Abstract:
We have performed global fits of $f_{\pi}$ and $m_{\pi}$, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at NNLO. We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the convergence of the expansion and use our large set of low energy constants to make predictions for the pion mass splitting due to QCD isospin breaking effects and the s-wave $\pi \pi$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.

Abstract:
We discuss recent algorithmic improvements in simulating finite temperature QCD on a lattice. In particular, the Rational Hybrid Monte Carlo(RHMC) algorithm is employed to generate lattice configurations for 2+1 flavor QCD. Unlike the Hybrid R Algorithm, RHMC is reversible, admitting a Metropolis accept/reject step that eliminates the $\mathcal{O}(\delta t^2)$ errors inherent in the R Algorithm. We also employ several algorithmic speed-ups, including multiple time scales, the use of a more efficient numerical integrator, and Hasenbusch pre-conditioning of the fermion force.

Abstract:
To provide a comprehensive introduction about the deteriorating items inventory management research status, this paper reviews the recent studies in relevant fields. Compared with the extant reviews (Raafat 1991; S.K.Goyal 2001), this paper reviews the recent studies from a different perspective. First, this paper proposes some key factors which should be considered in the deteriorating inventory studies; then, from the perspective of study scope, the current literatures are distinguished into two categories: the studies based on an enterprise and those based on supply chain. Literatures in each category are reviewed according to the key factors mentioned above. The literature review framework in this paper provides a clear overview of the deteriorating inventory study field, which can be used as a starting point for further study.

Abstract:
We present a study of the flavor symmetry breaking in the pion spectrum for various improved staggered fermion actions. To study the effects of link fattening and tadpole improvement, we use three different variants of the p4 action - p4fat3, p4fat7, and p4fat7tad. These are compared to Asqtad and also to naive staggered. To study the pattern of symmetry breaking, we measure all 15 meson masses in the 4-flavor staggered theory. The measurements are done on a quenched gauge background, generated using a one-loop improved Symanzik action with $\beta=10/g^2 = 7.40, 7.75,$ and 8.00, corresponding to lattice spacings of approximately a = .31 fm., .21 fm., and .14 fm. We also study how the lattice scale set by the $\rho$ mass on each of these ensembles compares to one set by the static quark potential.

Abstract:
We have measured the valence pion mass and the valence chiral condensate on lattice configurations generated with and without dynamical fermions. We find that our data and that of others is well represented by a linear relationship between $m_{\pi}^2$ and the valence quark mass, with a non-zero intercept. For our data, we relate the intercept to finite volume effects visible in the valence chiral condensate. We see no evidence for the singular behavior expected from quenched chiral logarithms.

Abstract:
The current status of United States projects pursuing Teraflops-scale computing resources for lattice field theory is discussed. Two projects are in existence at this time: the Multidisciplinary Teraflops Project, incorporating the physicists of the QCD Teraflops Collaboration, and a smaller project, centered at Columbia, involving the design and construction of a 0.8 Teraflops computer primarily for QCD.

Abstract:
We discuss a class of saddle-point configurations in SU(2) lattice gauge theory in three Euclidean dimensions. These configurations are smooth on the scale of the lattice and have an action density exhibiting localized peaks, as has been seen in cooled and extremized Monte Carlo generated lattices. Large Wilson loops centered on the action peaks show a unit of Z(2) flux. We discuss the generation of these configurations and measurements of the Creutz ratios on them.

Abstract:
One of the major frontiers of lattice field theory is the inclusion of light fermions in simulations, particularly in pursuit of accurate, first principles predictions from lattice QCD. With dedicated Teraflops-scale computers currently simulating QCD, another step towards precision full QCD simulations is underway. In addition to ongoing staggered and Wilson fermion simulations, first results from full QCD with domain wall fermions are available. After some discussion of work toward better algorithms, simulations completed to date will be discussed.

Abstract:
The QCDSP computer (Quantum Chromodynamics on Digital Signal Processors) is an inexpensive, massively parallel computer intended primarily for simulations in lattice gauge theory. Currently, two large QCDSP machines are in full-time use: an 8,192 processor, 0.4 Teraflops machine at Columbia University and an 12,288 processor, 0.6 Teraflops machine at the RIKEN-BNL Research Center at Brookhaven National Laboratory. We describe the design process, architecture, software and current physics projects of these computers.

Abstract:
We present a summary of the progress on QCDSP in the last year. QCDSP, Quantum Chromodynamics on Digital Signal Processors, is an inexpensive computer being built at Columbia that can achieve 0.8 teraflops for three million dollars.