The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε>0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples. Our approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that aren't necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art

Transfer and accumulation of cadmium, and the level of metallothionein in perfused human placentae.

The purpose of the present study was to investigate the effect of perfusion with a medium containing 12 or 24 micrograms Cadmium (as CdCl2) per ml on this metal's accumulation, transfer rate and metallothionein (MT) level. The experiments were performed with an isolated lobule of a dually-perfused human term placenta. Placental cell integrity and viability were characterised by their morphology and metabolic function, manifested in the tissue's electron microscopic structure and glucose and oxygen (O2) consumption, respectively. Perfusion with 24 micrograms Cd/ml medium for 5 h resulted in significant elevation in MT. The transfer rate of Cd to the fetal side of the placenta was very slow, and not until 40 min after the addition of Cd into the maternal side was a significant increase in the metal's level observed in the fetal perfusate. Thereafter, the level of the metal increased gradually and reached a steady state about 1 h later, at a level which was less than 1/20th of its concentration in the maternal perfusate. There was a 60-fold increase in Cd level in the cytosolic fraction obtained from the Cd-treated samples. At 12 micrograms Cd/ml no significant changes were noted in morphology, metabolic function and MT content. None of the Cd levels caused a significant change in O2 and glucose consumption, in spite of the fact that with the higher Cd dose the microstructure of the tissue showed some pathological changes. The observed elevation in MT may provide the fetus some protection against the harmful effects of the metal