R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

DNA sequence variation in the ITS-1 rDNA subunit and host relationships in sorghum midge, Stenodiplosis sorghicola (Coquillett) (Diptera : Cecidomyiidae), in Australia

Sequence variation in the internal transcribed spacer (ITS-1) ribosomal DNA subunit was examined for sorghum midge obtained from introduced and native hosts in south-eastern and central Queensland. No variation was observed relative to host plant or geographical distance for midges collected from two introduced hosts, grain sorghum (Sorghum bicolor ) and Johnson grass (S. halepense ); however, sequence differences were observed between midges from introduced and native hosts and among midges from a single native host, slender bluegrass (Dichanthium affine ). No evidence was observed of introduced midges on native hosts, or vice versa. These results agree with previously hypothesised host distributions for native and introduced midges in Australia, and expand the sample of introduced hosts to include Johnson grass. They suggest that Stenodiplosis sorghicola , the principal midge infesting grain sorghum, is also the most common species on Johnson grass. This confirms that Johnson grass plays a role in the population dynamics of S. sorghicola and suggests that midges originating from Johnson grass may influence levels of infestation in grain sorghum.

Floral structure, breeding system and fruit-set in the threatened sub-shrub Tetratheca juncea Smith (Tremandraceae)

Tetratheca juncea Smith (Tremandraceae) has undergone a range contraction of approx. 50 km in the last 100 years and is now listed as a vulnerable sub-shrub restricted to the central and north coast regions of New South Wales, Australia. There are approx. 250 populations in a 110 km north-south distribution and populations are usually small with fewer than 50 plants/clumps. The reproductive ecology of the species was studied to determine why seed-set is reportedly rare. Flowers are bisexual, odourless and nectarless. Flowers are presented dependentally and there are eight stamens recurved around the pistil. Anthers are poricidal, contain viable pollen and basally contain a deep-red tapetal fluid that is slightly oily. Thus flowers are presented for buzz pollinators, although none were observed at flowers during our study. The species was found to be facultatively xenogamous with only one in 50 glasshouse flowers setting seed autogamously, i.e. without pollinator assistance. Field studies revealed fertile fruit in 24 populations but production varied significantly across sites from exceedingly low (0.6 fruits per plant clump) to low (17 fruits per plant clump). Fruit-set ranged from 0 to 65%, suggesting that pollen vectors exist or that autogamy levels in the field are variable and higher than glasshouse results. Fruit production did not vary with population size, although in three of the five populations in the south-west region more than twice as much fruit was produced as in populations elsewhere. A moderately strong relationship between foliage volume and fruit : flower ratios suggests that bigger plants may be more attractive than smaller plants to pollinators. A review of Tetratheca pollination ecology revealed that several species are poorly fecund and pollinators are rare. The habitat requirements for Tetratheca, a genus of many rare and threatened species, is discussed. (C) 2003 Annals of Botany Company.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.

Automatic segmentation of the knee bones using 3D active shape models

This paper presents an automated segmentation approach for MR images of the knee bones. The bones are the first stage of a segmentation system for the knee, primarily aimed at the automated segmentation of the cartilages. The segmentation is performed using 3D active shape models (ASM), which are initialized using an affine registration to an atlas. The 3D ASMs of the bones are created automatically using a point distribution model optimization scheme. The accuracy and robustness of the segmentation approach was experimentally validated using an MR database of fat suppressed spoiled gradient recall images.