In this paper we give a conjectural refinement of the DavenportHeilbronn theorem on the density of cubic field discriminants. Our refinement is plausible theoretically and agrees very well with computational data.

We explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using Kummer theory, instead of the traditional (and much less efficient) method using the geometry of numbers. As an application, we describe the computation of quartic fields of discriminant up to 107, the corresponding table being available by anonymous ftp.

The work examines Karhunen-Loeve Transform and Linear Discriminant Analysis as means for designing optimized spectral bases for the projection of the critical-band auditory-like spectrum.

The Mahalanobis-Taguchi System is a diagnosis and predictive method for analyzing patterns in multivariate cases. The goal of this study is to compare the ability of the Mahalanobis- Taguchi System and a neural-network to discriminate using small data sets. We examine the discriminant ability as a function of data set size using an application area where reliable data is publicly available. The...

Testing hypotheses about variance parameters arises in contexts where uniformity is important and also in relation to checking assumptions as a preliminary to analysis of variance (ANOVA), dose-response modeling, discriminant analysis and so forth. In contrast to procedures for tests on means, tests for variances derived assuming normality of the parent populations are highly nonrobust to nonno...

Let N(5, D5, X) be the number of quintic number fields whose Galois closure has Galois group D5 and whose discriminant is bounded by X. By a conjecture of Malle, we expect that N(5, D5, X) ∼ C · X 1 2 for some constant C. The best known upper bound is N(5, D5, X) X 3 4, and we show this could be improved by counting points on a certain variety defined by a norm equation; computer calculations g...

A method for finding all the nonisomorphic complex cubic fields with discriminant D > -10 is described. Three different methods were used to find the class number of each of these fields. The speed of these techniques is discussed and several tables illustrating the computational results are presented. These include tables of the distribution of the fields and the class numbers and the class gr...

MOTIVATION High-dimensional data such as microarrays have created new challenges to traditional statistical methods. One such example is on class prediction with high-dimension, low-sample size data. Due to the small sample size, the sample mean estimates are usually unreliable. As a consequence, the performance of the class prediction methods using the sample mean may also be unsatisfactory. T...

In this paper, a novel face recognition method based on Gabor-wavelet and linear discriminant analysis (LDA) is proposed. Given training face images, discriminant vectors are computed using LDA. The function of the discriminant vectors is two-fold. First, discriminant vectors are used as a transform matrix, and LDA features are extracted by projecting original intensity images onto discriminant...