The relation between the cover (Tukey type) uniformities and the entourage (Weil type) ones, in the point-free context, is studied and a transparent translation is presented. In particular the natural uniformities on localic groups are discussed, and the uniformity of localic group homomorphisms is proved.

We prove that there is a Gδ σ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [4].

We generalize the Tukey depth to use cones instead of halfspaces. We prove a generalization of the center point theorem that for S ⊂ R, there is a point s ∈ S, with depth at least n d+1 for cones of half-angle 45 . This gives a notion of data depth for which an approximate median can always be found among the original set.

A method for measuring inter-sym cycle distortion, random jitter a described. The Blackman-Tukey method of s This allows the application of jitt ensure compliance to data communic Note: Mathematical analysis and have been performed. The autocorre FFT for clock jitter analysis have be current product. A provisional paten filed.

Domestic fowl in small groups are assumed to establish hierarchical systems based on individual recognition. Conversely, interactions in large groups are modulated by badges of status. Previous studies suggested that birds differing in phenotypic appearance (PA) became targets for aggression, possibly mistaking altered PA for badges of status. We evaluated the impact of altering PA on 0, 30, 50...

The concept of the spectral envelope was recently introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series. In the process of developing the spectral envelope methodology, many other interesting extensions became evident. In this article we explain the basic concept and give numerous examples of the usefulness of the technology. These exa...

In this paper, how to parallelize the Pre-corrected FFT algorithm for solving the scattering problem of large scale is presented and discussed. The P-FFT technique developed by our group earlier was extended in the current analysis. To show the efficiency of the MPI-based parallelization algorithm, the experiment results are given in the latter part of the paper and various comparisons are made...

Since the introduction of the median filter by John Tukey in 1971, many important classes of order statistic-based nonlinear filters have bccn developed. In this papcr we review some rcccnt results obtained for the two filter classes known as stack filters and weighted median filters. The highlights include new results on optimal filter design and fast training algorithms. .

We provide a polymorphic framework for radix-n Fast Fourier Transforms (FFTs) where all known kinds of monomoporhic radix-n algorithms can be obtained by specialization. The framework is mathematically based on the Cooley-Tukey mapping, and implemented as a C++ template meta-program. Avoiding run-time overhead, all specializations are performed statically.

Global weak continuity of M-functionals in a neighbourhood of the parametric distribution is established. This has implications for robustness of M-estimators vis a vis definitions put forward by Hampel. For instance the Tukey bisquare location estimator is robust on neighbourhoods of the parametric model, but the median is not. 2000 Mathematics subject classification: primary 62G35; secondary ...