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The aim of this paper is to determine the optimal balance between extraction and storage of a natural resource (in particular crude oil) over time under a large array of environmental, operational and financial constraints for an infinite maturity time. We consider a manager that owns an oil field from which he can extract oil and decides to sell or store it. This operational strategy has to be carried out in continuous time and has to satisfy physical, operational, environmental and financial constraints such as storage capacity, crude oil spot price volatility, amount available for possible extraction or maximum amount that could be invested at time t for the extraction choice. The costs of storage and extraction are also taken into account to better fit the real market scenario. We solve the optimization problem of the manager’s profit under this large array of constraints and provide an optimal strategy. We then examine different numerical scenarios to check the robustness and the corresponding optimal strategies given by our model, which is obtained by a numerical approach, with respect to different possible events related to the market, environmental policies or ecological constraints.

We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments. Mathematics Subject Classification (2010): 65C30, 65M75, 60H35, 93E20, 49L25.

We investigate the impact of a regulation policy imposed on an agent exploiting a possibly renewable natural resource. We adopt a principal-agent model in which the Principal looks for a contract, i.e. taxes/compensations, leading the Agent to a certain level of exploitation. For a given contract, we first describe the Agent's optimal harvest using the BSDE theory. Under regularity and boundedness assumptions on the coefficients, we express almost optimal contracts as solutions to HJB equations. We then extend the result to coefficients with less regularity and logistic dynamics for the natural resource. We end by numerical examples to illustrate the impact of the regulation in our model., Comment: 7 figures

Since 1997, more than 600 individuals worldwide have been infected with the poultry-originating influenza, H5N1. This report describes the first case of avian influenza A (H5N1) in the Western hemisphere in a 28-year-old woman who had just returned from a trip to Beijing, China. The typical manifestations of H5N1 are described, and signs and symptoms are discussed., In an urban centre in Alberta, an otherwise healthy 28-year-old woman presented to hospital with pleuritic chest and abdominal pain after returning from Beijing, China. After several days, this was followed by headache, confusion and, ultimately, respiratory failure, coma and death. Microbiology yielded influenza A subtype H5N1 from various body sites and neuroimaging was consistent with meningoencephalitis. While H5N1 infections in humans have been reported in Asia since 1997, this is the first documented case of H5N1 influenza in the Western Hemisphere. The present case demonstrated the typical manifestation of H5N1 influenza but, for the first time, also confirmed previous suggestions from human and animal studies that H5N1 is neurotropic and can manifest with neurological symptoms and meningoencephalitis.

The relation between plasma levels of 25-hydroxyvitamin D3, the main metabolite of sun-induced vitamin D, and major coronary heart disease risk factors was examined in 295 men, aged 35 to 64 years, who were randomly sampled from the general population. Men who did regular vigorous leisure-time activity had a mean plasma 25-hydroxyvitamin D3 level that was 4.8 nmol/L (95% confidence limits: 0.1, 9.5) higher than that in inactive men, with the increase greatest in the winter months. Plasma 25-hydroxyvitamin D3 was positively associated with weekly hours of sun exposure (r = 0.27, P < 0.01), and showed a weak inverse association with age (r = -0.12, P < 0.05) and diastolic blood pressure (r = -0.15, P < 0.05), although this latter finding was no longer significant when allowance was made for the effects of age and season on vitamin D levels. In contrast, plasma 25-hydroxyvitamin D3 had no relation with either serum total or high-density-lipoprotein cholesterol levels, body mass index, or cigarette smoking. We hypothesize that vigorous leisure-time activity may protect against coronary heart disease, in part, by increasing body levels of vitamin D.

The relation between the plasma level of 25-hydroxyvitamin D3, the main metabolite of sun-induced vitamin D, and myocardial infarction (MI) was investigated in a community-based case-control study. Some 179 MI patients presenting to hospital within 12 hours of the onset of symptoms were individually matched with controls by age, sex and date of blood collection. MI patients had significantly lower mean 25-hydroxyvitamin D3 levels than controls (32.0 versus 35.5 nmol/L; p = 0.017), with the case-control differences being greatest in winter and spring. The relative risk of MI for subjects with 25-hydroxyvitamin D3 levels equal to or above the median was 0.43 (95% confidence limits = 0.27, 0.69) compared to subjects below the median. The decrease in MI risk associated with raised vitamin D3 levels was observed in all seasons. These results provide support for the hypothesis that increased exposure to sunlight is protective against coronary heart disease.

Purpose: To assess rhe susceptibility of human squamous cell carcinoma to reovirus infection in vitro and in vivo using amurine model of cancer-contaminated wounds.Methods: The University of Michigan squamous carcinoma 22B cell line was cultured and inoculated with reovirus In vitro.The effect of the reovirus was assessed with microscopy and a standard 3-(4,5-dimethyi-2-thiazolyl)--2.,5-diphenyl-2H tetra-zolium bromide (MTT) assay. We used the previously established cancer-contaminated wound SCID mouse model to testsaline and reovirus irrigation in vivo. Fifty-five mice were used; 15 were controls., 20 had immediate irrigation, and 20 haddelayed irrigation. Surgical sites were assessed for palpable tumour biweekly.Results: The microscopy and MTT assay both showed evidence of reovirus-mediated squamous cancer cell lysis. The controlmice grew palpable tumours in 80% of the wounds. Immediate irrigation with saline delayed the onset of palpable tumourand demonstrated a persistent reduction in the rate of development of palpable rtJtTiours Ip = .004 compared with controls).This effect disappeared when the saline irrigation was delayed, resulting in a tumour development rate that was not signifi-cantly different from that of the control. Wounds that were irrigated wirh reovirus, both immediately and delayed, did notproduce palpable tumour (p < .0005 when compared with controls).Conclusions: (1) The University of Michigan squamous cell carcinoma 22B cell line is susceptible ro reovirus in vitro. (2)Immediate irrigation with saline resulted in a significant delay in clinically evident tumour growth and a reduction in therate of rumour development in the SCID mouse model. (3) The reovirus irrigation resulted in a significant reduction oftumour development in both the immediate and delayed groups in the SCID mouse model. (4) The efficacy of the reovirusirrigation in the delayed group suggests that the major mechanism of action is through a selective and specific targeting ofimplanted cancer cells.