Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups

In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that the existence of a such a metric is intrinsic to the underlying Lie algebra. More precisely, we show how one may determine the existence of such a metric by analyzing algebraic properties of the Lie algebra in question and infinitesimal deformations of any initial metric. Our second main result concerns the isometry groups of such distinguished metrics. Among the completely solvable unimodular Lie groups (this includes nilpotent groups), if the Lie group admits such a metric, we show that the isometry group of this special metric is maximal among all isometry groups of left-invariant metrics. We finish with a similar result for locally left-invariant metrics on compact nilmanifolds.Comment: 28 page

Bayesian curve fitting for lattice gauge theorists

A new method of extracting the low-lying energy spectrum from Monte Carlo estimates of Euclidean-space correlation functions which incorporates Bayesian inference is described and tested. The procedure fully exploits the information present in the correlation functions at small temporal separations and uses this information in a way consistent with fundamental probabilistic hypotheses. The computed errors on the best-fit energies include both statistical uncertainties and systematic errors associated with the treatment of contamination from higher-lying stationary states. Difficulties in performing the integrals needed to compute these error estimates are briefly discussed.Comment: 7 pages, 6 figures, 2 tables, uses espcrc2. Talk presented at the Workshop on Lattice Hadron Physics, Colonial Club Resort, Cairns, Australia, July 9-18, 200

DATA STRUCTURE WITH RESPECT TO THE MAIN EFFECTS MODEL: A DISCUSSION MOTIVATED BY A META-ANALYSIS DATA SET

A discussion on data structure relative to the main effects model is motivated by a severely unbalanced meta-analysis data set. This data set is used to highlight the difficulty of assessing data structure when multiple factor data sets are severely unbalanced. Both theoretical results and numerical examples are used to establish that simple approaches to examining data structure using two-way tables provide easily assimilated information about the effect of data unbalance on main effect contrast variances. In addition, notions of balance, proportionality, unbalance, and missing cells with respect to the main effects model are defined in terms of the two-way tables and are related to main effect contrast estimate variances as assessed using the D-optimality criterion

Multimedia data definition and requirements for construction applications

Ph.D.Nelson C. Bake

Alternative Methods of Regression

Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models.highly recommend[ed].for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." --Technometrics This book provides a balance between theory and practice supported by extensive displays of instructive geometrical constructs. Numerous in-depth case studies illustrate the use of nonlinear regression analysis--with all data