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.

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.

Characterization of electrical penetration graphs of Bucephalogonia xanthophis, a vector of Xylella fastidiosa in citrus

The sharpshooter Bucephalogonia xanthophis (Berg) (Homoptera: Cicadellidae) is a vector of the xylem-limited bacterium, Xylella fastidiosa (Wells, Raju, Hung, Weisburg, Mandelco-Paul, and Brenner), which causes citrus variegated chlorosis. Despite the importance of citrus variegated chlorosis, the probing behavior of vectors on citrus and its implications for transmission of X. fastidiosa have not been studied. Here we studied electrical penetration graph (EPG-DC system) waveforms produced by B. xanthophis on Citrus sinensis (L.) Osbeck (Rutaceae), and their relationships with stylet activities and xylem ingestion. Electrical penetration graph waveforms were described based on amplitude, frequency, voltage level, and electrical origin of the observed traces during stylet penetration on plant tissues. The main waveforms were correlated with histological observations of salivary sheaths in plant tissues and excretion analysis, in order to determine stylet activities and their precise position. Six waveforms and associated activities are described: (S) secretion of salivary sheath and intracellular stylet pathway, (R) resting during stylet pathway, (Xc) contact of stylets with xylem vessels, (Xi) active xylem ingestion, (N) interruption within the xylem phase (during Xc or Xi), and (W) withdrawal of stylet from the plant. The sharpshooter spent 91.8% of its probing time with its stylet in the xylem, where the main activity was ingestion (Xi: 97.5%). During a probe, the most likely sequence of events is secretion of salivary sheath and pathway (S) through epidermal and parenchyma cells (all individuals), followed by contact with xylem (Xc) (67.6% of all individuals) and ingestion (Xi) (88.3% of those that exhibit waveform Xc). The mean time to contact the xylem (Xc) and initiate ingestion (Xi) after onset of the first probe was 27.8 and 34.2 min, respectively. However, sustained xylem ingestion (Xi > 5 min) was established after 39.8 min, on average. This information is basic for future studies on the transmission mechanisms of X. fastidiosa and in order to establish control strategies aimed at interfering with this process.

Vector within-host feeding preference mediates transmission of a heterogeneously distributed pathogen

2. We documented the within-host distribution of two vector species that differ in transmission efficiency, the leafhoppers Draeculacephala minerva and Graphocephala atropunctata, and which are free to move throughout entirely caged alfalfa plants. The more efficient vector D. minerva fed preferentially at the base of the plant near the soil surface, whereas the less efficient G. atropunctata preferred overwhelming the top of the plant. 3. Next we documented X. fastidiosa heterogeneity in mechanically inoculated plants. Infection rates were up to 50% higher and mean bacterial population densities were 100-fold higher near the plant base than at the top or in the taproot. 4. Finally, we estimated transmission efficiency of the two leafhoppers when they were confined at either the base or top of inoculated alfalfa plants. Both vectors were inefficient when confined at the top of infected plants and were 20-60% more efficient when confined at the plant base. 5. These results show that vector transmission efficiency is determined by the interaction between leafhopper within-plant feeding behaviour and pathogen within-plant distribution. Fine-scale vector and pathogen overlap is likely to be a requirement generally for efficient transmission of vector-borne pathogens.

Endophytic population of Pantoea agglomerans in citrus plants and development of a cloning vector for endophytes

Harmless bacteria inhabiting inner plant tissues are termed endophytes. Population fluctuations in the endophytic bacterium Pantoea agglomerans associated with two species of field cultured citrus plants were monitored over a two-year period. The results demonstrated that populations of P. agglomerans fluctuated in Citrus reticulata but not C. sinensis. A cryptic plasmid pPA3.0 (2.9 kb) was identified in 35 out of 44 endophytic isolates of P. agglomerans and was subsequently sequenced. The origins of replication were identified and nine out of 18 open reading frames (ORFs) revealed homology with described proteins. Notably, two ORFs were related to cellular transport systems and plasmid maintenance. Plasmid pPA3.0 was cloned and the gfp gene inserted to generate the pPAGFP vector. The vector was introduced into P. agglomerans isolates and revealed stability was dependent on the isolate genotype, ninety-percent stability values were reached after 60 hours of bacterial cultivation in most evaluated isolates. In order to definitively establish P. agglomerans as an endophyte, the non-transformed bacterium was reintroduced into in vitro cultivated seedlings and the density of inner tissue colonization in inoculated plants was estimated by bacterium re-isolation, while the tissue niches preferred by the bacterium were investigated by scanning electronic microscopy (SEM). Cells from P. agglomerans (strain ARB18) at similar densities were re-isolated from roots, stems and leaves and colonization of parenchyma and xylem tissues were observed. Data suggested that P. agglomerans is a ubiquitous citrus endophyte harboring cryptic plasmids. These characteristics suggest the potential to use the bacterium as a vehicle to introduce new genes in host plants via endophytic bacterial transformation.

Use of virtual screening, flexible docking, and molecular interaction fields to design novel HMG-CoA reductase inhibitors for the treatment of hypercholesterolemia

Dietary changes associated with drug therapy can reduce high serum cholesterol levels and dramatically decrease the risk of coronary artery disease, stroke, and overall mortality. Statins are hypolipemic drugs that are effective in the reduction of cholesterol serum levels, attenuating cholesterol synthesis in liver by competitive inhibition regarding the substrate or molecular target HMG-CoA reductase. We have herewith used computer-aided molecular design tools, i.e., flexible docking, virtual screening in large data bases, molecular interaction fields to propose novel potential HMG-CoA reductase inhibitors that are promising for the treatment of hypercholesterolemia.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Modifying insect population age structure to control vector-borne disease

Age is a critical determinant of the ability of most arthropod vectors to transmit a range of human pathogens. This is due to the fact that most pathogens require a period of extrinsic incubation in the arthropod host before pathogen transmission can occur. This developmental period for the pathogen often comprises a significant proportion of the expected lifespan of the vector. As such, only a small proportion of the population that is oldest contributes to pathogen transmission. Given this, strategies that target vector age would be expected to obtain the most significant reductions in the capacity of a vector population to transmit disease. The recent identification of biological agents that shorten vector lifespan, such as Wolbachia, entomopathogenic fungi and densoviruses, offer new tools for the control of vector-borne diseases. Evaluation of the efficacy of these strategies under field conditions will be possible due to recent advances in insect age-grading techniques. Implementation of all of these strategies will require extensive field evaluation and consideration of the selective pressures that reductions in vector longevity may induce on both vector and pathogen.

Evidence of a spotted fever-like rickettsia and a potential new vector from northeastern Australia

A spotted fever-like rickettsia was identified in a Hemaphysalis tick by polymerase chain reaction (PCR) amplification and sequencing of the 16S rDNA, ompA, and ompB genes. A comparison of these nucleotide sequences with those of other spotted fever group (SFG) rickettsiae revealed that the Hemaphysalis tick rickettsia was distinct from other previously reported strains. Phylogenetic analysis based on both ompA and ompB also indicates that the strain’s closest relatives are the agents of Thai tick typhus (Rickettsia honei strain TT-118) and Flinders Island spotted fever (R. honei). This study represents the first report of an R. honei-like agent from a Hemaphysalis tick in Australia and of a spotted fever group rickettsia from Cape York Peninsula, Queensland.

Field prevalence of Wolbachia in the mosquito vector Aedes albopictus

The endosymbiotic bacteria in the genus Wolbachia have been proposed as a potential candidate to deliver pathogen-blocking genes into natural populations of medically important insects. The successful application of Wolbachia in insect vector control depends on the ability of the agent to successfully invade and maintain itself at high frequency under field conditions. Here, we evaluated the prevalence of Wolbachia infections in a field population of the Wolbachia-superinfected mosquito Aedes albopictus. A field prevalence of 100% (n = 1,016) was found in a single population in eastern Thailand via polymerase chain reaction (PCR) testing of Wolbachia both from individual parent females and their corresponding F1 offspring. This is the first report of accurate Wolbachia prevalence in a field population of an insect disease vector. The prevalence of superinfection was estimated to be 99.41%. All single-infected individual mosquitoes (n = 6) were found to harbor group A Wolbachia. For this particular population, none was found to be single-infected with group B Wolbachia. Our results also show that PCR testing of field materials alone without checking F1 offspring overestimated the natural prevalence of single infection. Thus, the confirmation of infection status by means of F1 offspring was critical to the accurate estimates of Wolbachia prevalence under field conditions.

Prospects for control of African trypanosomiasis by tsetse vector manipulation

The extensive antigenic variation phenomena African trypanosomes display in their mammalian host have hampered efforts to develop effective vaccines against trypanosomiasis. Human disease management aims largely to treat infected hosts by chemotherapy, whereas control of animal diseases relies on reducing tsetse populations as well as on drug therapy. The control strategies for animal diseases are carried out and financed by livestock owners, who have an obvious economic incentive. Sustaining largely insecticide-based control at a local level and relying on drugs for treatment of infected hosts for a disease for which there is no evidence of acquired immunity could prove extremely costly in the long run. It is more likely that a combination of several methods in an integrated, phased and area-wide approach would be more effective in controlling these diseases and subsequently improving agricultural output. New approaches that are environmentally acceptable, efficacious and affordable are clearly desirable for control of various medically and agriculturally important insects including tsetse. Here, Serap Aksoy and colleagues discuss molecular genetic approaches to modulate tsetse vector competence.

Semliki Forest virus as an expression vector in insect cell lines

Studies were undertaken to determine if replication-deficient Semliki Forest virus expression vectors could be successfully used to express foreign gene constructs in insect cell lines. Using green fluorescent protein (GFP) as a marker we recorded infection levels of nearly 100% in the Aedes albopictus cell lines C6/36 and Aa23T, as well as in the Ae. aegypti cell line MOS20. The virus was capable of infecting an Anopheles gambiae cell line MOS55. The amount of GFP protein produced in each cell line was quantified. Northern analysis of viral transcription revealed the presence of novel transcripts in Aa23T, C6/36, and MOS55 cell lines, but not in the BHK or MOS20. The initial characterization of these transcripts is described.

Control of vector-borne disease by genetic manipulation of insect populations: technological requirements and research priorities

The possibility of controlling vector-borne disease through the development and release of transgenic insect vectors has recently gained popular support and is being actively pursued by a number of research laboratories around the world. Several technical problems must be solved before such a strategy could be implemented: genes encoding refractory traits (traits that render the insect unable to transmit the pathogen) must be identified, a transformation system for important vector species has to be developed, and a strategy to spread the refractory trait into natural vector populations must be designed. Recent advances in this field of research make it seem likely that this technology will be available in the near future. In this paper we review recent progress in this area as well as argue that care should be taken in selecting the most appropriate disease system with which to first attempt this form of intervention. Much attention is currently being given to the application of this technology to the control of malaria, transmitted by Anopheles gambiae in Africa. While malaria is undoubtedly the most important vector-borne disease in the world and its control should remain an important goal, we maintain that the complex epidemiology of malaria together with the intense transmission rates in Africa may make it unsuitable for the first application of this technology. Diseases such as African trypanosomiasis, transmitted by the tsetse fly, or unstable malaria in India may provide more appropriate initial targets to evaluate the potential of this form of intervention.

Modification of arthropod vector competence via symbiotic bacteria

Some of the world's most devastating diseases are transmitted by arthropod vectors. Attempts to control these arthropods are currently being challenged by the widespread appearance of insecticide resistance. It is therefore desirable to develop alternative strategies to complement existing methods of vector control. In this review, Charles Beard, Scott O'Neill, Robert Tesh, Frank Richards and Serap Aksoy present an approach for introducing foreign genes into insects in order to confer refractoriness to vector populations, ie. the inability to transmit disease-causing agents. This approach aims to express foreign anti-parasitic or anti-viral gene products in symbiotic bacteria harbored by insects. The potential use of naturally occurring symbiont-based mechanisms in the spread of such refractory phenotypes is also discussed.