Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Generalized uncertainty inequalities

In this paper, Heisenberg-Pauli-Weyl-type uncertainty inequalities are obtained for a pair of positive-self adjoint operators on a Hilbert space, whose spectral projectors satisfy a ``balance condition'' involving certain operator norms. This result is then applied to obtain uncertainty inequalities on Riemannian manifolds, Riemannian symmetric spaces of non-compact type, homogeneous graphs and unimodular Lie groups with sublaplacians.Comment: 19 page

Mirror Symmetry and Other Miracles in Superstring Theory

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many string theorists in fact espouse. String theory leads to many surprising, useful, and well-confirmed mathematical 'predictions' - here I focus on mirror symmetry. These predictions are made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for framework that generated them. I attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a high (philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty Years Of String Theory: Reflecting On the Foundations" (edited by G. `t Hooft, E. Verlinde, D. Dieks and S. de Haro)

Characterization of a Nudix hydrolase from Deinococcus radiodurans with a marked specificity for (deoxy)ribonucleoside 5'-diphosphates

Background Nudix hydrolases form a protein family whose function is to hydrolyse intracellular nucleotides and so regulate their levels and eliminate potentially toxic derivatives. The genome of the radioresistant bacterium Deinococcus radiodurans encodes 25 nudix hydrolases, an unexpectedly large number. These may contribute to radioresistance by removing mutagenic oxidised and otherwise damaged nucleotides. Characterisation of these hydrolases is necessary to understand the reason for their presence. Here, we report the cloning and characterisation of the DR0975 gene product, a nudix hydrolase that appears to be unique to this organism. Results The DR0975 gene was cloned and expressed as a 20 kDa histidine-tagged recombinant product in Escherichia coli. Substrate analysis of the purified enzyme showed it to act primarily as a phosphatase with a marked preference for (deoxy)nucleoside 5'-diphosphates (dGDP > ADP > dADP > GDP > dTDP > UDP > dCDP > CDP). Km for dGDP was 110 µM and kcat was 0.18 s-1 under optimal assay conditions (pH 9.4, 7.5 mM Mg2+). 8-Hydroxy-2'-deoxyguanosine 5'-diphosphate (8-OH-dGDP) was also a substrate with a Km of 170 µM and kcat of 0.13 s-1. Thus, DR0975 showed no preference for 8-OH-dGDP over dGDP. Limited pyrophosphatase activity was also observed with NADH and some (di)adenosine polyphosphates but no other substrates. Expression of the DR0975 gene was undetectable in logarithmic phase cells but was induced at least 30-fold in stationary phase. Superoxide, but not peroxide, stress and slow, but not rapid, dehydration both caused a slight induction of the DR0975 gene. Conclusion Nucleotide substrates for nudix hydrolases conform to the structure NDP-X, where X can be one of several moieties. Thus, a preference for (d)NDPs themselves is most unusual. The lack of preference for 8-OH-dGDP over dGDP as a substrate combined with the induction in stationary phase, but not by peroxide or superoxide, suggests that the function of DR09075 may be to assist in the recycling of nucleotides under the very different metabolic requirements of stationary phase. Thus, if DR0975 does contribute to radiation resistance, this contribution may be indirect

The T2K experiment

The T2K experiment is a long baseline neutrino oscillation experiment. Its main goal is to measure the last unknown lepton sector mixing angle θ13 by observing νe appearance in a νμ beam. It also aims to make a precision measurement of the known oscillation parameters, and sin22θ23, via νμ disappearance studies. Other goals of the experiment include various neutrino cross-section measurements and sterile neutrino searches. The experiment uses an intense proton beam generated by the J-PARC accelerator in Tokai, Japan, and is composed of a neutrino beamline, a near detector complex (ND280), and a far detector (Super-Kamiokande) located 295 km away from J-PARC. This paper provides a comprehensive review of the instrumentation aspect of the T2K experiment and a summary of the vital information for each subsystem