Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Perceived dissimilarity and work group involvement: The moderating effects of group openness to diversity

Perceived dissimilarity and its association with work group involvement were examined in this study. Additionally, perceived group openness to diversity was examined as a moderator of this relationship. A longitudinal study was conducted with nurses in four departments of a public hospital. Results revealed that visible dissimilarity was negatively associated with work group involvement at both times, and informational dissimilarity was negatively associated with work group involvement at Time 1. Openness to diversity interacted with visible and informational dissimilarity in the prediction of work group involvement at both times. This interaction pattern showed that there was a negative relationship between dissimilarity and work group involvement when individuals perceived low group openness to diversity, whereas there was no relationship when individuals perceived high group openness to diversity. Results highlight the importance of managing perceptions of difference and introducing norms that encourage the active involvement of group members.

Profile of paediatric occupational therapy practice in Australia

Background: The purpose of the present study was to describe a profile of Australian paediatric occupational therapy practice in terms of theories, assessments and interventions used with the most frequently seen client groups. Methods: An ex post facto survey design was utilised. A purpose-designed survey was mailed to 600 occupational therapists identified by OT Australia as working in paediatrics. Results: The response rate was 55% (n = 330). Respondents in the sample worked chiefly with children with developmental delays, learning disabilities, neurological impairments, and infants/toddlers. Theoretical models used by paediatric clinicians that were common to the most frequently seen client groups focused on sensory integration/multisensory approaches, occupational performance, and client-centred practice. Assessment tools most frequently used were the Test of Visual Motor Integration, Sensory Profile, Bruininks-Oseretsky Test of Motor Proficiency, Handwriting Speed Test, and Motor-Free Visual Perception Test. The most often used treatment methods across the four most frequently seen client groups were parent/caregiver education, sensory integration/stimulation techniques, and managing activities of daily living. Conclusions: Paediatric occupational therapists appeared to draw on a range of theoretical models. With the exception of the Sensory Profile, the assessment and treatment methods most frequently used are not congruent with the most commonly used theoretical models. It is critical that the assessment and treatment methods used are conceptually consistent with the theoretical models that guide practice. Occupational therapists need to examine the evidence and determine whether their clinical practice is grounded in the best contemporary theoretical models, assessments and interventions.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

The genetic structure of Australasian green turtles (Chelonia mydas): exploring the geographical scale of genetic exchange

Ecological and genetic studies of marine turtles generally support the hypothesis of natal homing, but leave open the question of the geographical scale of genetic exchange and the capacity of turtles to shift breeding sites. Here we combine analyses of mitochondrial DNA (mtDNA) variation and recapture data to assess the geographical scale of individual breeding populations and the distribution of such populations through Australasia. We conducted multiscale assessments of mtDNA variation among 714 samples from 27 green turtle rookeries and of adult female dispersal among nesting sites in eastern Australia. Many of these rookeries are on shelves that were flooded by rising sea levels less than 10 000 years (c. 450 generations) ago. Analyses of sequence variation among the mtDNA control region revealed 25 haplotypes, and their frequency distributions indicated 17 genetically distinct breeding stocks (Management Units) consisting either of individual rookeries or groups of rookeries in general that are separated by more than 500 km. The population structure inferred from mtDNA was consistent with the scale of movements observed in long-term mark-recapture studies of east Australian rookeries. Phylogenetic analysis of the haplotypes revealed five clades with significant partitioning of sequence diversity (Phi = 68.4) between Pacific Ocean and Southeast Asian/Indian Ocean rookeries. Isolation by distance was indicated for rookeries separated by up to 2000 km but explained only 12% of the genetic structure. The emerging general picture is one of dynamic population structure influenced by the capacity of females to relocate among proximal breeding sites, although this may be conditional on large population sizes as existed historically across this region.

Oviposition and reproductive performance of a generalist parasitoid (Trichogramma pretiosum) exposed to host species that differ in their physical characteristics

The response of generalist egg parasitoids to alternative natural hosts that are present simultaneously is not well known. We investigated the behavior of Trichogramma pretiosum Riley (Hymenoptera: Trichogrammatidae) in relation to two field hosts Helicoverpa armigera Hubner and Spodoptera litura Fabricius, in choice and no choice tests. We quantified the effects of natal host species and post-emergence adult age on the oviposition preference of the parasitoids. H. armigera eggs were consistently preferred over S. litura eggs, regardless of the natal host and adult age. When only S. litura eggs were available as hosts, they were parasitized at statistically similar rates to H. armigera eggs (average of 17 +/- 2.7 vs. 13 +/- 3.0, H. armigera to S. litura). The adult lifespan and lifetime fecundity of T. pretiosum were variable but were affected by natal host species and/or host species to which they were exposed. Mean lifespan and fecundity of parasitoids that had developed in H. armigera eggs and were exposed to H. armigera eggs for oviposition were 13.9 +/- 1.8 days and 98.7 +/- 11.0 adult offspring. By contrast, those that developed in S. litura eggs and were exposed to S. litura eggs for oviposition lived for 7 +/- 0.9 days and produced 53.8 +/- 8.0 adult offspring. The ovigeny index (OI) was significantly lower in the parasitoids exposed to H. armigera eggs than in those exposed to S. litura eggs, regardless of the natal host, indicating that H. armigera eggs sustain the adult parasitoids better than S. litura eggs. These results are used to predict parasitoid behavior in the field when both hosts are available. (c) 2006 Elsevier Inc. All rights reserved.