Signatures of Galaxy-Cluster Interactions: Tully-Fisher Observations at z~0.1

We have obtained new optical imaging and spectroscopic observations of 78 galaxies in the fields of the rich clusters Abell 1413 (z = 0.14), Abell 2218 (z = 0.18) and Abell 2670 (z = 0.08). We have detected line emission from 25 cluster galaxies plus an additional six galaxies in the foreground and background, a much lower success rate than what was found (65%) for a sample of 52 lower-richness Abell clusters in the range 0.02 < z < 0.08. We have combined these data with our previous observations of Abell 2029 and Abell 2295 (both at z = 0.08), which yields a sample of 156 galaxies. We evaluate several parameters as a function of cluster environment: Tully-Fisher residuals, H-alpha equivalent width, and rotation curve asymmetry, shape and extent. Although H-alpha is more easily detectable in galaxies that are located further from the cluster cores, we fail to detect a correlation between H-alpha extent and galaxy location in those where it is detected, again in contrast with what is found in the clusters of lesser richness. We fail to detect any statistically significant trends for the other parameters in this study. The zero-point in the z~0.1 Tully-Fisher relation is marginally fainter (by 1.5 sigma) than that found in nearby clusters, but the scatter is essentially unchanged.Comment: 27 pages including 5 figures; accepted for publication in the Astronomical Journa

The frequency and properties of young tidal dwarf galaxies in nearby gas-rich groups

We present high-resolution Giant Metrewave Radio Telescope (GMRT) HI observations and deep Canada-France-Hawaii Telescope (CFHT) optical imaging of two galaxy groups: NGC 4725/47 and NGC 3166/9. These data are part of a multi-wavelength unbiased survey of the gas-rich dwarf galaxy populations in three nearby interacting galaxy groups. The NGC 4725/47 group hosts two tidal knots and one dIrr. Both tidal knots are located within a prominent HI tidal tail, appear to have sufficient mass (M_gas~10^8 M_sol) to evolve into long-lived tidal dwarf galaxies (TDGs) and are fairly young in age. The NGC 3166/9 group contains a TDG candidate, AGC 208457, at least three dIrrs and four HI knots. Deep CFHT imaging confirms that the optical component of AGC 208457 is bluer -- with a 0.28 mag g-r colour -- and a few Gyr younger than its purported parent galaxies. Combining the results for these groups with those from the NGC 871/6/7 group reported earlier, we find that the HI properties, estimated stellar ages and baryonic content of the gas-rich dwarfs clearly distinguish tidal features from their classical counterparts. We optimistically identify four potentially long-lived tidal objects associated to three separate pairs of interacting galaxies, implying that TDGs are not readily produced during interaction events as suggested by some recent simulations. The tidal objects examined in this survey also appear to have a wider variety of properties than TDGs of similar mass formed in current simulations of interacting galaxies, which could be the result of pre- or post-formation environmental influences.Comment: 18 pages, 14 figures, accepted for publication in MNRA

Ulcerative C2 neurocutaneous dysesthesia (trigeminal trophic syndrome in an alternative distribution)

Trigeminal trophic syndrome is an uncommon condition characterized by paresthesia, itch, and self-inflicted wounds following the trigeminal dermatome(s). Similar processes adhering to cervical nerve distributions have been reported, calling into question the specificity of trigeminal trophic syndrome for the trigeminal network. Herein, we report patient with trigeminal trophic syndrome adhering to the C2 dermatome, a previously unreported distribution

Approximation Algorithms for the Capacitated Domination Problem

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models for this problem on general graphs, which also establishes the corresponding approximation results to the well-known approximations of the traditional {\em Dominating Set} problem. Together with our previous work, this closes the problem of generally approximating the optimal solution. On the other hand, from the perspective of parameterization, we prove that this problem is {\it W[1]}-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms when parameterized by treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs