Computational optimal control for the time fractional convection-diffusion-reaction system

This paper proposes a numerical approximation method for computational optimal control of a time fractional convection-diffusion-reaction system. The proposed method involves discretizing the spatial domain by finite element method, approximating the admissible controls by control parameterization, and then obtaining an optimal parameter selection problem which can be solved by numerical optimization algorithms such as sequential quadratic programming. Specifically, an implicit finite difference method is employed to solve the time fractional system, and the sensitivity method for gradient computation in integer order optimal control problems is adjusted to the fractional order case. Simulation results demonstrate the validity and accuracy of the proposed numerical approximation method.     

The optimal allocation of time during the diving cycle

Previous research has used a "marginal value" approach to determinehow long a diver should spend on the surface obtaining oxygenif it is to maximize the proportion of time in the foragingarea. In this paper we develop an explicit and general versionof this model and show how it results in predictions about bothtime on the surface and time under water. We also extend theanalysis to include the maximization of the net rate of energeticgain and the maximization of energetic efficiency. We show thatthe various currencies can be distinguished qualitatively interms of the way in which their predictions depend on the parametersthat characterize the animal and its environment. A generalfeature of the results is that the time in the foraging areashould first increase and then decrease as round-trip traveltime, , from the surface to the foraging area and back againincreases.     

On optimal propagule size and developmental time

A negative relationship between propagule size and development time is often imposed as a constraint on the evolution of optimal propagule size. Here I argue that when mortality is size-dependent, the optimisation of propagule size is in fact independent of the length of the ensuing developmental period. Furthermore, I show that whether larger or smaller propagules are favoured in response to factors that affect growth and mortality rates will depend on which of these variables scale more sharply with size. I use marine fish to exemplify some of the points raised in this note.     

Experimental designs for the study of allelopathy

The primary aim of this paper is to discuss the methodological approaches that may best develop studies of allelopathy in the future. Laboratory studies on the functions of isolated chemicals, no matter how mechanistically detailed, cannot demonstrate the significance of allelopathy in communities. Evidence for allelopathy in natural plant communities should include information of concentrations and release rates such as demonstrated in field soils for (±)-catechin and Centaurea maculosaLam. Community-relevant evidence for allelopathy should include some manipulation of exudates such as performed in many experiments with activated carbon and gel filtration columns. Realistic evidence for allelopathy should include separation of resource effects from chemical effects; such as demonstrated by experiments with activated carbon additions, density-dependent responses to additions of competitors and chemicals, and resource addition treatments. Community-relevant evidence should link laboratory effects to field patterns and experiments; such as the links between the inhibitory effects of roots of Larrea tridentataCov., the highly spatially segregated root systems and regular above-ground spacing of this species, strong spatial disassociation of L. tridentata with other species, and removal experiments indicating that segregation of L. tridentata root systems via allelopathy may feed back to sequestering of resource use. Studies of allelopathy should consider chemically initiated shifts in microbial populations, and the effects of organic and inorganic soil components on the function of exudates; which has been done in a number of studies. Finally, studies of allelopathy should include large-scale manipulation of chemical effects; such as performed in field experiments in boreal forests in Sweden with Empetrum hermaphroditumHagerup and Scots pine (Pinus sylvestrisL.). Demonstrating the occurrence and importance of chemically mediated interactions among plants is not trivial. If even a small portion of the thousands of chemicals produced by different plant species have effects on their neighbours, then species-specific interactions, natural selection, community integration, and community coevolution may be quite different than predicted by conceptual models based solely on resource competition. Appropriate methodology is crucial for integrating chemically mediated interactions into ecological theory.     

A 'polarisation sun-dial' dictates the optimal time of day for dispersal by flying aquatic insects

1. Daily changes in the flight activity of aquatic insects have been investigated in only a few water beetles and bugs. The diel flight periodicity of aquatic insects and the environmental factors governing it are poorly understood. 2. We found that primary aquatic insects belonging to 99 taxa (78 Coleoptera, 21 Heteroptera) fly predominantly in mid‐morning, and/or around noon and/or at nightfall. There appears to be at least four different types of diurnal flight activity rhythm in aquatic insects, characterised by peak(s): (i) in mid‐morning; (ii) in the evening; (iii) both in mid‐morning and the evening; (iv) around noon and again in the evening. These activity maxima are quite general and cannot be explained exclusively by daily fluctuations of air temperature, humidity, wind speed and risks of predation, which are all somewhat stochastic. 3. We found experimental evidence that the proportion (%) P(θ) of reflecting surfaces detectable polarotactically as ‘water’ is always maximal at the lowest (dawn and dusk) and highest (noon) angles of solar elevation (θ) for dark reflectors while P(θ) is maximal at dawn and dusk (low solar elevations) for bright reflectors under clear or partly cloudy skies. 4. From the temporal coincidence between peaks in the diel flight activity of primary aquatic insects and the polarotactic detectability P(θ) of water surfaces we conclude that the optimal times of day for aquatic insects to disperse are the periods of low and high solar elevations θ. The θ‐dependent reflection–polarisation patterns, combined with an appropriate air temperature, clearly explain why polarotactic aquatic insects disperse to new habitats in mid‐morning, and/or around noon and/or at dusk. We call this phenomenon the ‘polarisation sun‐dial’ of dispersing aquatic insects.     

The optimal allocation of time and respiratory metabolism over the dive cycle

Because anaerobic metabolism is much less efficient than aerobicmetabolism in supplying energy, it is widely believed that diversrely predominantly on aerobic metabolism for diving. In thispaper, a time budget model, which assumes that the diver canuse either completely aerobic or partially aerobic metabolismwith additional anaerobic metabolism for diving, is developedand is used to make predictions about patterns in optimal allocationof time and respiratory metabolism during the dive cycle. Theresults derived from the model are (1) a diver that can varythe ratio of energy supplied anaerobically to total energy spentduring dive time is favored by natural selection, but the patternsof time allocation over the dive cycle by the diver do not differ fromthose of a diver that cannot vary the ratio. (2) Even if itis assumed that divers switch their metabolism for diving, anobvious upturn in the surface time with respect to dive timedoes not occur at the aerobic dive limit (ADL) but occurs beyondthe ADL. (3) Use of additional anaerobic metabolism can be favoredfor dives shorter than the ADL. These findings provide a usefulguide to understanding the factors that limit diving behavior.     

Experimental and clinical rationale for the choice of optimal methods of x-ray diagnosis of kidney diseases

Limits of potentialities of methods of radiodiagnosis of renal diseases were studied by way of experimental simulation of organs with various pathomorphological changes (urolithiasis, kidney tumors and tuberculosis). Special attention was paid to the detection of pathomorphological elements which were characteristic for the initial forms of disease. Photofilm and thermoluminescent dosimetry were used to study radiation-hygienic characteristics of radiation methods of kidney investigation. Recommendations for establishing diagnosis were worked out in suspected urolithiasis, kidney tumors and tuberculosis. The thickness of a studied object played an important role in the detectability of minor and low contrast details. An objective method of the control over the quality of roentgenocontrast images was proposed.     

Experimental validation of the solvent-gradient simulated moving bed process for optimal separation of phenylalanine and tryptophan

A solvent-gradient simulated moving bed (SG-SMB) process for separation of two useful amino acids, phenylalanine and tryptophan, has been studied in previous researches, which confirmed that the SG-SMB outperformed the corresponding isocratic SMB for the same separation task. However, all of the previous studies on the SG-SMB for separation of the two amino acids have been limited to process simulation and optimization, including some batch-chromatography tests. The experimental validation of such an SG-SMB process was attempted in this article. This task began by assembling the experimental unit of the SG-SMB process. Its operating conditions were determined from the SG-SMB optimization tool based on genetic algorithm, in which the mass-transfer parameters as well as the adsorption isotherm parameters of the feed components (two amino acids) were entered as the mathematical models expressed as a function of liquid-phase composition (i.e., modifier concentration in the liquid phase). Based on the determined operating conditions, the relevant SG-SMB experiment was conducted until a cyclic steady-state was reached. The assay of all the resultant product samples verified that the SG-SMB separation of interest was performed successfully as designed. The experimental data were also found to agree closely with the model predictions.     

Just in time: Circadian defense patterns and the optimal defense hypothesis

The optimal defense hypothesis (ODH) provides a functional explanation for the inhomogeneous distribution of defensive structures and defense metabolites throughout a plant’s body: tissues that are most valuable in terms of fitness and have the highest probability of attack are generally the best defended. In a previous review,¹ we argue that ontogenically-controlled accumulations of defense metabolites are likely regulated through an integration of developmental and defense signaling pathways. In this addendum, we extend the discussion of ODH patterns by including the recent discoveries of circadian clock-controlled defenses in plants.     

杨桃园桔小实蝇的防治适期研究

杨桃园桔小实蝇种群数量动态具有明显的规律,且与杨桃果实的成熟期密切相关。通常3月实蝇种群数量开始上升,4月～10月为发生盛期,其间出现3—4个发生高峰,11月次至年2月虫量较低。桔小实蝇对杨桃果实的成熟度具明显选择性,偏好硬度（成熟度）在89度以下的果实。单个果实中约有6个产卵孔、30头幼虫,杨桃从被害到落果时间长度一般为9d。经分析,发现产卵孔数和落果中的幼虫数量、产卵孔数与落果时间长度之间显著相关,建立了两者间关系方程。在以上研究基础上,确定了杨桃园桔小实蝇防治的一些关键时期。     

Phenotypic plasticity and optimal timing of metamorphosis under uncertain time constraints

Life-history theory suggests that optimal timing of metamorphosis should depend on growth conditions and time constraints under which individuals develop. Current models cannot make reliable predictions for species in ephemeral habitats where individuals often face an increasing mortality risk over time because these models assume time-invariant mortality rates (i.e., daily mortality rates remain constant) and fixed seasons. We examined the plasticity of growth, development, and body mass at metamorphosis in tadpoles of the tree-hole breeding frog Phrynobatrachus guineensis in relation to an unpredictable time constraint in the field and in controlled experiments along a fixed density and food gradient. Mean mass and age at metamorphosis of sibships were positively correlated with per capita food level. Based on our results, we developed a simple model of the optimal timing of metamorphosis under time-dependent mortality rates showing that development rates are not only adjusted to growth conditions but also to time-variant mortality rates. The increasing mortality rate represents a time constraint that favors a reduced larval period, but because it is based on probabilities of survival it allows a trade-off between development time and mass. We extend this model to different types of time constraints and show that it can predict the range of documented reaction norms. Differences between species in␣the correlation of age and mass at metamorphosis may have evolved due to differences in their time-variant mortality rates.     

Experimental and computational approaches for the study of calmodulin interactions

Ca²⁺, a universal messenger in eukaryotes, plays a major role in signaling pathways that control many growth and developmental processes in plants as well as their responses to various biotic and abiotic stresses. Cellular changes in Ca²⁺ in response to diverse signals are recognized by protein sensors that either have their activity modulated or that interact with other proteins and modulate their activity. Calmodulins (CaMs) and CaM-like proteins (CMLs) are Ca²⁺ sensors that have no enzymatic activity of their own but upon binding Ca²⁺ interact and modulate the activity of other proteins involved in a large number of plant processes. Protein-protein interactions play a key role in Ca²⁺/CaM-mediated in signaling pathways. In this review, using CaM as an example, we discuss various experimental approaches and computational tools to identify protein-protein interactions. During the last two decades hundreds of CaM-binding proteins in plants have been identified using a variety of approaches ranging from simple screening of expression libraries with labeled CaM to high-throughput screens using protein chips. However, the high-throughput methods have not been applied to the entire proteome of any plant system. Nevertheless, the data provided by these screens allows the development of computational tools to predict CaM-interacting proteins. Using all known binding sites of CaM, we developed a computational method that predicted over 700 high confidence CaM interactors in the Arabidopsis proteome. Most (>600) of these are not known to bind calmodulin, suggesting that there are likely many more CaM targets than previously known. Functional analyses of some of the experimentally identified Ca²⁺ sensor target proteins have uncovered their precise role in Ca²⁺-mediated processes. Further studies on identifying novel targets of CaM and CMLs and generating their interaction network - “calcium sensor interactome” - will help us in understanding how Ca²⁺ regulates a myriad of cellular and physiological processes.     

Rabies in raccoons: optimal control for a discrete time model on a spatial grid

An epidemic model for rabies in raccoons is formulated with discrete time and spatial features. The goal is to analyze the strategies for optimal distribution of vaccine baits to minimize the spread of the disease and the cost of implementing the control. Discrete optimal control techniques are used to derive the optimality system, which is then solved numerically to illustrate various scenarios.     

Experimental methods for kinetic study of suicide substrates

The kinetic study of the enzymatic inactivation originated by suicide substrates can be carried out by means of two alternative approaches. One method considers the substrate concentration as practically constant during the assay time and provides explicit equations of product concentration vs. time. The other method involves the significant consumption of the substrate, yielding implicit equations of time vs. product concentration. The utility of both methods is discussed and adequate experimental conditions for their correct application are established.