Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. This is in good agreement with recent analytical results.Comment: 14 pages in plain TeX, 6 figures upon reques

The impact of school reopening on the spread of COVID-19 in England

By mid-May, cases of COVID-19 in the UK had been declining for over a month; a multi-phase emergence from lockdown was planned, including a scheduled partial reopening of schools on 1st June. Although evidence suggests that children generally display mild symptoms, the size of the school-age population means the total impact of reopening schools is unclear. Here, we present work from mid-May that focused on the imminent opening of schools and consider what these results imply for future policy. We compared eight strategies for reopening primary and secondary schools in England. Modifying a transmission model fitted to UK SARS-CoV-2 data, we assessed how reopening schools affects contact patterns, anticipated secondary infections and the relative change in the reproductive number, R. We determined the associated public health impact and its sensitivity to changes in social-distancing within the wider community. We predicted reopening schools with half-sized classes or focused on younger children was unlikely to push R above one. Older children generally have more social contacts, so reopening secondary schools results in more cases than reopening primary schools, while reopening both could have pushed R above one in some regions. Reductions in community social-distancing were found to outweigh and exacerbate any impacts of reopening. In particular, opening schools when the reproductive number R is already above one generates the largest increase in cases. Our work indicates that while any school reopening will result in increased mixing and infection amongst children and the wider population, reopening schools alone in June was unlikely to push R above one. Ultimately, reopening decisions are a difficult trade-off between epidemiological consequences and the emotional, educational and developmental needs of children. Into the future, there are difficult questions about what controls can be instigated such that schools can remain open if cases increase

Smoothed universal correlations in the two-dimensional Anderson model

We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.Comment: 12 pages, 14 figures submitted to Phys. Rev.

Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.Comment: Revtex file, 23 pages, no figure

Laboratory and molecular surveillance of paediatric typhoidal Salmonella in Nepal: Antimicrobial resistance and implications for vaccine policy.

BACKGROUND: Children are substantially affected by enteric fever in most settings with a high burden of the disease, including Nepal. However pathogen population structure and transmission dynamics are poorly delineated in young children, the proposed target group for immunization programs. Here we present whole genome sequencing and antimicrobial susceptibility data on 198 S. Typhi and 66 S. Paratyphi A isolated from children aged 2 months to 15 years of age during blood culture surveillance at Patan Hospital, Nepal, 2008-2016. PRINCIPAL FINDINGS: S. Typhi was the dominant agent and comprised several distinct genotypes, dominated by 4.3.1 (H58). The heterogeneity of genotypes in children under five was reduced compared to data from 2005-2006, attributable to ongoing clonal expansion of H58. Most isolates (86%) were non-susceptible to fluoroquinolones, associated mainly with S. Typhi H58 lineage II and S. Paratyphi A harbouring mutations in the quinolone resistance-determining region (QRDR); non-susceptible strains from these groups accounted for 50% and 25% of all isolates. Multi-drug resistance (MDR) was rare (3.5% of S. Typhi, 0 S. Paratyphi A) and restricted to chromosomal insertions of resistance genes in H58 lineage I strains. Temporal analyses revealed a shift in dominance from H58 Lineage I to H58 Lineage II, with the latter being significantly more common after 2010. Comparison to global data sets showed the local S. Typhi and S. Paratyphi A strains had close genetic relatives in other South Asian countries, indicating regional strain circulation. Multiple imports from India of ciprofloxacin-resistant H58 lineage II strains were identified, but these were rare and showed no evidence of clonal replacement of local S. Typhi. SIGNIFICANCE: These data indicate that enteric fever in Nepal continues to be a major public health issue with ongoing inter- and intra-country transmission, and highlights the need for regional coordination of intervention strategies. The absence of a S. Paratyphi A vaccine is cause for concern, given its prevalence as a fluoroquinolone resistant enteric fever agent in this setting

Modeling Disordered Regions in Proteins Using Rosetta

Protein structure prediction methods such as Rosetta search for the lowest energy conformation of the polypeptide chain. However, the experimentally observed native state is at a minimum of the free energy, rather than the energy. The neglect of the missing configurational entropy contribution to the free energy can be partially justified by the assumption that the entropies of alternative folded states, while very much less than unfolded states, are not too different from one another, and hence can be to a first approximation neglected when searching for the lowest free energy state. The shortcomings of current structure prediction methods may be due in part to the breakdown of this assumption. Particularly problematic are proteins with significant disordered regions which do not populate single low energy conformations even in the native state. We describe two approaches within the Rosetta structure modeling methodology for treating such regions. The first does not require advance knowledge of the regions likely to be disordered; instead these are identified by minimizing a simple free energy function used previously to model protein folding landscapes and transition states. In this model, residues can be either completely ordered or completely disordered; they are considered disordered if the gain in entropy outweighs the loss of favorable energetic interactions with the rest of the protein chain. The second approach requires identification in advance of the disordered regions either from sequence alone using for example the DISOPRED server or from experimental data such as NMR chemical shifts. During Rosetta structure prediction calculations the disordered regions make only unfavorable repulsive contributions to the total energy. We find that the second approach has greater practical utility and illustrate this with examples from de novo structure prediction, NMR structure calculation, and comparative modeling

The CMB and the measure of the multiverse

In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the predictions of the fat geodesic and causal patch measures. To highlight the effect of the measure---as opposed to any effects related to a possible landscape of vacua---we take the cosmological model, including the model of inflation, to be fixed. We also condition on the average CMB temperature accompanying the measurement. Both measures predict a 1-point expectation value for the gauge-invariant Newtonian potential, which takes the form of a (scale-dependent) monopole, in addition to a related contribution to the 3-point correlation function, with the detailed form of these quantities differing between the measures. However, for both measures both effects are well within cosmic variance. Our results make clear the theoretical relevance of the measure, and at the same time validate the standard inflationary predictions in the context of eternal inflation.Comment: 28 pages; v2: reference added, some clarification

Of Bounces, Branes and Bounds

Some recent studies have considered a Randall-Sundrum-like brane world evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole. For this scenario, it has been shown that, when the bulk charge is non-vanishing, a singularity-free ``bounce'' universe will always be obtained. However, for the physically relevant case of a de Sitter brane world, we have recently argued that, from a holographic (c-theorem) perspective, such brane worlds may not be physically viable. In the current paper, we reconsider the validity of such models by appealing to the so-called ``causal entropy bound''. In this framework, a paradoxical outcome is obtained: these brane worlds are indeed holographically viable, provided that the bulk charge is not too small. We go on to argue that this new finding is likely the more reliable one.Comment: 15 pages, Revtex; references added and very minor change

Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps.Comment: 29 pages, 3 figure