Optimization of Gaussian Random Fields

Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of the system outputs. We present an approach for computing the sensitivity of the statistics of system outputs with respect to the parameters describing the mean and covariance of the distributed uncertainty. This sensitivity information is then incorporated into a gradient-based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics. This framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade

Degeneracy Implies Non-abelian Statistics

A non-abelian anyon can only occur in the presence of ground state degeneracy in the plane. It is conceivable that for some strange anyon with quantum dimension $>1$ that the resulting representations of all $n$-strand braid groups $B_n$ are overall phases, even though the ground state manifolds for $n$ such anyons in the plane are in general Hilbert spaces of dimensions $>1$. We observe that degeneracy is all that is needed: for an anyon with quantum dimension $>1$ the non-abelian statistics cannot all be overall phases on the degeneracy ground state manifold. Therefore, degeneracy implies non-abelian statistics, which justifies defining a non-abelian anyon as one with quantum dimension $>1$. Since non-abelian statistics presumes degeneracy, degeneracy is more fundamental than non-abelian statistics.Comment: State the main result as a theorem and add several clarification

A cascade MPC control structure for PMSM with speed ripple minimization

This paper addresses the problem of reducing the impact of periodic disturbances arising from the current sensor offset error on the speed control of a PMSM. The new results are based on a cascade model predictive control scheme with embedded disturbance model, where the per unit model is utilized to improve the numerical condition of the scheme. Results from an experimental application are given to support the design

A Time Series Model of Multiple Structural changes in Level, Trend and Variance

We consider a deterministically trending dynamic time series model in which multiple changes in level, trend and error variance are modeled explicitly and the number but not the timing of the changes are known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection and we compare the use of marginal likelihoods, posterior odds ratios and Schwarz' BIC model selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex-post real interest rate and in a long time series of U.S. GDP.BIC, Gibbs sampling, multiple structural changes, posterior odds ratio