Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Statistical modeling and projections of lung cancer mortality in 4 industrialized countries

The purpose of this work was to model lung cancer mortality as a function of past exposure to tobacco and to forecast age-sex-specific lung cancer mortality rates. A 3-factor age-period-cohort (APC) model, in which the period variable is replaced by the product of average tar content and adult tobacco consumption per capita, was estimated for the US, UK, Canada and Australia by the maximum likelihood method. Age- and sex-specific tobacco consumption was estimated from historical data on smoking prevalence and total tobacco consumption. Lung cancer mortality was derived from vital registration records. Future tobacco consumption, tar content and the cohort parameter were projected by autoregressive moving average (ARIMA) estimation. The optimal exposure variable was found to be the product of average tar content and adult cigarette consumption per capita, lagged for 2530 years for both males and females in all 4 countries. The coefficient of the product of average tar content and tobacco consumption per capita differs by age and sex. In all models, there was a statistically significant difference in the coefficient of the period variable by sex. In all countries, male age-standardized lung cancer mortality rates peaked in the 1980s and declined thereafter. Female mortality rates are projected to peak in the first decade of this century. The multiplicative models of age, tobacco exposure and cohort fit the observed data between 1950 and 1999 reasonably well, and time-series models yield plausible past trends of relevant variables. Despite a significant reduction in tobacco consumption and average tar content of cigarettes sold over the past few decades, the effect on lung cancer mortality is affected by the time lag between exposure and established disease. As a result, the burden of lung cancer among females is only just reaching, or soon will reach, its peak but has been declining for I to 2 decades in men. Future sex differences in lung cancer mortality are likely to be greater in North America than Australia and the UK due to differences in exposure patterns between the sexes. (c) 2005 Wiley-Liss, Inc.

Theory of mind and mental state discourse during book reading and story-telling tasks

This article presents three studies conducted in Canada and Australia that relate theory of mind (ToM) development to mental state discourse. In Study 1, mental state discourse was examined while parents and their 5-7-year-old children jointly read a storybook which had a surprise ending about the identity of the main character. Comments specific to the mental states of the story characters and discourse after the book had ended were positively related to children's ToM, and this was due to parent elaborations. Studies 2 and 3 examined children's mental state discourse during storytelling tasks, and in both, mental state discourse of children during narrative was concurrently related to ToM performance. While research has shown that mental state discourse of parents is related to children's ToM acquisition, the current research indicates that children's spontaneous use of mental state language examined outside of the interactional context is also a strong correlate.

Analysis of stroke patients' and carers' reading ability and the content and design of written materials: Recommendations for improving written stroke information

Objective: This study (a) evaluated the reading ability of patients following stroke and their carers and the reading level and content and design characteristics of the written information provided to them, (b) explored the influence of sociodemographic and clinical characteristics on patients' reading ability, and (c) described an education package that provides well-designed information tailored to patients' and carers' informational needs. Methods: Fifty-seven patients and 12 carers were interviewed about their informational needs in an acute stroke unit. Their reading ability was assessed using the Rapid Estimate of Adult Literacy in Medicine (REALM). The written information provided to them in the acute stroke unit was analysed using the SMOG readability formula and the Suitability Assessment of Materials (SAM). Results: Thirteen (22.8%) patients and 5 (41.7%) carers had received written stroke information. The mean reading level of materials analysed was 11th grade while patients read at a mean of 7-8th grade. Most materials (89%) scored as only adequate in content and design. Patients with combined aphasia read significantly lower (4-6th grade) than other patients (p = 0.001). Conclusion: Only a small proportion of patients and carers received written materials about stroke and the readability level and content and design characteristics of most materials required improvement. Practice implications: When developing and distributing written materials about stroke, health professionals should consider the reading ability and informational needs of the recipients, and the reading level and content and design characteristics of the written materials. A computer system can be used to generate written materials tailored to the informational needs and literacy skills of patients and carers. (c) 2005 Elsevier Ireland Ltd. All rights reserved.

Evidence for conservation and selection of upstream open reading frames suggests probable encoding of bioactive peptides

Background: Approximately 40% of mammalian mRNA sequences contain AUG trinucleotides upstream of the main coding sequence, with a quarter of these AUGs demarcating open reading frames of 20 or more codons. In order to investigate whether these open reading frames may encode functional peptides, we have carried out a comparative genomic analysis of human and mouse mRNA 'untranslated regions' using sequences from the RefSeq mRNA sequence database. Results: We have identified over 200 upstream open reading frames which are strongly conserved between the human and mouse genomes. Consensus sequences associated with efficient initiation of translation are overrepresented at the AUG trinucleotides of these upstream open reading frames, while comparative analysis of their DNA and putative peptide sequences shows evidence of purifying selection. Conclusion: The occurrence of a large number of conserved upstream open reading frames, in association with features consistent with protein translation, strongly suggests evolutionary maintenance of the coding sequence and indicates probable functional expression of the peptides encoded within these upstream open reading frames.

Interpretation of the temperature dependence of equilibrium and rate constants

The objective of this review is to draw attention to potential pitfalls in attempts to glean mechanistic information from the magnitudes of standard enthalpies and entropies derived from the temperature dependence of equilibrium and rate constants for protein interactions. Problems arise because the minimalist model that suffices to describe the energy differences between initial and final states usually comprises a set of linked equilibria, each of which is characterized by its own energetics. For example, because the overall standard enthalpy is a composite of those individual values, a positive magnitude for AHO can still arise despite all reactions within the subset being characterized by negative enthalpy changes: designation of the reaction as being entropy driven is thus equivocal. An experimenter must always bear in mind the fact that any mechanistic interpretation of the magnitudes of thermodynamic parameters refers to the reaction model rather than the experimental system For the same reason there is little point in subjecting the temperature dependence of rate constants for protein interactions to transition-state analysis. If comparisons with reported values of standard enthalpy and entropy of activation are needed, they are readily calculated from the empirical Arrhenius parameters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Ultrastructure of the spermatozoon of Myrmecocichla formicivora (Vieillot, 1881) and Philetairus socius (Latham, 1790) (Aves; Passeriformes), with a new interpretation of the passeridan acrosome

Passerine spermatozoa exhibit apomorphies that distinguish them from non-passerine neognaths and palaeognaths. The acrosome is longer than the nucleus (excepting the suboscines, most Corvida, and a few Passerida). A perforatorium and endonuclear canals are absent. The proximal centriole is absent (except in the suboscines). The distal centriole is secondarily short, contrasting with its elongate condition in palaeognaths and Galloanserae. In the Passerida a single mitochondrial strand winds extensively along the axoneme (restricted to the anterior axoneme in suboscines and Corvida). A fibrous, or amorphous, periaxonemal sheath, seen in palaeognaths and many non-passerines, respectively, is absent. The acrosome in Myrmecocichla formicivora and Philetairus socius is bipartite: an acrosome core is surmounted by an acrosome crest; the core is ensheathed by a layer which is a posterior extension of the crest. The acrosome helix is a lateral extension of the crest and the crest layer with (Myrmecocichla) or without (Philetairus) protrusion of material of the acrosome core into it. In M. formicivora, as in other muscicapoids, a fibrous helix is intertwined with at least the more proximal region of the mitochondrial helix. The fibrous helix is absent at maturity in Philetairus and other described passeroid spermatozoa with the possible exception of Passer italiae. In Philetairus a granular helix precedes the mitochondrial helix.