Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Colorectal cancer screening in Australia: an economic evaluation of a potential biennial screening program using faecal occult blood tests

Objective: To evaluate whether the introduction of a national, co-ordinated screening program using the faecal occult blood test represents 'value-for-money' from the perspective of the Australian Government as third-party funder. Methods: The annual equivalent costs and consequences of a biennial screening program in 'steady-state' operation were estimated for the Australian population using 1996 as the reference year. Disability-adjusted life years (DALYs) and the years of life lost (YLLs) averted, and the health service costs were modelled, based on the epidemiology and the costs of colorectal cancer in Australia together with the mortality reduction achieved in randomised controlled trials. Uncertainty in the model was examined using Monte Carlo simulation methods. Results: We estimate a minimum or 'base program' of screening those aged 55 to 69 years could avert 250 deaths per annum (95% uncertainty interval 99-400), at a gross cost of $A55 million (95% UI $A46 million to $A96 million) and a gross incremental cost-effectiveness ratio of $A17,000/DALY (95% UI $A13,000/DALY to $A52,000/DALY). Extending the program to include 70 to 74-year-olds is a more effective option (cheaper and higher health gain) than including the 50 to 54-year-olds. Conclusions: The findings of this study support the case for a national program directed at the 55 to 69-year-old age group with extension to 70 to 74-year-olds if there are sufficient resources. The pilot tests recently announced in Australia provide an important opportunity to consider the age range for screening and the sources of uncertainty, identified in the modelled evaluation, to assist decisions on implementing a full national program.

Sunscreen penetration of human skin and related keratinocyte toxicity after topical application

Sunscreen skin penetration and safety assessment should be considered together in order to ensure that in vitro cytotoxicity studies examine relevant doses of these organic chemical UV filters to which viable epidermal cells are realistically exposed. In this study, we sought to determine whether sufficient topically applied sunscreens penetrated into human viable epidermis to put the local keratinocyte cell populations at risk of toxicity. The penetration and retention of five commonly used sunscreen agents ( avobenzone, octinoxate, octocrylene, oxybenzone and padimate O) in human skin was evaluated after application in mineral oil to isolated human epidermal membranes. Sunscreen concentration - human keratinocyte culture response curves were then defined using changes in cell morphology and proliferation ( DNA synthesis using radiolabelled thymidine uptake studies) as evidence of sunscreens causing toxicity. Following 24 h of human epidermal exposure to sunscreens, detectable amounts of all sunscreens were present in the stratum corneum and viable epidermis, with epidermal penetration most evident with oxybenzone. The concentrations of each sunscreen found in human viable epidermis after topical application, adjusting for skin partitioning and binding effects, were at least 5-fold lower, based on levels detected in viable epidermal cells, than those appearing to cause toxicity in cultured human keratinocytes. It is concluded that the human viable epidermal levels of sunscreens are too low to cause any significant toxicity to the underlying human keratinocytes. Copyright (C) 2005 S. Karger AG, Basel.

Inconclusiveness of chytridiomycosis as the agent in widespread frog declines

Although there is considerable evidence to support the hypothesis that the chytrid fungus Batrachochytrium dendrobatidis is the primary agent responsible for widespread declines in amphibian populations, particularly rainforest frog populations in Australia and Central America, I argue the case has not yet been made conclusively. Few specimens were collected at the time of population declines, so it may never be possible to conclusively determine their cause. It remains unclear whether the pathogen is novel where declines have occurred. Although it is not necessary that the infection be novel for it to be implicated in declines, if a preexisting pathogen has only recently caused extinctions, cofactors must be important. Whether the pattern of outbreaks represents a wave of extinctions is unclear, but if it does, the rate of spread in Australia is implausibly high for a waterborne pathogen, given the most likely estimates of epidemiological parameters. Although B. dendrobatidis is an amphibian pathogen according to Koch's postulates, the postulates are neither necessary nor sufficient criteria to identify a pathogen. The following key pieces of information are necessary to better understand the impact of this fungus on frog communities: better knowledge of the means and rate of transmission under field conditions, prevalence of infection among frog populations, as distinct from morbid individuals, and the effect of the fungus on frogs in the wild. It is crucial to determine whether there are strains of the fungus with differing pathogenicity to particular frog species and whether host-pathogen coevolution has occurred or is occurring. Recently developed diagnostic tools bring into reach the possibility of addressing these questions and thus developing appropriate strategies to manage frog communities that may be affected by this fungus.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.