Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Intrathecal Ziconotide in the Treatment of Chronic Nonmalignant Pain: A Randomized,Double‐Blind,Placebo‐Controlled Clinical Trial

Objective. The safety and efficacy of intrathecal (IT) ziconotide was studied in a randomized, double‐blind, placebo‐controlled trial. Materials and Methods. Patients (169 ziconotide, 86 placebo) with severe chronic nonmalignant pain unresponsive to conventional therapy and a visual analog scale of pain intensity (VASPI score) ≥ 50 mm were treated over a 6‐day period in an inpatient hospital setting. Initial starting dose was 0.4 µg/hour and was titrated to analgesia or intolerance (maximum dose 7.0 µg/hour). The starting and maximum doses were reduced to 0.1 µg/hour and 2.4 µg/hour, respectively, due to adverse events (AEs). Results. The mean percent reduction in VASPI score from baseline was 31.2% and 6.0% for ziconotide‐ and placebo‐treated patients, respectively (p ≤ 0.001). During the initial titration phase, a significantly greater percentage of patients in the ziconotide group compared to the placebo group reported AEs, including abnormal gait, amblyopia, dizziness, nausea, nystagmus, pain, urinary retention, and vomiting. Conclusion. Ziconotide provided significant analgesia in patients for whom conventional therapy failed. However, there was a considerable incidence of ziconotide‐associated AEs due to the rapid titration and high doses administered.     

Identifying Risk Drinking in Expectant Fathers

Abstract: Background: Identification of risk drinking in expectant fathers may be helpful as an important part of efforts to minimize maternal alcohol use, and as an opportunity to inform them about a problematic practice during a critical developmental stage for the couple. The purpose of this study was to evaluate the T‐ACE screening questionnaire, which asks about t olerance to alcohol, being a nnoyed by other's comments about drinking, attempts to c ut down, and having a drink first thing in the morning (“ e ye‐opener”), in the male partners of pregnant women who themselves were T‐ACE positive. Methods: Two hundred fifty‐four male partners were asked to complete the T‐ACE embedded in a health survey, the Alcohol Use Disorders Identification Test (AUDIT), and other questions about their alcohol use in the past 30 days when their pregnant partners had a median gestation of 11.5 weeks (T₁). After delivery, male partners again completed the T‐ACE and quantity‐frequency questions (T₂). The predictive ability of the T‐ACE and AUDIT was compared, using risk drinking (>4 drinks/day or >14 drinks/week) as the criterion standard. Results: A substantial minority of male partners had risk drinking, 31 percent at T₁ and 25 percent at T₂. Although the AUDIT was better than the T‐ACE as an independent predictor of risk drinking, the latter was most accurate when the tolerance threshold exceeded 2 drinks, the same established for pregnant women. The sensitivity (T₁ = 84.6%, T₂ = 82.8%) and specificity (T₁ = 43.8%, T₂ = 51.1%) of the T‐ACE at this threshold compared favorably with those of the AUDIT at the standard cut point of 8. Conclusions: The T‐ACE may be a practical way for clinicians to identify risk drinking in both pregnant women and expectant fathers. (BIRTH 33:2 June 2006)     

Dry skin in dermatology: a complex physiopathology

Dry skin (xerosis) is a common dermatosis affecting people of varying skin types and ages and various areas of the body. It is associated with both skin thickening and skin thinning and is triggered by both exogenous (e.g. climate, environment, lifestyle) and endogenous (e.g. medication, hormone fluctuations, organ diseases) factors. Skin requires a water content of 10–15% to remain supple and intact. This water is either ‘static’ (i.e. bound) or ‘dynamic’. The predominance of hydrophobic substances in intercellular constituents is a means of regulating the humidity of the skin. Emollients, highly effective treatment adjuncts in the management of all dry skin disorders, help to restore damaged intercorneocyte lipid structures and increase the water content of the skin, helping to reduce scaling and improving its barrier function.     

Localized bullous pemphigoid in a patient with primary lymphoedema tarda

We report a case of localized bullous pemphigoid (BP) in a woman patient with primary lymphoedema tarda. There is only one previous case reported of localized pemphigoid in an area of lymphoedema, this being of the cicatricial variant. Slow circulation in the lymphatic vessels, increased capillary permeability with preferential localization of antibodies in the area, and potential cleavage of the epidermal junction due to increased hydrostatic pressure leading to autoimmunity, have all been advocated as possible pathogenic mechanisms. Nevertheless, we consider that the mechanism by which localized pemphigoid arises on lymphoedema remains elusive, based on a previous case of generalized BP sparing an area of postsurgical lymphoedema.