Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior

Proteins of Leishmania (Viannia) shawi confer protection associated with Th1 immune response and memory generation

<p>Abstract</p> <p>Background</p> <p><it>Leishmania (Viannia) shawi </it>parasite was first characterized in 1989. Recently the protective effects of soluble leishmanial antigen (SLA) from <it>L. (V.) shawi </it>promastigotes were demonstrated using BALB/c mice, the susceptibility model for this parasite. In order to identify protective fractions, SLA was fractionated by reverse phase HPLC and five antigenic fractions were obtained.</p> <p>Methods</p> <p>F1 fraction was purified from L. (V.) shawi parasite extract by reverse phase HPLC. BALB/c mice were immunized once a week for two consecutive weeks by subcutaneous routes in the rump, using 25 μg of F1. After 1 and 16 weeks of last immunization, groups were challenged in the footpad with L. (V.) shawi promastigotes. After 2 months, those same mice were sacrificed and parasite burden, cellular and humoral immune responses were evaluated.</p> <p>Results</p> <p>The F1 fraction induced a high degree of protection associated with an increase in IFN-γ, a decrease in IL-4, increased cell proliferation and activation of CD8⁺T lymphocytes. Long-term protection was acquired in F1-immunized mice, associated with increased CD4⁺central memory T lymphocytes and activation of both CD4⁺and CD8⁺T cells. In addition, F1-immunized groups showed an increase in IgG2a levels.</p> <p>Conclusions</p> <p>The inductor capability of antigens to generate memory lymphocytes that can proliferate and secrete beneficial cytokines upon infection could be an important factor in the development of vaccine candidates against American Tegumentary Leishmaniasis.</p