On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.Comment: 6 revtex page

SU(3) vortex-like configurations in the maximal center gauge

A new algorithm for fixing the gauge to (direct) maximal center gauge in SU(N) lattice gauge theory is presented. We check how this method works on SU(3) configurations which are vortex-like, and show how these configurations look like when center projected.Comment: LATTICE99(confine)-3p,5 postscript figure

Estimating causal effects with matching methods in the presence and absence of bias cancellation

This paper explores the implications of possible bias cancellation using Rubin-style matching methods with complete and incomplete data. After reviewing the naïve causal estimator and the approaches of Heckman and Rubin to the causal estimation problem, we show how missing data can complicate the estimation of average causal effects in different ways, depending upon the nature of the missing mechanism. While - contrary to published assertions in the literature - bias cancellation does not generally occur when the multivariate distribution of the errors is symmetric, bias cancellation has been observed to occur for the case where selection into training is the treatment variable, and earnings is the outcome variable. A substantive rationale for bias cancellation is offered, which conceptualizes bias cancellation as the result of a mixture process based on two distinct individual-level decision-making models. While the general properties are unknown, the existence of bias cancellation appears to reduce the average bias in both OLS and matching methods relative to the symmetric distribution case. Analysis of simulated data under a set of difference scenarios suggests that matching methods do better than OLS in reducing that portion of bias that comes purely from the error distribution (i.e., from “selection on unobservables”). This advantage is often found also for the incomplete data case. Matching appears to offer no advantage over OLS in reducing the impact of bias due purely to selection on unobservable variables when the error variables are generated by standard multivariate normal distributions, which lack the bias-cancellation property. (AUTHORS)

One-dimensional classical adjoint SU(2) Coulomb Gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur

Lattice QCD study of the Boer-Mulders effect in a pion

The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentum-dependent parton distribution functions (TMDs). This work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. Particular emphasis is placed on the behavior as a function of a Collins-Soper evolution parameter quantifying the relative rapidity of the struck quark and the initial hadron, e.g., in a semi-inclusive deep inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass m_pi = 518 MeV, utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. In contrast to an earlier nucleon study, due to the lower mass of the pion, the calculated data enable quantitative statements about the physically interesting limit of large relative rapidity. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is noted.Comment: 16 pages, 9 figures, 3 table

Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data

Estimating Causal Effects with Matching Methods in the Presence and Absence of Bias Cancellation

This paper explores the implications of possible bias cancellation using Rubin-style matching methods with complete and incomplete data. After reviewing the naïve causal estimator and the approaches of Heckman and Rubin to the causal estimation problem, we show how missing data can complicate the estimation of average causal effects in different ways, depending upon the nature of the missing mechanism. While - contrary to published assertions in the literature - bias cancellation does not generally occur when the multivariate distribution of the errors is symmetric, bias cancellation has been observed to occur for the case where selection into training is the treatment variable, and earnings is the outcome variable. A substantive rationale for bias cancellation is offered, which conceptualizes bias cancellation as the result of a mixture process based on two distinct individual-level decision-making models. While the general properties are unknown, the existence of bias cancellation appears to reduce the average bias in both OLS and matching methods relative to the symmetric distribution case. Analysis of simulated data under a set of difference scenarios suggests that matching methods do better than OLS in reducing that portion of bias that comes purely from the error distribution (i.e., from "selection on unobservables"). This advantage is often found also for the incomplete data case. Matching appears to offer no advantage over OLS in reducing the impact of bias due purely to selection on unobservable variables when the error variables are generated by standard multivariate normal distributions, which lack the bias-cancellation property.

Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills theory

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.Comment: reference added, submitted to Phys. Lett.