On Free Quotients of Complete Intersection Calabi-Yau Manifolds

In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.Comment: 39 pages, 3 tables, LaTe

Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.Comment: 4 pages, RevTe

On the dual nature of partial theta functions and Appell-Lerch sums

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums. In this sense, Appell--Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers-Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral $q$-series with mixed mock modular behaviour.Comment: To be published in Advances in Mathematic

Spatial patterns of HIV prevalence and Service Use in East Zimbabwe: implications for future targeting of interventions

Introduction: Focusing resources for HIV control on geographic areas of greatest need in countries with generalised epidemics has been recommended to increase cost-effectiveness. However, socio-economic inequalities between areas of high and low prevalence could raise equity concerns and have been largely overlooked. We describe spatial patterns in HIV prevalence in east Zimbabwe and test for inequalities in accessibility and uptake of HIV services prior to the introduction of spatially-targeted programmes. Methods: 8092 participants in an open-cohort study were geo-located to 110 locations. HIV prevalence and HIV testing and counselling (HTC) uptake were mapped with ordinary kriging. Clusters of high or low HIV prevalence were detected with Kulldorff statistics, and the socio-economic characteristics and sexual risk behaviours of their populations, and levels of local HIV service availability (measured in travel distance) and uptake were compared. Kulldorff statistics were also determined for HTC, antiretroviral therapy (ART), and voluntary medical male circumcision (VMMC) uptake. Results: One large and one small high HIV prevalence cluster (relative risk [RR]=1.78, 95% confidence interval [CI]=1.53–2.07; RR=2.50, 95% CI=2.08–3.01) and one low-prevalence cluster (RR=0.70, 95% CI=0.60–0.82) were detected. The larger high-prevalence cluster was urban with a wealthier population and more high-risk sexual behaviour than outside the cluster. Despite better access to HIV services, there was lower HTC uptake in the high-prevalence cluster (odds ratio [OR] of HTC in past 3 years: OR=0.80, 95% CI=0.66–0.97). The low-prevalence cluster was predominantly rural with a poorer population and longer travel distances to HIV services; however, uptake of HIV services was not reduced. Conclusions: High-prevalence clusters can be identified to which HIV control resources could be targeted. To date, poorer access to HIV services in the poorer low-prevalence areas has not resulted in lower service uptake, while there is significantly lower uptake of HTC in the high-prevalence cluster where health service access is better. Given the high levels of risky sexual behaviour and lower uptake of HTC services, targeting high-prevalence clusters may be cost-effective in this setting. If spatial targeting is introduced, inequalities in HIV service uptake may be avoided through mobile service provision for lower prevalence areas

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

On the multiplicativity of quantum cat maps

The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group, known as Weil's representation. We prove that there exists an appropriate choice of phases in the propagators that defines a proper representation of the theta group. We also give explicit formulae for the propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page

Obstructing extensions of the functor Spec to noncommutative rings

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M_n(C) for n >= 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gelfand spectrum functor for C*-algebras is also proved.Comment: 23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline the exposition; final section was rewritten to omit an error in the earlier proof of Theorem 1.

Fourier-Space Crystallography as Group Cohomology

We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge transformation, the cohomological description becomes natural. We review Fourier-space crystallography and group cohomology, quote the fact that cohomology is dual to homology, and exhibit several results, previously established for special cases or by intricate calculation, that fall immediately out of the formalism. In particular, we prove that {\it two phase functions are gauge equivalent if and only if they agree on all their gauge-invariant integral linear combinations} and show how to find all these linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint number for reference 22