A New Look at the Easy-Hard-Easy Pattern of Combinatorial Search Difficulty

The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easy-hard-easy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions.Comment: See http://www.jair.org/ for any accompanying file

A List of Wisconsin Springtails With New Records and Annotations (Hexapoda: Parainsecta: Collembola)

Twenty Collembola species new to Wisconsin were collected from soil at two agricultural sites in southern Wisconsin, including an undescribed species of Isotomidae. The state faunal list now contains 52 species representing seven families

The dependence on morphology of the gas content in galactic disks

The classification S0 was introduced by Hubble to serve as a description of galaxies whose morphological characteristics seemed to lie between the disk-dominated spirals and the spheroidal elliptical systems. Since then there has been extensive discussion as to whether this classification sequence is also an evolutionary sequence. Many studies have focussed on a particular feature such as the luminosity profile, the bulge-to-disk ratio, or the nature of the interstellar matter, but the question of the evolution remains contentious. Equally contentious is the question of the classification itself. For systems with well-developed disks there usually is no problem. Many spheroidal systems also are unambiguously classified as ellipticals in most catalogs. However, there are a number of early systems which have been reclassified following review using improved optical material. For example, Eder et al. (AJ, 102, 572, 1991) found that many of the S0 galaxies which are rich in neutral hydrogen have faint spiral features. The confusion about classification propagates into the discussion of the properties of early-type systems. Attempts to put the classification system on a quantitative basis have in general been unsuccessful. Recently Sandage (private communication) has reviewed the classification of early systems and has defined a set of sub-classes for these objects. The S0 galaxies are divided into three groups, depending on the prominence of the disk. There are six subdivisions of Sa galaxies, depending upon the relative prominence of knots and other arm-like characteristics. We have explored the total gas content in these objects to see if there is a dependence on the galaxy morphology, as denoted by these new subclasses

The faint-galaxy hosts of gamma-ray bursts

The observed redshifts and magnitudes of the host galaxies of gamma-ray bursts (GRBs) are compared with the predictions of three basic GRB models, in which the comoving rate density of GRBs is (1) proportional to the cosmic star formation rate density, (2) proportional to the total integrated stellar density and (3) constant. All three models make the assumption that at every epoch the probability of a GRB occuring in a galaxy is proportional to that galaxy's broad-band luminosity. No assumption is made that GRBs are standard candles or even that their luminosity function is narrow. All three rate density models are consistent with the observed GRB host galaxies to date, although model (2) is slightly disfavored relative to the others. Models (1) and (3) make very similar predictions for host galaxy magnitude and redshift distributions; these models will be probably not be distinguished without measurements of host-galaxy star-formation rates. The fraction of host galaxies fainter than 28 mag may constrain the faint end of the galaxy luminosity function at high redshift, or, if the fraction is observed to be low, may suggest that the bursters are expelled from low-luminosity hosts. In all models, the probability of finding a z<0.008 GRB among a sample of 11 GRBs is less than 10^(-4), strongly suggesting that GRB 980425, if associated with supernova 1998bw, represents a distinct class of GRBs.Comment: 7 pages, ApJ in press, revised to incorporate yet more new and revised observational result