On central tendency and dispersion measures for intervals and hypercubes

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of summary statistics (central tendency and dispersion measures) for interval-valued variables

Remark on lattice BRST invariance

A recently claimed resolution to the lattice Gribov problem in the context of chiral lattice gauge theories is examined. Unfortunately, I find that the old problem remains.Comment: 4 pages, plain TeX, presentation improved (see acknowledgments

Studies on the bit rate requirements for a HDTV format with 1920 timestimes 1080 pixel resolution, progressive scanning at 50 Hz frame rate targeting large flat panel displays

This paper considers the potential for an HDTV delivery format with 1920 times 1080 pixels progressive scanning and 50 frames per second in broadcast applications. The paper discusses the difficulties in characterizing the display to be assumed for reception. It elaborates on the required bit rate of the 1080p/50 format when critical content is coded in MPEG-4 H.264 AVC Part 10 and subjectively viewed on a large, flat panel display with 1920 times 1080 pixel resolution. The paper describes the initial subjective quality evaluations that have been made in these conditions. The results of these initial tests suggest that the required bit-rate for a 1080p/50 HDTV signal in emission could be kept equal or lower than that of 2nd generation HDTV formats, to achieve equal or better image qualit

The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory

We consider a lattice discretization of a covariantly gauge-fixed abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we construct those explicitly. We show that the proper adjustment of these counterterms drives the theory to a new type of phase transition, at which we recover a continuum theory of (free) photons. We present both numerical and (one-loop) perturbative results, and show that they are in good agreement near this phase transition. Since perturbation theory plays an important role, it is important to choose a discretization of the gauge-fixing action such that lattice perturbation theory is valid. Indeed, we find numerical evidence that lattice actions not satisfying this requirement do not lead to the desired continuum limit. While we do not consider fermions here, we argue that our results, in combination with previous work, provide very strong evidence that this new phase transition can be used to define abelian lattice chiral gauge theories.Comment: 42 pages, 30 figure

Chiral Gauge Theory on Lattice with Domain Wall Fermions

We investigate a U(1) lattice chiral gauge theory with domain wall fermions and compact gauge fixing. In the reduced model limit, our perturbative and numerical investigations show that there exist no extra mirror chiral modes. The longitudinal gauge degrees of freedom have no effect on the free domain wall fermion spectrum consisting of opposite chiral modes at the domain wall and at the anti-domain wall which have an exponentially damped overlap.Comment: 16 pages revtex, 5 postscript figures, PRD versio

Factors Limiting Sexual Reproduction in Platanus Wrightii in Southeastern Arizona

Arizona sycamore (Platanus wrightii: Platanaceae) is a riparian tree of the southwestern United States and adjacent Mexico. It is failing to reproduce in certain canyons where mature, seed-producing trees of this species occur. Three hypotheses were tested to explain this reproductive failure: I) the presence of domestic cattle prevents reproduction, 2) seeds produced in certain canyons are inviable, and 3) annual flash floods destroy seedlings and young saplings but not the large, mature trees. Canyons, either grazed or ungrazed by domestic animals, were surveyed for the presence of seedlings and young trees. In the laboratory, seeds were tested for viability, germinability in petri dishes, and emergence of seedlings from soil. Canyons which possessed seedlings and young saplings were censused before and after flooding. From these efforts, we conclude that reproductive failure of Arizona sycamore in certain canyons cannot be explained either by activities of domestic animals or by a lack of viable, germinable seeds. Flash flooding events in some canyons washed out the seedlings and saplings present, but left viable larger trees. We also found that a permanent, high water table was essential to propagule survival