Multigrid Monte Carlo in the Sine Gordon model

We pose two questions about the dynamical critical behavior of multigrid Monte Carlo: Will a multigrid Monte Carlo simulation of the two dimensional Sine Gordon model exhibit critical slowing down, as expected by a theoretical analysis of Metropolis acceptance rates? Can we reduce critical slowing down caused by decreasing acceptance rates on large blocks by performing more updates on coarser lattices? To this end we simulate the model with a W-cycle (gamma = 2) and a higher cycle with gamma = 4 using piecewise constant interpolation. The answer to the first question is positive, the answer to the second one is negative.Comment: 3 pages in ps-format, to appear in the Proceedings of LATTICE 93, Dallas, USA, October 199

Multigrid Monte Carlo with higher cycles in the Sine Gordon model

We study the dynamical critical behavior of multigrid Monte Carlo for the two dimensional Sine Gordon model on lattices up to 128 x 128. Using piecewise constant interpolation, we perform a W-cycle (gamma=2). We examine whether one can reduce critical slowing down caused by decreasing acceptance rates on large blocks by doing more work on coarser lattices. To this end, we choose a higher cycle with gamma = 4. The results clearly demonstrate that critical slowing down is not reduced in either case.Comment: 7 pages, 1 figure, whole paper including figure contained in ps-file, DESY 93-00

Analysis and Development of Stochastic Multigrid Methods in Lattice Field Theory

We study the relation between the dynamical critical behavior and the kinematics of stochastic multigrid algorithms. The scale dependence of acceptance rates for nonlocal Metropolis updates is analyzed with the help of an approximation formula. A quantitative study of the kinematics of multigrid algorithms in several interacting models is performed. We find that for a critical model with Hamiltonian H(phi) absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant term (mass term). The predictions of this rule are verified in a multigrid Monte Carlo simulation of the Sine Gordon model in two dimensions. Our analysis can serve as a guideline for the development of new algorithms: We propose a new multigrid method for nonabelian lattice gauge theory, the time slice blocking. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method, in accordance with the theoretical prediction. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems.Comment: (PhD thesis), 90 pages, latex file + epsfigures as uuencoded file, preprint DESY 94-00

Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions

We study a multigrid method for nonabelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This result is in accordance with theoretical arguments based on the analysis of the scale dependence of acceptance rates for nonlocal Metropolis updates. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint MS-TPI-94-

Kinematics of Multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.Comment: 28 pages, 8 ps-figures, DESY 92-09

Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo

We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to overcome critial slowing down for a given model. Our method is introduced in the context of spin models. A multigrid Monte Carlo procedure for nonabelian lattice gauge theory is described, and its kinematics is analyzed in detail.Comment: 7 pages, no figures, (talk at LATTICE 92 in Amsterdam

Progress in Lattice Field Theory Algorithms

I present a summary of recent algorithmic developments for lattice field theories. In particular I give a pedagogical introduction to the new Multicanonical algorithm, and discuss the relation between the Hybrid Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the role of the dynamical critical exponent z and its connection with `computational cost.' [Includes four PostScript figures]Comment: 27 page

Frequency of Adverse Events after Vaccination with Different Vaccinia Strains

BACKGROUND: Large quantities of smallpox vaccine have been stockpiled to protect entire nations against a possible reintroduction of smallpox. Planning for an appropriate use of these stockpiled vaccines in response to a smallpox outbreak requires a rational assessment of the risks of vaccination-related adverse events, compared to the risk of contracting an infection. Although considerable effort has been made to understand the dynamics of smallpox transmission in modern societies, little attention has been paid to estimating the frequency of adverse events due to smallpox vaccination. Studies exploring the consequences of smallpox vaccination strategies have commonly used a frequency of approximately one death per million vaccinations, which is based on a study of vaccination with the New York City Board of Health (NYCBH) strain of vaccinia virus. However, a multitude of historical studies of smallpox vaccination with other vaccinia strains suggest that there are strain-related differences in the frequency of adverse events after vaccination. Because many countries have stockpiled vaccine based on the Lister strain of vaccinia virus, a quantitative evaluation of the adverse effects of such vaccines is essential for emergency response planning. We conducted a systematic review and statistical analysis of historical data concerning vaccination against smallpox with different strains of vaccinia virus. METHODS AND FINDINGS: We analyzed historical vaccination data extracted from the literature. We extracted data on the frequency of postvaccinal encephalitis and death with respect to vaccinia strain and age of vaccinees. Using a hierarchical Bayesian approach for meta-analysis, we estimated the expected frequencies of postvaccinal encephalitis and death with respect to age at vaccination for smallpox vaccines based on the NYCBH and Lister vaccinia strains. We found large heterogeneity between findings from different studies and a time-period effect that showed decreasing incidences of adverse events over several decades. To estimate death rates, we then restricted our analysis to more-recent studies. We estimated that vaccination with the NYCBH strain leads to an average of 1.4 deaths per million vaccinations (95% credible interval, 0–6) and that vaccination with Lister vaccine leads to an average of 8.4 deaths per million vaccinations (95% credible interval, 0–31). We combined age-dependent estimates of the frequency of death after vaccination and revaccination with demographic data to obtain estimates of the expected number of deaths in present societies due to vaccination with the NYCBH and Lister vaccinia strains. CONCLUSIONS: Previous analyses of smallpox vaccination policies, which rely on the commonly assumed value of one death per million vaccinations, may give serious underestimates of the number of deaths resulting from vaccination. Moreover, because there are large, strain-dependent differences in the frequency of adverse events due to smallpox vaccination, it is difficult to extrapolate from predictions for the NYCBH-derived vaccines (stockpiled in countries such as the US) to predictions for the Lister-derived vaccines (stockpiled in countries such as Germany). In planning for an effective response to a possible smallpox outbreak, public-health decision makers should reconsider their strategies of when to opt for ring vaccination and when to opt for mass vaccination