On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

Actual and preferred work activites of mental health Occupational Therapists: Congruence or Discrepancy

The reform of Australian mental health services has resulted in new models of care and changed work practices for all mental health professionals. Occupational therapists today are as likely to be working in multidisciplinary teams performing a range of generic clinical roles as they are to be working in specialist rehabilitation units. These kinds of changes have taken place in other countries, with anecdotal and some empirical evidence that the changes have resulted in concerns about loss of professional identity and roles. This study sought to identify the current work activities carried out by occupational therapists and to determine whether there was a discrepancy between their actual and desired work activities. It was expected that, overall, they would indicate a preference to do more specialist rehabilitation focused work and less generic case management work. A survey of 196 occupational therapists investigated their actual and preferred work activities in 55 specific roles across four broad categories (senior administration, specialist clinical, general clinical and community development). As expected, the participants indicated that they would prefer to be undertaking more specialist rehabilitation oriented work activities than they were actually doing. Contrary to expectations, they also wished to undertake more rather than less generic clinical work activities, to be more engaged in community development work and to take on more senior and administrative roles. They indicated a preference for less rather than more activity on only 5 of the 55 work roles examined. On examining a subset of 113 participants who reported that 50% or more of their time was spent in case management, there was greater evidence of resistance to generic clinical roles. It was therefore concluded that occupational therapists in Australia are seeking to deploy their specialist skills to a greater degree than the current practice environment permits. They have broadly accepted the generic roles required in multidisciplinary community case management, but those who are actually working in these roles are most likely to have reservations about this kind of work.

Genes, morphology and agreement: congruence in Australian anthracine bee flies (Diptera : Bombyliidae : Anthracinae)

Almost half of the 4547 described bee flies (Bombyliidae: Diptera) in the world belong to the subfamily Anthracinae, with most of the world's diversity in three cosmopolitan tribes: Villini, Anthracini and Exoprosopini. Molecular data from 815 base pairs of 16S mitochondrial DNA and morphological characters from species-groups of these tribes in Australia were analysed cladistically. The results show that the relationships between the anthracine tribes reflect those found in a previous morphological analysis. The genera of the Anthracinae in Australia are monophyletic, except for Ligyra Newman, and are assigned to tribes. Although simultaneous analysis of the combined molecular and morphological data produced clades found in both separate analyses, the different data sources are significantly incongruent. We use phylogenetic measures to examine support for the relationships among the Australian Anthracinae inferred by the molecular and morphological data.

An investigation into the antecedents of goal congruence in retail-service settings

The authors report the results of two studies that model the antecedents of goal congruence in retail-service settings. They draw the antecedents from extant research and propose that goal congruence is related to employees' perceptions of morale, leadership support, fairness in reward allocation, and empowerment. They hypothesize and test direct and indirect relationships between these constructs and goal congruence. Results of structural equations modeling suggest an important mediating role for morale and interesting areas of variation across retail and service settings.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Congruence in QTL for adventitious rooting in Pinus elliottii X Pinus caribaea hybrids resolves between and within-species effects

Targeting between-species effects for improvement in synthetic hybrid populations derived from outcrossing parental tree species may be one way to increase the efficacy and predictability of hybrid breeding. We present a comparative analysis of the quantitative trait loci (QTL) which resolved between from within-species effects for adventitious rooting in two populations of hybrids between Pinus elliottii and P. caribaea, an outbred F-1 (n=287) and an inbred-like F-2 family (n=357). Most small to moderate effect QTL (each explaining 2-5% of phenotypic variation, PV) were congruent (3 out of 4 QTL in each family) and therefore considered within-species effects as they segregated in both families. A single large effect QTL (40% PV) was detected uniquely in the F-2 family and assumed to be due to a between-species effect, resulting from a genetic locus with contrasting alleles in each parental species. Oligogenic as opposed to polygenic architecture was supported in both families (60% and 20% PV explained by 4 QTL in the F-2 and F-1 respectively). The importance of adventitious rooting for adaptation to survive water-logged environments was thought in part to explain oligogenic architecture of what is believed to be a complex trait controlled by many hundreds of genes.

Experimental validation of the regulated expression of large numbers of non-coding RNAs from the mouse genome

Recent large-scale analyses of mainly full-length cDNA libraries generated from a variety of mouse tissues indicated that almost half of all representative cloned sequences did flat contain ail apparent protein-coding sequence, and were putatively derived from non-protein-coding RNA (ncRNA) genes. However, many of these clones were singletons and the majority were unspliced, raising the possibility that they may be derived from genomic DNA or unprocessed pre-rnRNA contamination during library construction, or alternatively represent nonspecific transcriptional noise. Here we Show, using reverse transcriptase-dependent PCR, microarray, and Northern blot analyses, that many of these clones were derived from genuine transcripts Of unknown function whose expression appears to be regulated. The ncRNA transcripts have larger exons and fewer introns than protein-coding transcripts. Analysis of the genomic landscape around these sequences indicates that some cDNA clones were produced not from terminal poly(A) tracts but internal priming sites within longer transcripts, only a minority of which is encompassed by known genes. A significant proportion of these transcripts exhibit tissue-specific expression patterns, as well as dynamic changes in their expression in macrophages following lipopolysaccharide Stimulation. Taken together, the data provide strong support for the conclusion that ncRNAs are an important, regulated component of the mammalian transcriptome.