A Perturbation Scheme for Spherical Arrangements with Application to Molecular Modeling

We describe a software package for computing and manipulating the subdivision of a sphere by a collection of (not necessarily great) circles and for computing the boundary surface of the union of spheres. We present problems that arise in the implementation of the software and the solutions that we have found for them. At the core of the paper is a novel perturbation scheme to overcome degeneracies and precision problems in computing spherical arrangements while using floating point arithmetic. The scheme is relatively simple, it balances between the efficiency of computation and the magnitude of the perturbation, and it performs well in practice. In one O(n) time pass through the data, it perturbs the inputs necessary to insure no potential degeneracies and then passes the perturbed inputs on to the geometric algorithm. We report and discuss experimental results. Our package is a major component in a larger package aimed to support geometric queries on molecular models; it is currently employed by chemists working in "rational drug design." The spherical subdivisions are used to construct a geometric model of a molecule where each sphere represents an atom. We also give an overview of the molecular modeling package and detail additional features and implementation issues.

Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Gough, John; Van Handel, R., (2007) 'Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode', Journal of Statistical Physics 127(3) pp.575-607 RAE2008

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Secular Trends in Substance Use: The Conflict and Young People in Northern Ireland

The resolution of political conflict has led some to suggest that Northern Ireland will now face a range of social problems that have been ignored or suppressed by the Troubles. One such area is adolescent drug use. In this article, a review of a range of data sources shows that drug use, with few exceptions, has increased since the emergence of the ongoing peace process. Social and political changes and enhanced paramilitary involvement in the drugs trade appear to have somehow created an environment where drug use has flourished. In reviewing current drug policy and practice, the article highlights the lack of prevention, treatment, and harm reduction services established in Northern Ireland as a cause for concern.

The Secular Beyond: Free Religious Dissent and Debates over the Afterlife in Nineteenth-Century Germany

Toward the end of the first third of the nineteenth century, German writers began to favor a new metaphor for the afterlife: “das Jenseits” (“the Beyond”). At first glance, the emergence of such a term may appear to have little bearing on our understanding of the history of religious thought. However, as the late historian Reinhart Koselleck maintained, the study of semantic changes can betray tectonic shifts in the matrix of ideas that underpin the worlds of politics, learning, and religion. Drawing on Koselleck's method of conceptual history, the following essay takes the popularization of “the Beyond” as a point of departure for investigating secularization and secularism as two linked, yet distinct, sources of pressure on the fault lines of nineteenth-century German religious thought.

Secular trends, disease maps and ecological analyses of the incidence of childhood onset type 1 diabetes in Northern Ireland, 1989-2003

Aims To investigate secular trends in the incidence of Type 1 diabetes in Northern Ireland over the period 1989-2003. To highlight geographical variations in the incidence of Type 1 diabetes by producing disease maps and to compare incidence rates by relevant area characteristics.