Large deviations associated with Poisson--Dirichlet distribution and Ewens sampling formula

Several results of large deviations are obtained for distributions that are associated with the Poisson--Dirichlet distribution and the Ewens sampling formula when the parameter $\theta$ approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of $\theta$ going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of $\theta$ going to infinity in a Poisson--Dirichlet distribution corresponds to a finite allele model where the mutation rate per individual is fixed and the number of alleles going to infinity. We call this the finite allele approximation. The first main result of this article is concerned with the relation between this finite allele approximation and the Poisson--Dirichlet distribution in terms of large deviations. Large $\theta$ can also be viewed as a limiting procedure of the effective population size going to infinity. In the second result a comparison is done between the sample size and the effective population size based on the Ewens sampling formula.Comment: Published in at http://dx.doi.org/10.1214/105051607000000230 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A general theory of minimum aberration and its applications

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.Comment: Published at http://dx.doi.org/10.1214/009053604000001228 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A database ATP simulated waveforms of shunt reactor switching cases with vacuum breakers on motor circuits

This paper presents a database ATP (Alternative Transient Program) simulated waveforms for shunt reactor switching cases with vacuum breakers in motor circuits following interruption of the starting current. The targeted objective is to provide multiple reignition simulated data for diagnostic and prognostic algorithms development, but also to help ATP users with practical study cases and component data compilation for shunt reactor switching. This method can be easily applied with different data for the different dielectric curves of circuit-breakers and networks. This paper presents design details, discusses some of the available cases and the advantages of such simulated data

Development of diagnostic and prognostic algorithms for SF6 puffer circuit breakers from transient waveforms: a validation proposal

- This paper presents a validation proposal for development of diagnostic and prognostic algorithms for SF6 puffer circuit-breakers reproduced from actual site waveforms. The re-ignition/restriking rates are duplicated in given circuits and the cumulative energy dissipated in interrupters by the restriking currents. The targeted objective is to provide a simulated database for diagnosis of re-ignition/restrikes relating to the phase to earth voltage and the number of re-ignition/restrikes as well as estimating the remaining life of SF6 circuit-breakers. The model-based diagnosis of a tool will be useful in monitoring re-ignition/restrikes as well as predicting a nozzle’s lifetime. This will help ATP users with practical study cases and component data compilation for shunt reactor switching and capacitor switching. This method can be easily applied with different data for the different dielectric curves of circuit breakers and networks. This paper presents modelling details and some of the available cases, required project support, the validation proposal, the specific plan for implementation and the propsed main contributions

Describing a Quantum Channel by State Tomography of a Single Probe State

A general law is presented for (composite) quantum systems which directly describes the time evolution of quantum states (with one or both components) through an arbitrary noisy quantum channel. It is shown that the time evolution of all quantum states through a quantum channel can be completely captured by the evolution of a single 'probe state'. Thus in order to grasp the information of the final output states subject to a quantum channel, especially an unknown one, it only requires quantum state tomography of a single probe state, which dramatically simplifies the practical operations in experiment.Comment: 3 pages, To be publised in EP