with no acetate flux (8.36 mmol L(-1)) and fully active acetate flux (6.22 mmol L(-1)). We also examine the effects of growth inhibition due to high ethanol concentrations and variations in final batch time on ethanol production.     

Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a “healthy” steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.     

Optimal sufficient dimension reduction for the conditional mean in multivariate regression

The aim of this article is to develop optimal sufficient dimensionreduction methodology for the conditional mean in multivariateregression. The context is roughly the same as that of a relatedmethod by Cook & Setodji (2003), but the new method hasseveral advantages. It is asymptotically optimal in the sensedescribed herein and its test statistic for dimension alwayshas a chi-squared distribution asymptotically under the nullhypothesis. Additionally, the optimal method allows tests ofpredictor effects. A comparison of the two methods is provided.     

Combined harvesting of a stage structured prey–predator model incorporating cannibalism in competitive environment

In this paper, we propose a prey–predator system with stage structure for predator. The proposed system incorporates cannibalism for predator populations in a competitive environment. The combined fishing effort is considered as control used to harvest the populations. The steady states of the system are determined and the dynamical behavior of the system is discussed. Local stability of the system is analyzed and sufficient conditions are derived for the global stability of the system at the positive equilibrium point. The existence of the Hopf bifurcation phenomenon is examined at the positive equilibrium point of the proposed system. We consider harvesting effort as a control parameter and subsequently, characterize the optimal control parameter in order to formulate the optimal control problem under the dynamic framework towards optimal utilization of the resource. Moreover, the optimal system is solved numerically to investigate the sustainability of the ecosystem using an iterative method with a Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. Results are analyzed with the help of graphical illustrations.     

乳糖代替IPTG诱导重组人胸腺肽α1在大肠杆菌中的表达

研究以乳糖代替IPTG作为诱导剂诱导重组人胸腺肽α1表达的可行性,对乳糖诱导的时机、乳糖浓度、诱导持续时间以及其它诱导条件进行研究,确定了乳糖诱导的最佳条件。结果表明,乳糖能有效地诱导重组人胸腺肽α1的表达,并且目的蛋白的表达量略高于IPTG的诱导量。     

Effort fluctuations in a harvest model with random prices

The effect of a single increase in the unit price of biomass on the optimal harvest policy for an exploited population is studied numerically. The price of a unit is assumed constant until a random time, when the price increases by a given amount. The optimal policy corresponding to the expected return is computed from the Bellman equation of dynamic programming. The results are compared with a model in which prices remain constant as well as a “well-timed” model in which the price increases at the expected increase time of the random case. Both optimal expected return and optimal policy computed from the deterministic models may differ substantially from that calculated from the random model, particularly if marginal costs are large. The emphasis is on numerical computation.     

Optimal foraging shapes host preference of a polyphagous leafminer

Abstract.  1. Most research on host selection by arthropods is based on optimal oviposition theory. This theory, also called the oviposition preference–offspring performance hypothesis, predicts that a female will choose those hosts for oviposition on which larvae perform best. Recent studies suggested, however, that optimal foraging by adults, or the quality of the host for adult performance, might also influence host choice.
2. This study investigated whether host preference of the polyphagous leafminer Liriomyza trifolii is determined by optimal foraging and/or optimal oviposition.
3. Female realised fecundity correlated nearly perfectly with feeding and oviposition preference of L. trifolii . The relationships between host preference and the offspring performance measures were always weaker. Hosts optimal for adult nutrition were also optimal for offspring performance but not vice versa . Hence, it was concluded that optimal foraging shapes feeding and oviposition preference of L. trifolii as this is the best strategy in order to maximise female fitness.     

甘南高寒草甸退化对植物功能群多样性与物种多度分布的影响

为分析甘南高寒草甸植物功能群多样性及其物种多度分布对退化的响应,探讨其多样性的形成与维持机制,采用样地调查法收集数据,并使用物种多度模型对其进行拟合分析。结果表明:随着退化程度的加深,植被优势种以禾草科和莎草科植物为主,逐渐变为杂草功能群植物为主,杂草功能群在群落多样性分布中起着主导作用;全部物种多度分布随着退化程度的加深发生变化,其中,无退化草甸的最优拟合模型是VOLKOV,轻度退化草甸的最优拟合模型是GEO,中度退化草甸和重度退化草甸的最优拟合模型为BRO,资源分配模式由随机分配转向固定分配的分配模式;禾草功能群的最优拟合模型以生态位模型为主,资源分配方式由固定分配和随机分配共同主导,豆科功能群的最优拟合模型是BRO,资源分配方式以固定分配为主,杂草功能群的最优拟合模型从中性模型向生态位模型转变,与全部物种多度分布的最优模型基本一致,且资源分配由随机分配向固定分配转变,可以认为杂草功能群是影响群落物种多度分布的主要原因,但是禾草和豆科功能群的贡献也不可忽视。     

Optimal risk management of human alveolar echinococcosis with vermifuge

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.     

酿酒酵母菌培养条件的研究

目的：优化酿酒酵母液体发酵得到菌体的最佳条件。方法：通过单因素试验,以吸光度为指标,研究碳源、氮源、接种量、pH值及无机离子对酿酒酵母菌生长的影响。结果：酿酒酵母生长的最佳碳源是葡萄糖,最佳氮源是蛋白胨,最佳接种量2％,最佳初始pH为4．5,添加无机盐硫酸亚铁能够促进其生长。结论：得到了酿酒酵母液体生长的最佳培养基配方。     

Non-parametric optimal design in dose finding studies

We describe a non-parametric optimal design as a theoretical gold standard for dose finding studies. Its purpose is analogous to the Cramer-Rao bound for unbiased estimators, i.e. it provides a bound beyond which improvements are not generally possible. The bound applies to the class of non-parametric designs where the data are not assumed to be generated by any known parametric model. Whenever parametric assumptions really hold it may be possible to do better than the optimal non-parametric design. The goal is to be able to compare any potential dose finding scheme with the optimal non-parametric benchmark. This paper makes precise what is meant by optimal in this context and also why the procedure is described as non-parametric.     

Optimization of harvesting age in an integral age-dependent model of population dynamics

The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.