Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The chance constraint is then required to hold for all distributions that are close to the empirical distribution constructed from the samples (where the distance between two distributions is defined via the Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein ambiguity sets and a general class of constraint functions. When the feasibility set of the chance constraint program is replaced by its convex inner approximation, we present a convex reformulation of the program and show its tractability when the constraint function is affine in both the decision variable and the uncertainty. For constraint functions concave in the uncertainty, we show that a cutting-surface algorithm converges to an approximate solution of the convex inner approximation of DRCCPs. Finally, for constraint functions convex in the uncertainty, we compare the feasibility set with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference, 201

The durability of oral diabetic medications: Time to A1c baseline and a review of common oral medications used by the primary care provider.

Introduction:Cost of generic medications has risen more in the past few years than any other time in history. While medical insurance covers much of these costs, health care professionals can better provide medications that have the longest duration of action when compared to placebo-treated controls. This will save health care costs and improve prescribing accuracy. Methods:Papers in PubMed were identified with keywords placebo. The study must be at least 2 years in length to evaluate the change in A1c over time. The primary endpoint was time to A1c neutrality (return of A1c to baseline at a maximum dose of single oral agent). A medication would be considered at neutrality if the 95% CI crossed baseline. Time to neutrality was averaged for each medication within the class and each summarized for class effect. Results:Effective therapy for the DPP-4 and sulfonylurea classes of medications are 3-4 years as compared to a 5-year time to A1c neutrality for metformin usage. In comparison, the projected time to A1c neutrality was approximately 6-8 years for rosiglitazone and pioglitazone. While only a few studies have been published in the SGLT-2 class of medication, the time to A1c neutrality was also 6-8 years with Canagliflozin and full dosage of Empagliflozin. Conclusion:Metformin appears to have a 5-year duration of effect before the A1c returns to baseline. The sulfonylureas and DPP-4 inhibitors class of medications have one of the shortest durability which ranges between 3.3 to 4.4 years. In contrast, the SGLT-2 class of medication and the TZD class of medications has a projected time to A1c neutrality from 6-8 years. Diabetic duration of therapy as compared to placebo should be listed with those medications tested so the provider can choose wisely

The Role of Breastfeeding in Mother-to-Child Transmission of HIV/AIDS: A Comparative Case Study of Three Countries

The HIV pandemic has affected millions of people around the world both medically and socially, since there is a stigma associated with this disease. Common methods of transmission include sexual intercourse and sharing needles, but there are other lesser known methods through which people can contract this disease. One such way is mother-to-child transmission (MTCT), in which a mother could transmit the virus to her child either during pregnancy, childbirth, or through breastfeeding. This paper focuses on the role of breastfeeding in the transmission of HIV from mother to child. Many studies have investigated how breastfeeding results in the transmission of the virus, and effective common treatment methods have been established. However, the issue of MTCT of HIV still exists even though it can easily be eradicated with the proper techniques. This suggests that there are still factors that contribute to HIV transmission from mother to child that have yet to be eliminated. Thus, this paper reviews the breastfeeding rates and breastfeeding practices of three different countries: South Africa, India, and the United Kingdom. This paper analyzes epidemiological data, studies from medical journals, and studies from anthropology journals to determine what social influences surround breastfeeding practices in each of these countries to see how these may contribute to MTCT of HIV via breastfeeding. While there were no apparent trends between child HIV prevalence rates and breastfeeding rates in these countries, there were some social and cultural factors that were similar across all three nations. This information may be useful in creating more effective treatment plans that are conducive to the social environments in these countries

Land/Water Interface Delineation Using Neural Networks.

The rapid decline in acreage of land areas in wetlands caused by frequent inundations and flooding has brought about an increased awareness and emphasis on the identification and inventory of land and water areas. This dissertation evaluates three classification methods--Normalized Difference Vegetation Index technique, Artificial Neural Networks, and Maximum-Likelihood classifier for the delineation of land/water interface conditions using Landsat-TM imagery. The effects of three scaling algorithms, including resampling by aggregation, Gaussian smoothing, and local variance analysis, on the classification accuracy are analyzed to determine how the delineation, quantification and analysis of land/water boundaries relate to problems of mixed pixels, scale and resolution. Bands 3, 4, and 5 of a Landsat TM image from Huntsville, Alabama were used as a multispectral data set, and ancillary data included USGS 7.5 minute Digital Line Graphs for classification accuracy assessment. The 30 m resolution multispectral imagery was used as baseline data and the images were degraded to a series of resolution levels and Gaussian smoothed through various scaling constants to simulate images of coarser resolution. Local variance was applied at each aggregation and scaling level to analyze the textural pattern. Classifications were then performed to delineate land/water interface conditions. To study effects of scale and resolution on the land/water boundaries delineated, overall percent classification accuracies, fractal analysis (area-perimeter relationships), and lacunarity analysis were applied to identify the range of spatial resolutions within which land/water boundaries were scale dependent. Results from maximum-likelihood classifier indicate that the method marginally produced higher overall accuracies than either NDVI or neural network methods. Effects from applying the three scaling algorithms indicate that overall classification accuracies decrease with coarser resolution, increase marginally with scaling constant, and vary non-linearly with local variance mask sizes. It was discovered that the application of Gaussian smoothing to neural network classifier produces very encouraging results in classifying the transition zone between land and water (mixed pixels) areas. Fractal analysis on the classified images indicates that coarser resolutions, higher scaling constants and higher degrees of complexity, wiggliness or contortion of the perimeter of water polygons span higher ranges of fractal dimension. As the water polygons become more complex, the perimeter becomes increasingly plane filling. From the changes in fractal dimension, lacunarity analysis and local variance analysis, it is observed that at 150 m, a peak value of measured index is obtained, before dropping off. This suggests that at 150 m, the aggregated water bodies shift to a different \u27characteristic\u27 scale and the water features formed are smooth, compact, have more regular boundaries and form connected regions. This scale dependence phenomenon can help to optimize efficient data resampling methodologies