The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions

We describe an implementation of the Rational Hybrid Monte Carlo (RHMC) algorithm for dynamical computations with two flavours of staggered quarks. We discuss several variants of the method, the performance and possible sources of error for each of them, and we compare the performance and results to the inexact R algorithm.Comment: Lattice2003(machine) 3 pages, 1 figure. Added referenc

Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, \bra\Delta H^2\ket^{1/2}, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in Quantum Monte Carlo.Comment: 14 pages, 6 figure

Algorithm Shootout: R versus RHMC

We present initial results comparing the RHMC and R algorithms on large lattices with small quark masses using chiral fermions. We also present results concerning staggered fermions near the deconfinement/chiral phase transition. We find that the RHMC algorithm not only eliminates the step-size error of the R algorithm, but is also considerably more efficient. We discuss several possibilities for further improvement to the RHMC algorithm.Comment: Proceedings from Lattice 2005 (Dublin

Systematic errors of L\"uscher's fermion method and its extensions

We study the systematic errors of L\"uscher's formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite $\beta$. We confirm the existence of an optimal window in the cutoff parameter $\varepsilon$, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.Comment: 10 pages LaTeX, Comprehensive revision; figures adde

The Length of an SLE - Monte Carlo Studies

The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter kappa. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also correcte

Recent Developments in Fermion Simulation Algorithms

A summary of recent developments in the field of simulation algorithms for dynamical fermions is given.Comment: Plenary talk given at the International Symposium on Lattice Field Theory, 4-8 June 1996, St. Louis, Mo, USA, Latex, 3 Figures, 7 page

Noisy Monte Carlo Algorithm

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by simulating SU(2) lattice gauge theory with a 5-loop improved action. A new approach for dynamical fermion simulations is proposed.Comment: Lattice 2000 (Algorithms), latex, espcrc2.sty, 4 page

The shifting nature of women’s experiences and perceptions of ductal carcinoma in situ

Aim: This paper is a report of a descriptive qualitative study of the evolution of women’s perceptions and experiences of ductal carcinoma in situ from the period near to diagnosis to one year later. Background: Ductal carcinoma in situ is a non-invasive breast condition where cancer cells are detected but confined to the ducts of the breast. With treatment, the condition has a positive prognosis but ironically patients undergo treatment similar to that for invasive breast cancer. There is a lack of longitudinal qualitative research studying women’s experiences of ductal carcinoma in situ, especially amongst newly diagnosed patients and how experiences change over time. Methods: Forty-five women took part in an initial interview following a diagnosis of ductal carcinoma in situ and twenty-seven took part in a follow-up interview 9-13 months later. Data were collected between January 2007 and October 2008. Transcripts were analysed using a hybrid approach to thematic analysis. Findings: Women’s early perceptions of ductal carcinoma in situ merged and sometimes conflicted with their lay beliefs of breast cancer. Perceptions and experiences of the condition shifted over time. These overriding aspects were evident within four themes identified across the interviews: 1) perceptions of DCIS versus breast cancer, 2) from paradox to acceptance, 3) personal impact, and 4) support and interactions with others. Conclusion: This study represents one of the few longitudinal qualitative studies with newly diagnosed patients, capturing women’s initial and shifting experiences and perceptions of the condition. The issues identified need to be recognised in clinical practice and supported appropriately

Approximation Theory for Matrices

We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range (\epsilon \leq |z| \leq1). We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.Comment: 10 pages, 7 figure