Cost of Generalised HMC Algorithms for Free Field Theory

We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the autocorrelation functions of operators quadratic in the fields, and optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize. We show that long trajectories are optimal for GHMC, and that standard HMC is much more efficient than algorithms based on the Second Order Langevin (L2MC) or Kramers Equation. We show that contrary to naive expectations HMC and L2MC have the same volume dependence, but their dynamical critical exponents are z=1 and z=3/2 respectively.Comment: LATTICE99(Algorithms and Machines) - 3 pages, 1 PostScript figur

Tuning the generalized Hybrid Monte Carlo algorithm

We discuss the analytic computation of autocorrelation functions for the generalized Hybrid Monte Carlo algorithm applied to free field theory and compare the results with numerical results for the $O(4)$ spin model in two dimensions. We explain how the dynamical critical exponent $z$ for some operators may be reduced from two to one by tuning the amount of randomness introduced by the updating procedure, and why critical slowing down is not a problem for other operators.Comment: 4 pages, to be published in the Proceedings of Lattice 95, uuencoded PostScript fil

Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory

We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis acceptance probability for leapfrog and higher-order discretisations of the Molecular Dynamics (MD) equations of motion. We show how to calculate autocorrelation functions of arbitrary polynomial operators, and use these to optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize for the special cases of linear and quadratic operators. We show that long trajectories are optimal for GHMC, and that standard HMC is more efficient than algorithms based on Second Order Langevin Monte Carlo (L2MC), sometimes known as Kramers Equation. We show that contrary to naive expectations HMC and L2MC have the same volume dependence, but their dynamical critical exponents are z = 1 and z = 3/2 respectively.Comment: 54 pages, 3 figure

Expected Utility in Models with Chaos

In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X ! X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the backward dynamics xt = f(xt+1). If f represents the forward/backward dynamics, the set of equilibria forms a direct/inverse limit space. We use a natural f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is a natural ¾-invariant measure where ¾ is the shift operator. We utilize this framework in the cash-in-advance model of money where f is the backward map to calculate expected utility when equilibria are chaotic.chaos, inverse limits, direct limits, natural invariant measure, cash-in-advance

Moving Away from Certainty: Using Mediation to Avoid Unpredictable Outcomes in Relocation Disputes Involving Joint Physical Custody

This Note describes the frameworks used by the courts of various states to modify joint physical custody plans when one parent wishes to relocate with the child to a different jurisdiction. The standards currently used by all states (variants of the “best interests of the child” standard) are too unpredictable, unfairly punish one parent with a substantial loss of parenting time, and fail to take into account alternative solutions that may be acceptable for all parties. Therefore, states should adopt a plan of mandated mediation, using litigation under the “best interests of the child” standard only when mediation utterly fails. This Note also argues for the increased use of guardians ad litem when such court decisions become necessary

The Enigmatic Role of Sir2 in Aging

In this issue of Cell, Longo and colleagues (Fabrizio et al., 2005) examine the role of Sir2, a histone deacetylase, in chronological aging in yeast by measuring the long-term survival of nondividing cells. In contrast to measurements of aging for mitotic cells, cell survival in the nonmitotic state is decreased by Sir2 activity under conditions that mimic calorie restriction

Short- & Long-Run Effects of Seafood Imports on Domestic Price

Agribusiness, Community/Rural/Urban Development, Demand and Price Analysis, International Relations/Trade,

The Theory of Planned Behavior and Financial Literacy: A Predictive Model for Credit Card Debt?

The primary purpose of this study was to predict credit card debt among college students by augmenting Ajzen’s (1991) theory of planned behavior to include the construct of financial literacy. One hundred and forty-three undergraduates completed an online survey measuring attitudes toward credit cards, subjective norms, perceived behavioral control, and financial literacy. Statistical analyses revealed that attitudes toward credit, subjective norms, and perceived behavioral control successfully predicted students’ intention to use credit cards (R2=.32). Financial literacy failed to predict intention to use credit cards. However, a positive correlation was found between attitudes toward credit cards and amount of credit card debt. This information may be incorporated into the development of programs aimed to improve personal finance behavior of college students and also to shape policy designed to protect consumers from predatory lending practices

The Impact of Microeconomic Structure Adjustment and Macroeconomic Variables under NAFTA on U.S. Agriculture

Agribusiness, International Relations/Trade,