We show that for any integer p ≥ 46, the Shortest Vector Problem in `p norm is hard to approximate within factor (4/3)1−45.7/p. We also show a hardness factor of (3/2)1−111.7/p for p ≥ 112. As p grows, these factors approach 4/3 and 3/2 respectively. Both results hold under the assumption NP 6⊆ ZPP. We give a very simple reduction from known hardness results for Hypergraph Independent Set Probl...

Recently, Watanabe proposed a framework for testing the correctAbstract-1 ness and average-case performance of algorithms that purport to solve a given NP search problem efficiently on average with respect to some distribution on the instances. The idea is to randomly generate certified instances under some distribution that resembles the input distribution. Watanabe showed that unless RE = NE,...

We evaluated the incidence of all-cause and malaria-specific clinic visits during follow-up of a recent trial of iron therapy. In the main trial, Ugandan children 6-59 months with smear-confirmed malaria and iron deficiency [zinc protoporphyrin (ZPP > = 80 μmol/mol heme)] were treated for malaria and randomized to start a 27-day course of oral iron concurrently with (immediate group) or 28 days...

Are there too many complexity classes? Merely trying to understand one aspect of computation, such as the power of randomness, leads to a whole range of complexity classes, such as ZPP, RP, and BPP, to name but a few. Do we really need all of these classes? One of the most exciting developments in complexity theory in the past few years is the growing body of evidence that all of the aforementi...

Maternal iron status is thought to be related to postpartum depressive symptoms. The purpose of the present study was to evaluate the relationship between pre- and postnatal maternal iron status and depressive symptoms in pilot (n = 137) and confirmatory (n = 567) samples of Chinese women. Iron status was evaluated at mid- and late pregnancy and 3 days postpartum. The Edinburgh Postnatal Depres...

Alcohol has been shown to interact with lead to influence haem biosynthesis. The aim of this study was to define the dependence of this interaction on the degree of exposure to lead. Exposure to alcohol was estimated by measurement of alcohol concentrations in a sample of urine collected during the morning (AlcUM) (0.82 (SD 4.36) mmol/l) and in a sample collected during the afternoon (AlcUA) (1...

Prolyl oligopeptidase (POP), a member of the prolyl endopeptidase family, is known to play a role in several neurological disorders. Its primary function is to cleave a wide range of small oligopeptides, including neuroactive peptides. We have used force biased molecular dynamics simulation to study the binding mechanism of POP. We examined three possible binding pathways using Steered Molecula...

The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graphG(V,E) is an assignment function : V → N such that | (u)− (v)| 2, when u, v are neighbors in ...

We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log(1/ε)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2n with error bounded by ε. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations wit...