Constructing the general partial waves and renormalization in EFT

We construct the general partial wave amplitude basis for the $N\to M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, with Lorentz invariant forms given in terms of spinor-helicity variables. The inner product of the Clebsch-Gordan coefficients is defined, which converts on-shell phase space integration into an algebraic problem. We also develop the technique of partial wave expansions of arbitrary amplitudes, including those with infrared divergence. These are applied to the computation of anomalous dimension matrix for general effective operators, where unitarity cuts for the loop amplitudes, with an arbitrary number of external particles, are obtained via partial wave expansion.Comment: 6 pages, 1 figure, 1 tabl

Toward optimal multistep forecasts in non-stationary autoregressions

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and accumulated prediction errors of two important methods, plug-in and direct prediction. These expressions not only characterize how the prediction errors are influenced by the model orders, prediction methods, values of parameters and unit roots, but also inspire us to construct some new predictor selection criteria that can ultimately choose the best combination of the model order and prediction method with probability 1. Finally, simulation analysis confirms the satisfactory finite sample performance of the newly proposed criteria.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ165 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Summary of a Topical Forum FAQ Based on the Chinese Composition Structure

An automatic multiple-document summarization system for producing frequently asked questions (FAQ) of a topical forum can save forum Webmasters a great deal of time in theory. This work will address summary composition issue of a previous work by proposing a structured presentation based on a four-part pattern of traditional Chinese articles. The result of the experiment shows that the enhanced system with both domain-terminology corpus methods produced a significantly better summary presentation than the original system. Recall rate and precision rate performance indices and user evaluations are also presented and discussed to show their practical implications