Algorithms in Lattice QCD

The enormous computing resources that large-scale simulations in Lattice QCD require will continue to test the limits of even the largest supercomputers into the foreseeable future. The efficiency of such simulations will therefore concern practitioners of lattice QCD for some time to come. I begin with an introduction to those aspects of lattice QCD essential to the remainder of the thesis, and follow with a description of the Wilson fermion matrix M, an object which is central to my theme. The principal bottleneck in Lattice QCD simulations is the solution of linear systems involving M, and this topic is treated in depth. I compare some of the more popular iterative methods, including Minimal Residual, Corij ugate Gradient on the Normal Equation, BI-Conjugate Gradient, QMR., BiCGSTAB and BiCGSTAB2, and then turn to a study of block algorithms, a special class of iterative solvers for systems with multiple right-hand sides. Included in this study are two block algorithms which had not previously been applied to lattice QCD. The next chapters are concerned with a generalised Hybrid Monte Carlo algorithm (OHM C) for QCD simulations involving dynamical quarks. I focus squarely on the efficient and robust implementation of GHMC, and describe some tricks to improve its performance. A limited set of results from HMC simulations at various parameter values is presented. A treatment of the non-hermitian Lanczos method and its application to the eigenvalue problem for M rounds off the theme of large-scale matrix computations

Tuning Actions and Observables in Lattice QCD

We propose a strategy for conducting lattice QCD simulations at fixed volume but variable quark mass so as to investigate the physical effects of dynamical fermions. We present details of techniques which enable this to be carried out effectively, namely the tuning in bare parameter space and efficient stochastic estimation of the fermion determinant. Preliminary results and tests of the method are presented. We discuss further possible applications of these techniques.Comment: 17 pages, 4 eps figures; affiliation correction in this header + minor post-referee addition

Instability in the Molecular Dynamics Step of Hybrid Monte Carlo in Dynamical Fermion Lattice QCD Simulations

We investigate instability and reversibility within Hybrid Monte Carlo simulations using a non-perturbatively improved Wilson action. We demonstrate the onset of instability as tolerance parameters and molecular dynamics step sizes are varied. We compare these findings with theoretical expectations and present limits on simulation parameters within which a stable and reversible algorithm is obtained for physically relevant simulations. Results of optimisation experiments with respect to tolerance prarameters are also presented

Instability in the molecular dynamics step of a hybrid Monte Carlo algorithm in dynamical fermion lattice QCD simulations

We investigate instability and reversibility within Hybrid Monte Carlo simulations using a non-perturbatively improved Wilson action. We demonstrate the onset of instability as tolerance parameters and molecular dynamics step sizes are varied. We compare these findings with theoretical expectations and present limits on simulation parameters within which a stable and reversible algorithm is obtained for physically relevant simulations. Results of optimisation experiments with respect to tolerance prarameters are also presented.Comment: RevTeX, Some results here were presented at Vielat 99, Vienna, Austria, Sept 1999 22 Pages, 10 figures, to be submitted to PR

Chelator free gallium-68 radiolabelling of silica coated iron oxide nanorods via surface interactions

The commercial availability of combined magnetic resonance imaging (MRI)/positron emission tomography (PET) scanners for clinical use has increased demand for easily prepared agents which offer signal or contrast in both modalities. Herein we describe a new class of silica coated iron–oxide nanorods (NRs) coated with polyethylene glycol (PEG) and/or a tetraazamacrocyclic chelator (DO3A). Studies of the coated NRs validate their composition and confirm their properties as in vivo T₂ MRI contrast agents. Radiolabelling studies with the positron emitting radioisotope gallium-68 (t1/2 = 68 min) demonstrate that, in the presence of the silica coating, the macrocyclic chelator was not required for preparation of highly stable radiometal-NR constructs. In vivo PET-CT and MR imaging studies show the expected high liver uptake of gallium-68 radiolabelled nanorods with no significant release of gallium-68 metal ions, validating our innovation to provide a novel simple method for labelling of iron oxide NRs with a radiometal in the absence of a chelating unit that can be used for high sensitivity liver imaging

Parallel Tempering in Lattice QCD with O(a)-Improved Wilson Fermions

We present details of our investigation of the Parallel Tempering algorithm. We consider the application of action matching technology to the selection of parameters. We then present a simple model of the autocorrelations for a particular parallel tempered system. Finally we present numerical results from applying the algorithm to lattice QCD with O(a)-improved dynamical fermions with twin ensemble system

Cost-eff ectiveness of HIV prevention for high-risk groups at scale: an economic evaluation of the Avahan programme in south India

Background Avahan is a large-scale, HIV preventive intervention, targeting high-risk populations in south India. We assessed the cost-eff ectiveness of Avahan to inform global and national funding institutions who are considering investing in worldwide HIV prevention in concentrated epidemics. Methods We estimated cost eff ectiveness from a programme perspective in 22 districts in four high-prevalence states. We used the UNAIDS Costing Guidelines for HIV Prevention Strategies as the basis for our costing method, and calculated eff ect estimates using a dynamic transmission model of HIV and sexually transmitted disease transmission that was parameterised and fi tted to locally observed behavioural and prevalence trends. We calculated incremental cost-eff ective ratios (ICERs), comparing the incremental cost of Avahan per disability-adjusted life-year (DALY) averted versus a no-Avahan counterfactual scenario. We also estimated incremental cost per HIV infection averted and incremental cost per person reached. Findings Avahan reached roughly 150 000 high-risk individuals between 2004 and 2008 in the 22 districts studied, at a mean cost per person reached of US$327 during the 4 years. This reach resulted in an estimated 61 000 HIV infections averted, with roughly 11 000 HIV infections averted in the general population, at a mean incremental cost per HIV infection averted of$785 (SD 166). We estimate that roughly 1 million DALYs were averted across the 22 districts, at a mean incremental cost per DALY averted of $46 (SD 10). Future antiretroviral treatment (ART) cost savings during the lifetime of the cohort exposed to HIV prevention were estimated to be more than$77 million (compared with the slightly more than $50 million spent on Avahan in the 22 districts during the 4 years of the study). Interpretation This study provides evidence that the investment in targeted HIV prevention programmes in south India has been cost eff ective, and is likely to be cost saving if a commitment is made to provide ART to all that can benefi t from it. Policy makers should consider funding and sustaining large-scale targeted HIV prevention programmes in India and beyond

Assessment of the population-level eff ectiveness of the Avahan HIV-prevention programme in South India: a preplanned, causal-pathway-based modelling analysis

Background Avahan, the India AIDS initiative of the Bill & Melinda Gates Foundation, was a large-scale, targeted HIV prevention intervention. We aimed to assess its overall eff ectiveness by estimating the number and proportion of HIV infections averted across Avahan districts, following the causal pathway of the intervention. Methods We created a mathematical model of HIV transmission in high-risk groups and the general population using data from serial cross-sectional surveys (integrated behavioural and biological assessments, IBBAs) within a Bayesian framework, which we used to reproduce HIV prevalence trends in female sex workers and their clients, men who have sex with men, and the general population in 24 South Indian districts over the fi rst 4 years (2004–07 or 2005–08 dependent on the district) and the full 10 years (2004–13) of the Avahan programme. We tested whether these prevalence trends were more consistent with self-reported increases in consistent condom use after the implementation of Avahan or with a counterfactual (assuming consistent condom use increased at slower, pre-Avahan rates) using a Bayes factor, which gave a measure of the strength of evidence for the eff ectiveness estimates. Using regression analysis, we extrapolated the prevention eff ect in the districts covered by IBBAs to all 69 Avahan districts. Findings In 13 of 24 IBBA districts, modelling suggested medium to strong evidence for the large self-reported increase in consistent condom use since Avahan implementation. In the remaining 11 IBBA districts, the evidence was weaker, with consistent condom use generally already high before Avahan began. Roughly 32 700 HIV infections (95% credibility interval 17 900–61 600) were averted over the fi rst 4 years of the programme in the IBBA districts with moderate to strong evidence. Addition of the districts with weaker evidence increased this total to 62 800 (32 000–118 000) averted infections, and extrapolation suggested that 202 000 (98 300–407 000) infections were averted across all 69 Avahan districts in South India, increasing to 606 000 (290 000–1 193 000) over 10 years. Over the fi rst 4 years of the programme 42% of HIV infections were averted, and over 10 years 57% were averted. Interpretation This is the fi rst assessment of Avahan to account for the causal pathway of the intervention, that of changing risk behaviours in female sex workers and high-risk men who have sex with men to avert HIV infections in these groups and the general population. The fi ndings suggest that substantial preventive eff ects can be achieved by targeted behavioural HIV prevention initiatives

Interim modelling analysis to validate reported increases in condom use and assess HIV infections averted among female sex workers and clients in southern India following a targeted HIV prevention programme

OBJECTIVES: This study assesses whether the observed declines in HIV prevalence since the beginning of the 'Avahan' India HIV/AIDS prevention initiative are consistent with self-reported increases in condom use by female sex workers (FSWs) in two districts of southern India, and provides estimates of the fraction of new infections averted among FSWs and clients due to increases in condom use in commercial sex after 2004. METHODS: A deterministic compartmental model of HIV/sexually transmitted infection (STI) transmission incorporating heterogeneous sexual behaviour was developed, parameterised and fitted using data from two districts in Karnataka, India. Three hypotheses of condom use among FSWs were tested: (H(0)), that condom use increased in line with reported FSW survey data prior to the Avahan initiative but remained constant afterwards; (H(1)) that condom use increased following the Avahan initiative, in accordance with survey data; (H(2)) that condom use increased according to estimates derived from condom distribution data. The proportion of fits to HIV/STI prevalence data was examined to determine which hypothesis was most consistent. RESULTS: For Mysore 0/36/82.7 fits were identified per million parameter sets explored under hypothesis H(0)/H(1)/H(2), respectively, while for Belgaum 9.7/8.3/0 fits were identified. The HIV epidemics in Belgaum and Mysore are both declining. In Mysore, increases in condom use during commercial sex between 2004 and 2009 may have averted 31.2% to 47.4% of new HIV infections in FSWs, while in Belgaum it may have averted 24.8% to 43.2%, if there was an increase in condom use. DISCUSSION: Increased condom use following the Avahan intervention is likely to have played a role in curbing the HIV epidemic in Mysore. In Belgaum, given the limitations in available data, this method cannot be used alone to decide if there has been an increase in condom use

A three-dimensional analysis of the effect of atopy on face shape

Three-dimensional (3D) imaging technology has been widely used to analyse facial morphology and has revealed an influence of some medical conditions on craniofacial growth and morphology. The aim of the study is to investigate whether craniofacial morphology is different in atopic Caucasian children compared with controls. Study design included observational longitudinal cohort study. Atopy was diagnosed via skin-prick tests performed at 7.5 years of age. The cohort was followed to 15 years of age as part of the Avon Longitudinal Study of Parents and Children (ALSPAC). A total of 734 atopic and 2829 controls were identified. 3D laser surface facial scans were obtained at 15 years of age. Twenty-one reproducible facial landmarks (x, y, z co-ordinates) were identified on each facial scan. Inter-landmark distances and average facial shells for atopic and non-atopic children were compared with explore differences in face shape between the groups. Both total anterior face height (pg–g, pg–men) and mid-face height (Is–men, sn–men, n–sn) were longer (0.6 and 0.4mm respectively) in atopic children when compared with non-atopic children. No facial differences were detected in the transverse and antero-posterior relationships. Small but statistically significant differences were detected in the total and mid-face height between atopic and non-atopic children. No differences were detected in the transverse and antero-posterior relationships