Application of Pad\'{e} interpolation to stationary state problems

If the small and large coupling behavior of a physical system can be computed perturbatively and expressed respectively as power series in a coupling parameter $g$ and $1/g$, a Pad\'{e} approximant embracing the two series can interpolate between these two limits and provide an accurate estimate of the system's behavior in the generally intractable intermediate coupling regime. The methodology and validity of this approach are illustrated by considering several stationary state problems in quantum mechanics.Comment: RevTeX4, 7 pages (including 7 tables); v4 typos correcte

On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Gauge Independence and Chiral Symmetry Breaking in a Strong Magnetic Field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.Comment: 10 pages, 1 eps figure, version to appear in Annals of Physic

A multiple-filter-multiple-wrapper approach to gene selection and microarray data classification

Filters and wrappers are two prevailing approaches for gene selection in microarray data analysis. Filters make use of statistical properties of each gene to represent its discriminating power between different classes. The computation is fast but the predictions are inaccurate. Wrappers make use of a chosen classifier to select genes by maximizing classification accuracy, but the computation burden is formidable. Filters and wrappers have been combined in previous studies to maximize the classification accuracy for a chosen classifier with respect to a filtered set of genes. The drawback of this single-filter-single-wrapper (SFSW) approach is that the classification accuracy is dependent on the choice of specific filter and wrapper. In this paper, a multiple-filter-multiple-wrapper (MFMW) approach is proposed that makes use of multiple filters and multiple wrappers to improve the accuracy and robustness of the classification, and to identify potential biomarker genes. Experiments based on six benchmark data sets show that the MFMW approach outperforms SFSW models (generated by all combinations of filters and wrappers used in the corresponding MFMW model) in all cases and for all six data sets. Some of MFMW-selected genes have been confirmed to be biomarkers or contribute to the development of particular cancers by other studies. © 2006 IEEE.published_or_final_versio