Split rank of triangle and quadrilateral inequalities

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu´ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook et al. [12], it is known that one particular class of facet- defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.mixed integer programs, split rank, group relaxations

Global microscopic calculations of ground-state spin and parity for odd-mass nuclei

Systematic calculations of ground-state spin and parity of odd-mass nuclei have been performed within the Hartree--Fock--BCS (HFBCS) approach and the Finite-Range Droplet Model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set give assignments of spin and parity with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.Comment: 5 pages, 4 figures (three in color), 1 table, to be submitted to Physical Review

Newly discovered halos and outer features around southern planetary nebulae

We have used the SuperCOSMOS H-alpha Survey to look for faint outer structures such as halos, ansae and jets around known planetary nebulae across 4000 square degrees of the southern Milky Way. Our search will contribute to a more accurate census of these features in the Galactic PN population. Candidate common-envelope PNe have also been identified on the basis of their microstructures. We also intend to determine more reliable distances for these PNe, which should allow a much better statistical basis for the post-AGB total mass budget. Our survey offers fresh scope to address this important issue.Comment: 2 pages, 1 figure. To be published in Planetary Nebulae: an Eye to the Future, Proceedings of IAU Symposium 283, held in Puerto de la Cruz, Tenerife, Spain, July 25-29 201

The Hα\alpha surface brightness −- radius plane as a diagnostic tool for photoionized nebulae

The H$\alpha$ surface brightness $-$ radius ($S-r$) relation is a robust distance indicator for planetary nebulae (PNe), further enhanced by different populations of PNe having distinct loci in $S-r$ space. Other types of photoionized nebulae also plot in quite distinct regions in the $S-r$ plane, allowing its use as a diagnostic tool. In particular, the nova shells and massive star ejecta (MSE) plot on relatively tight loci illustrating their evolutionary sequences. For the MSE, there is potential to develop a distance indicator for these objects, based on their trend in $S-r$ space. As high-resolution, narrowband surveys of the nearest galaxies become more commonplace, the $S-r$ plane is a potentially useful diagnostic tool to help identify the various ionized nebulae in these systems.Comment: 4 pages, 2 figures. To appear in the proceedings of the 11th Pacific Rim Conference on Stellar Astrophysics: Physics and Chemistry of the Late Stages of Stellar Evolution, held in Hong Kong, Dec 201

Evidence for a Role of Early Oestrogens in the Central Processing of Sexually Relevant Olfactory Cues in Female Mice

We previously found that female aromatase knockout (ArKO) mice showed less investigation of socially relevant odours as well as reduced sexual behaviour. We now ask whether these behavioural deficits might be due to an inadequate processing of odours in female ArKO mice. Therefore, we exposed female ArKO mice to same- and opposite-sex urinary odours and determined the expression of the immediate early gene c-Fos along the main and accessory olfactory projection pathways. We included ArKO males in the present study as we previously observed that they show female-typical detection thresholds of urinary odours, suggesting a role for perinatal oestrogens in these behavioural responses. No sex or genotype differences were observed in the olfactory bulb after urine exposure. By contrast, sex differences in c-Fos responses were observed in wild-type (WT) mice following exposure to male urine in the more central regions of the olfactory pathway; only WT females showed a significant Fos induction in the amygdala, central medial pre-optic area and ventromedial hypothalamus. However, ArKO females did not show a c-Fos response to male odours in the ventromedial hypothalamus, suggesting that the processing of male odours is affected in ArKO females and thus that oestrogens may be necessary for the development of neural responses to sexually relevant odours in female mice. By contrast, c-Fos responses to either male or oestrous female urine were very similar between ArKO and WT males, pointing to a central role of androgen vs. oestrogen signalling in the male circuits that control olfactory investigation and preferences