Natural Boundaries and Spectral Theory

We present and exploit an analogy between lack of absolutely continuous spectrum for Schroedinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples for random power series where independence is not assumed

Landslide Denied: Exit Polls vs. Vote Count 2006

There was an unprecedented level of concern approaching the 2006 Election ("E2006") about the vulnerability of the vote counting process to manipulation. With questions about the integrity of the 2000, 2002 and 2004 elections remaining unresolved, with e-voting having proliferated nationwide, and with incidents occurring with regularity through 2005 and 2006, the alarm spread from computer experts to the media and the public at large. It would be fair to say that America approached E2006 with held breath.For many observers, the results on Election Day permitted a great sigh of relief -- not because control of Congress shifted from Republicans to Democrats, but because it appeared that the public will had been translated more or less accurately into electoral results, not thwarted as some had feared. There was a relieved rush to conclude that the vote counting process had been fair and the concerns of election integrity proponents overblown.Unfortunately the evidence forces us to a very different and disturbing conclusion: there was gross vote count manipulation and it had a great impact on the results of E2006, significantly decreasing the magnitude of what would have been, accurately tabulated, a landslide of epic proportions. Because much of this manipulation appears to have been computer-based, and therefore invisible to the legions of at-the-poll observers, the public was informed of the usual "isolated incidents and glitches" but remains unaware of the far greater story: The electoral machinery and vote counting systems of the United States did not honestly and accurately translate the public will and certainly can not be counted on to do so in the future

High concentration of 28,30-bisnorhopane and 25,28,30-trisnorhopane at the PETM in the Faroe-Shetland basin

Petroleum exploration in the Faroe-Shetland basin has resulted in the drilling of wells some of which contain expanded sections across the Palaeocene Eocene thermal maximum event (PETM). Here we present data from a Faroe – Shetland Basin well. Samples analysed have a mixture of terrestrial and marine inputs. PETM events, are recorded in both bulk and compound specific carbon isotope excursions of 2-3'. In addition, the PETM is marked by a change in palynology and we have observed changes in the distribution of biomarkers across the PETM and recognise a sharply defined spike in 25,28,30- trisnorhopane (TNH) and 28,30-bisnorhopane (BNH) concentrations at the PETM boundary. Firstly, while we have been able to identify variation in a range of compounds present in the core, their variation reassuringly mostly follow associated palynological changes. Demethylated hopanes 28,30-bisnorhopane (BNH) and 25,28,30-trisnorhopane (TNH), are present in relatively low concentrations just below and above the carbon isotope excursion (CIE), but in high concentrations at the PETM (Fig 1). The actual bacteria responsible for TNH and BNH in geological samples has so far not been determined [1]. However, BNH and TNH are thought to be produced by chemoautotrophic bacteria, their presence in rocks which formed in inner neritic environments may indicate strong upwelling or perhaps ocean overturn. Extreme shallowing of the CCD is well documented at the PETM, but there has previously been no clear indicator for a potential ocean overturn, although this has previously been mentioned as a potential driver for the event. While this has been dismissed as a mechanism driving the PETM events because it was envisaged as a local basin overturn, and can not explain the global extent of the PETM [2], we propose that the presence of TNH and BNH indicates ocean overturn may have played a role in the PETM. While it may not explain the isotopically light carbon in its entirety, stratification and ocean overturn may be a consequence of high temperatures, since palynological evidence indicates very low salinity conditions in surface waters at the PETM

Effective three-body interactions via photon-assisted tunneling in an optical lattice

We present a simple, experimentally realizable method to make coherent three-body interactions dominate the physics of an ultracold lattice gas. Our scheme employs either lattice modulation or laser-induced tunneling to reduce or turn off two-body interactions in a rotating frame, promoting three-body interactions arising from multi-orbital physics to leading-order processes. This approach provides a route to strongly-correlated phases of lattice gases that are beyond the reach of previously proposed dissipative three-body interactions. In particular, we study the mean-field phase diagram for spinless bosons with three- and two- body interactions, and provide a roadmap to dimer states of varying character in 1D. This new toolset should be immediately applicable in state-of-the-art cold atom experiments.Comment: 11 pages, 6 figure