The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Watershed scale temporal stability of soil water content

The recognition of temporally stable locations with respect to soil water content is of importance for soil water management decisions, especially in sloping land of watersheds. Neutron probe soil water content (0 to 0.8 m), evaluated at 20 dates during a year in the Loess Plateau of China, in a 20 ha watershed dominated by Ust-Sandiic Entisols and Aeolian sandy soils, were used to define their temporal stability through two indices: the standard deviation of relative difference (SDRD) and the mean absolute bias error (MABE). Specific concerns were (a) the relationship of temporal stability with soil depth, (b) the effects of soil texture and land use on temporal stability, and (c) the spatial pattern of the temporal stability. Results showed that temporal stability of soil water content at 0.2 m was significantly weaker than those at the soil depths of 0.6 and 0.8 m. Soil texture can significantly (P<0.05) affect the stability of soil water content except for the existence of an insignificant difference between sandy loam and silt loam textures, while temporal stability of areas covered by bunge needlegrass land was not significantly different from those covered by korshinsk peashrub. Geostatistical analysis showed that the temporal stability was spatially variable in an organized way as inferred by the degree of spatial dependence index. With increasing soil depth, the range of both temporal stability indices showed an increasing trend, being 65.8-120.5 m for SDRD and 148.8-214.1 m for MABE, respectively. This study provides a valuable support for soil water content measurements for soil water management and hydrological applications on sloping land areas. (C) 2010 Elsevier B.V. All rights reserved.

Why don`t our stands grow even faster? Control of production and carbon cycling in eucalypt plantations

The growth of Eucalyptus stands varies several fold across sites, under the influence of resource availability, stand age and stand structure. We describe a series of related studies that aim to understand the mechanisms that drive this great range in stand growth rates. In a seven-year study in Hawaii of Eucalyptus saligna at a site that was not water limited, we showed that nutrient availability differences led to a two-fold difference in stand wood production. Increasing nutrient supply in mid-rotation raised productivity to the level attained in continuously fertilised plots. Fertility affected the age-related decline in wood and foliage production; production in the intensive fertility treatments declined more slowly than in the minimal fertility treatments. The decline in stem production was driven largely by a decline in canopy photosynthesis. Over time, the fraction of canopy photosynthesis partitioned to below-ground allocation increased, as did foliar respiration, further reducing wood production. The reason for the decline in photosynthesis was uncertain, but it was not caused by nutrient limitation, a decline in leaf area or in photosynthetic capacity, or by hydraulic limitation. Most of the increase in carbon stored from conversion of the sugarcane plantation to Eucalyptus plantation was in the above-ground woody biomass. Soil carbon showed no net change. This study and other studies on carbon allocation showed that resource availability changes the fraction of annual photosynthesis used below-ground and for wood production. High resources (nutrition or water) decrease the partitioning below-ground and increase partitioning to wood production. Annual foliage and wood respiration and foliage production as a fraction of annual photosynthesis was remarkably constant across a wide range of fertility treatments and forest age. In the Brazil Eucalyptus Productivity Project, stand structure was manipulated by planting clonal Eucalyptus all at once or in three groups at three-monthly intervals, producing a stand where trees did not segregate into dominants and one that had strong dominance. The uneven stand structure reduced production 10-15% throughout the rotation.

Bait and Habitat Preferences, and Temporal Variability of Social Wasps (Hymenoptera: Vespidae) Attracted to Vertebrate Carrion

In addition to feeding on carrion tissues and fluids, social wasps can also prey on immature and adult carrion flies, thereby reducing their populations and retarding the decomposition process of carcasses. In this study, we report on the occurrence and behavior of social wasps attracted to vertebrate carrion. The collections were made monthly from September 2006 to October 2007 in three environments (rural, urban, and forest) in six municipalities of southeast Brazil, using baited bottle traps. We collected Agelaia pallipes (Olivier, 1791) (n = 143), Agelaia vicina (Saussure, 1854) (n = 106), Agelaia multipicta (Haliday, 1836) (n = 18), and Polybia paulista Ihering, 1896 (n = 3). The wasps were observed feeding directly on the baits and preying on adult insects collected in the traps. Bait and habitat associations, temporal variability of social wasps, and possible forensic implications of their actions are discussed.

Role of entomopathogenic fungi in the control of Tetranychus evansi and Tetranychus urticae (Acari: Tetranychidae), pests of horticultural crops

The spider mites Tetranychus urticae Koch and Tetranychus evansi Baker and Pritchard are important pests of horticultural crops. They are infected by entomopathogenic fungi naturally or experimentally. Fungal pathogens known to cause high infection in spider mite populations belong to the order Entomophthorales and include Neozygites spp. Studies are being carried out to develop some of these fungi as mycoacaricides, as standalone control measures in an inundative strategy to replace the synthetic acaricides currently in use or as a component of integrated mite management. Although emphasis has been put on inundative releases, entomopathogenic fungi can also be used in classical, conservation and augmentative biological control. Permanent establishment of an exotic agent in a new area of introduction may be possible in the case of spider mites. Conservation biological control can be achieved by identifying strategies to promote any natural enemies already present within crop ecosystems, based on a thorough understanding of their biology, ecology and behaviour. Further research should focus on development of efficient mass production systems, formulation, and delivery systems of fungal pathogens.

Drip fungigation in early blight control of tomato

The aim was to verify if the fungigation via drip irrigation is an alternative to the conventional method of spraying on tomato for controlling early blight. Tomato plants (variety Santa Clara) were grown in pots inside a greenhouse. Fifty days after transplanting, the plants were inoculated with Alternaria solani and treated with four different fungicides: azoxystrobin (8 g 100 L(-1)), difeconazole (50 mL 100 L(-1)), metiram+piraclostrobin (200 g 100 L(-1)) and tebuconazole (100 mL 100 L(-1)) using two applications methods: conventional spraying and fiingigation dripping. The control plants did not receive fungicide application. To assess the severity of the disease, we used a rating scale expressed as the area under the disease progress curve (AUDPC) and production factors, such as number, weight and average diameter of the fruit and its productivity. The experimental design was completely randomized in factorial scheme 4 x 2 + 1 with eight replicates. Each plot had one plant in one pot. A 27% reduction in disease severity was observed when compared with the control plants, with no significant difference noted regarding the application method. The number of fruits did not statistically differ between the treatments. The average weight and diameter of the fruits were superior in the plants that had fungicide application compared to the control plant, reflecting an increase in productivity. Fungigation through water dripping is an alternative to the conventional method of spraying cultured tomatoes.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Copper sprays and windbreaks for control of citrus canker on young orange trees in southern Brazil

The benefit of windbreaks and copper sprays for control of citrus canker caused by Xanthomonas axonopodis pv. citri was investigated in a commercial citrus orchard located in a citrus canker endemic area in southern Brazil. Control of canker was evaluated as incidence and severity of lesions on foliage and by the effect on premature leaf and fruit drop for three production seasons. Effect of the treatments on fruit production was evaluated as incidence of citrus canker on prematurely abscised fruits and harvested fruits. Copper application significantly reduced damage to foliage and fruit, while windbreaks made little contribution to disease control. Copper sprays increased fruit yield for 3 years. This could be attributed to lower incidence of fruit with lesions and fewer fruits abscised due to canker infection. Incidence and severity on the leaves were inversely related to the number of fruits harvested per tree and directly related to the number of fruits abscised per tree. Published by Elsevier Ltd.

Determination of the median lethal concentration (LC(50)) of mycoinsecticides for the control of Ceratitis capitata (Diptera: Tephritidae)

The aim of this study was to determine the median lethal concentration (LC(50)) of the commercial products Boveril WP (R) (Beauveria bassiana) and Metarril WP (R) (Metarhizium anisopliae) on the larvae and pupae of the fruit Ceratitis capitata. Insects used in this study came from a laboratory colony. The evaluated product concentrations were 10.00, 15.00, 20.00 and 25.00 g/L of water, which correspond, respectively, to 5.00x10(9), 7.50x10(9), 10.00x10(9) and 12.50x10(9) viable conidia/L of water for the two products, and in the control only water was applied. Third instar larvae and pupae of C. capitata were used in this study. Results showed an overall mortality of larvae with all conidial concentrations of M. anisopliae. The LC(50) values for larvae were 2.99 and 2.97 g/L for Boveril (R) and Metarril (R), respectively, while for pupae they were 3.12 and 4.74 g/L for Boveril (R) and Metarril (R), respectively. The high pathogenicity demonstrated by lower conidial concentrations of the tested products may mean greater efficiency from both economic and environmental points of view.

Ultra-Fast Gradient LC Method for Omeprazole Analysis Using a Monolithic Column: Assay Development, Validation, and Application to the Quality Control of Omeprazole Enteric-Coated Pellets

A method was optimized for the analysis of omeprazole (OMZ) by ultra-high speed LC with diode array detection using a monolithic Chromolith Fast Gradient RP 18 endcapped column (50 x 2.0 mm id). The analyses were performed at 30 degrees C using a mobile phase consisting of 0.15% (v/v) trifluoroacetic acid (TFA) in water (solvent A) and 0.15% (v/v) TFA in acetonitrile (solvent B) under a linear gradient of 5 to 90% B in 1 min at a flow rate of 1.0 mL/min and detection at 220 nm. Under these conditions, OMZ retention time was approximately 0.74 min. Validation parameters, such as selectivity, linearity, precision, accuracy, and robustness, showed results within the acceptable criteria. The method developed was successfully applied to OMZ enteric-coated pellets, showing that this assay can be used in the pharmaceutical industry for routine QC analysis. Moreover, the analytical conditions established allow for the simultaneous analysis of OMZ metabolites, 5-hydroxyomeprazole and omeprazole sulfone, in the same run, showing that this method can be extended to other matrixes with adequate procedures for sample preparation.

Antinociceptive and anti-inflammatory properties of 7-hydroxycoumarin in experimental animal models: potential therapeutic for the control of inflammatory chronic pain

Objectives In the present study we investigated the anti nociceptive, anti-inflammatory and antipyretic effects of 7-hydroxycoumarin (7-HC) in animal models. Methods The effects of oral 7-HC were tested against acetic acid-induced writhing, formalin test, tail flick test, complete Freund`s adjuvant (CFA)-induced hypemociception, carrageenan-induced paw oedema, lipopolysaccharide-induced fever and the rota rod test. Key findings 7-HC (3-60 mg/kg) produced a dose-related antinociception against acetic acid-induced writhing in mice and in the formalin test. In contrast, treatment with 7-HC did not prevent thermal nociception in the tail flick test. A single treatment with 7-HC, 60 mg/kg, produced a long-lasting antinociceptive effect against CFA-induced hypernociception, a chronic inflammatory pain stimulus. Notably, at 60 mg/kg per day over 4 days the administration of 7-HC produced a continuous antinociceptive effect against CFA-induced hypernociception. 7-HC (30-120 mg/kg) produced anti-inflammatory and antipyretic effects against carrageenan-induced inflammation and lipopolysaccharide-induced fever, respectively. Moreover, 7-HC was found to be safe with respect to ulcer induction. In the rota rod test, 7-HC-treated mice did not show any motor performance alterations. Conclusions The prolonged antinociceptive and anti-inflammatory effects of 7-HC, in association with its low ulcerogenic activity, indicate that this molecule might be a good candidate for development of new drugs for the control of chronic inflammatory pain and fever.