We prove that poly-sized AC0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07, Baz09], who showed that O(logn)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazz...

In trying to improve Weinstock's results on approximation by holomorphic functions on certain product domains, we are led to estimates in Sobolev spaces for the ∂-operator on polycylinders for (γ, q)-forms. This generalizes our results for the same operator on poly-cylinders previously obtained, and can be applied to a number of other problems such as the Corona problem. 1. Introduction. Had we...

Triclosan, a widely used antimicrobial, is known to undergo phototransformation in aqueous solution to form 2,8-dichlorodibenzo-p-dioxin (2,8-DCDD). Two sediment cores from a wastewater-impacted depositional zone of the Mississippi River were analyzed for triclosan by ultra performance liquid chromatography-triple quadrupole mass spectrometry (UPLC-MS-Q(3)) and for a suite of polychlorinated di...

We prove that any Resolution proof for the weak pigeon hole principle, with n holes and any number of pigeons, is of length (2 n), (for some global constant > 0). One corollary is that a certain propositional formulation of the statement N P 6 6 P =poly does not have short Resolution proofs.

It is shown that, with respect to a random oracle, EXP \ P=poly and EXP ? P=poly do not have resource-bounded measure zero in EXP:

OBJECTIVES Inconsistent epidemiological findings, debate over interpretation, and extrapolation of findings from animal studies to humans have produced uncertainty surrounding the carcinogenicity of trichloroethylene (TCE) exposure in occupational settings. We updated meta-analyses of published case-control and cohort studies exploring occupational TCE exposure and kidney cancer risk, incorpora...

Many commonly-used auction mechanisms are “maximal-in-range”. We show that any maximalin-range mechanism for n bidders and m items cannot both approximate the social welfare with a ratio better than min(n,m) for any constant η < 1/2 and run in polynomial time, unless NP ⊆ P/poly. This significantly improves upon a previous bound on the achievable social welfare of polynomial time maximal-in-ran...