Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Site-directed mutagenesis and kinetic studies of the West Nile virus NS3 protease identify key enzyme-substrate interactions

The flavivirus West Nile virus (WNV) has spread rapidly throughout the world in recent years causing fever, meningitis, encephalitis, and fatalities. Because the viral protease NS2B/NS3 is essential for replication, it is attracting attention as a potential therapeutic target, although there are currently no antiviral inhibitors for any flavivirus. This paper focuses on elucidating interactions between a hexapeptide substrate (Ae-KPGLKR-p-nitroanilide) and residues at S1 and S2 in the active site of WNV protease by comparing the catalytic activities of selected mutant recombinant proteases in vitro. Homology modeling enabled the predictions of key mutations in VWNV NS3 protease at S1 (V115A/F, D129A/ E/N, S135A, Y150A/F, S160A, and S163A) and S2 (N152A) that might influence substrate recognition and catalytic efficiency. Key conclusions are that the substrate P1 Arg strongly interacts with S1 residues Asp-129, Tyr-150, and Ser-163 and, to a lesser extent, Ser-160, and P2 Lys makes an essential interaction with Asn-152 at S2. The inferred substrate-enzyme interactions provide a basis for rational protease inhibitor design and optimization. High sequence conservation within flavivirus proteases means that this study may also be relevant to design of protease inhibitors for other flavivirus proteases.

Group-directed criticism in Indonesia: Role of message source and audience

Research in individualist cultures has shown that group members are more likely to agree with criticisms of their group when the criticisms are made by another ingroup member as opposed to an outgroup member (the intergroup sensitivity effect). However, evaluations of ingroup critics are often harsher when they take their comments to an outgroup audience. In light of research on facework and tolerance for dissent, it seems important to test whether these effects are generalizable to a collectivist culture. Indonesian Muslims (N = 191) received a criticism of their religion stemming either from another Muslim or a Christian, and published in either a Muslim or a Christian newspaper. Participants agreed with the comments more when they were made by an ingroup as opposed to an outgroup member. Furthermore, consistent with previous research in Australia, the effects of audience on agreement were moderated by levels of group identification. Results are discussed in relation to theory about the functional role internal critics can play in group life.

Decomposition of complete graphs into 5-cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5-cubes are that 5 divides it - 1 and 80 divides it (it - 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for it even, thus completing the spectrum problem for the 5-cube and lending further weight to a long-standing conjecture of Kotzig. (c) 2005 Wiley Periodicals, Inc.

Some equitably 2-colourable cycle decompositions of multipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has x(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar x(i) - x(j)vertical bar

On Hamilton cycle decomposition of 6-regular circulant graphs

The circulant graph Sn, where S ⊆ Zn \ {0}, has vertex set Zn and edge set {{x, x + s}|x ∈ Zn, s ∈ S}. It is shown that there is a Hamilton cycle decomposition of every 6-regular circulant graph Sn in which S has an element of order n.

Theoretical interfaces in the acute paediatric context: A psychotherapeutic understanding of the application of infant-directed singing

Psychotherapy literature provides a theoretical understanding of parent-infant attachment. This article will reflect upon the specific need to give thoughtful consideration to those infants admitted to the acute-care setting, such as neonatal and paediatric intensive care units, and the potential for this environment to affect infant development and the parent-infant relationship. Infant-directed singing, as described in this article, is an improvised form of vocal interaction that is specifically informed by an understanding of the musical parameters of pitch, rhythm, phrasing, timbre, register, dynamic, tempo and silence. This article will detail a theoretical understanding of using infant-directed singing to foster parent-infant interaction within the acute care environment. In particular, the potentially sensitive, reciprocal and engaging nature of infant-directed singing, coupled with its ability to promote and support maternal demonstrations of empathy, will be discussed with a view to the psychological and physical development of the hospitalised infant.

Are parent-reported outcomes for self-directed or telephone-assisted behavioral family intervention enhanced if parents are observed?

The study examined the effects of conducting observations as part of a broader assessment of families participating in behavior family intervention (BFI). It was designed to investigate whether the observations improve intervention outcomes. Families were randomly assigned to different levels of BFI or a waitlist control condition and subsequently randomly assigned to either observation or no-observation conditions. This study demonstrated significant intervention and observation effects. Mothers in more intensive BFI reported more improvement in their child’s behavior and their own parenting. Observed mothers reported lower intensity of child behavior problems and more effective parenting styles. There was also a trend for less anger among mothers who were observed and evidence of an observation-intervention interaction for parental anger, with observed mothers in more intensive intervention reporting less anger compared to those not observed. Implications for clinical and research intervention contexts are discussed.