The Rational Hybrid Monte Carlo Algorithm

The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.Comment: 15 pages. Proceedings from Lattice 200

Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

We introduce a simple general method for finding the equilibrium distribution for a class of widely used inexact Markov Chain Monte Carlo algorithms. The explicit error due to the non-commutivity of the updating operators when numerically integrating Hamilton's equations can be derived using the Baker-Campbell-Hausdorff formula. This error is manifest in the conservation of a ``shadow'' Hamiltonian that lies close to the desired Hamiltonian. The fixed point distribution of inexact Hybrid algorithms may then be derived taking into account that the fixed point of the momentum heatbath and that of the molecular dynamics do not coincide exactly. We perform this derivation for various inexact algorithms used for lattice QCD calculations.Comment: 24 pages, accepted for publication in Physics Review

Accelerating Staggered Fermion Dynamics with the Rational Hybrid Monte Carlo (RHMC) Algorithm

Improved staggered fermion formulations are a popular choice for lattice QCD calculations. Historically, the algorithm used for such calculations has been the inexact R algorithm, which has systematic errors that only vanish as the square of the integration step-size. We describe how the exact Rational Hybrid Monte Carlo (RHMC) algorithm may be used in this context, and show that for parameters corresponding to current state-of-the-art computations it leads to a factor of approximately seven decrease in cost as well as having no step-size errors.Comment: 4 pages, 2 figures, 1 tabl

The government's child poverty target: how much progress has been made?

Before the 2001 election the Treasury said that `tax and benefit reforms announced in this Parliament will lift over 1.2 million children out of relative poverty'. But official figures released on 11 April show a smaller fall in child poverty, of only 0.5 million since 1996-97. This commentary attempts to explain the discrepancy. Using the data that lie behind the official Households Below Average Income publications, we analyse trend in child poverty, measured against various poverty lines, since 1979. We show how the government's choice of a relative poverty line is making its goal to abolish child poverty more difficult and more expensive. We also discuss how easy the government will find it to make further reductions in child poverty

Exact 2+1 flavour RHMC simulations

We consider the Rational Hybrid Monte Carlo algorithm for performing exact 2+1 flavour fermion simulations. The specific cases of ASQTAD and domain wall fermions are considered. We find that in both cases the naive performance is similar to conventional hybrid algorithms.Comment: 3 pages, no figure

Probabilistic Quantum Control Via Indirect Measurement

The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability on the state space become less restrictive if unitary control operations may be supplemented by projective measurement. The present work builds on this idea, introducing the additional element of indirect measurement to achieve a kind of remote control. The target system that is to be remotely controlled is first entangled with another identical system, called the control system. The control system is then subjected to unitary transformations plus projective measurement. As anticipated by Schrodinger, such control via entanglement is necessarily probabilistic in nature. On the other hand, under appropriate conditions the remote-control scenario offers the special advantages of robustness against decoherence and a greater repertoire of unitary transformations. Simulations carried out for a two-level system demonstrate that, with optimization of control parameters, a substantial gain in the population of reachable states can be realized.Comment: 9 pages, 2 figures; typos added, reference added, reference remove

An Examination of Relational-interdependent Self-construal, Communal Strength, and Pro-relationship Behaviors in Friendships

Individual differences in relational-interdependent self-construal (RISC) are associated with positive relationship characteristics. This suggests that RISC is positively associated with the degree to which individuals view their relationships as communally-oriented (i.e., governed by norms of responsiveness), which should in turn be associated with increased use of pro-relationship behaviors. Thus, the current study explored the associations between RISC, communal strength, and pro-relationship behaviors in friendships. As predicted, RISC was positively associated with pro-relationship behavior use, but this association was mediated by greater communal strength. This suggests that increased RISC is associated with greater relationship satisfaction because the manner in which individuals view their relationships (i.e., communally) explains the association between RISC and constructive relationship behavior