Christian Growth Groups

Problem: Members of the larger churches often are deprived of the advantages of close fellowship. Consequently, they either remain in the church with social needs unfulfilled, or they seek fulfilment outside the Adventist church in ways that may conflict with a Christian lifestyle. Many withdraw from the church permanently. A Christian growth group was formed at Hillview Seventh-day Adventist Church with this problem in mind

Cold dark matter models with high baryon content

Recent results have suggested that the density of baryons in the Universe, OmegaB, is much more uncertain than previously thought, and may be significantly higher. We demonstrate that a higher OmegaB increases the viability of critical-density cold dark matter (CDM) models. High baryon fraction offers the twin benefits of boosting the first peak in the microwave anisotropy power spectrum and of suppressing short-scale power in the matter power spectrum. These enable viable CDM models to have a larger Hubble constant than otherwise possible. We carry out a general exploration of high OmegaB CDM models, varying the Hubble constant h and the spectral index n. We confront a variety of observational constraints and discuss specific predictions. Although some observational evidence may favour baryon fractions as high as 20 per cent, we find that values around 10 to 15 per cent provide a reasonable fit to a wide range of data. We suggest that models with OmegaB in this range, with h about 0.5 and n about 0.8, are currently the best critical-density CDM models.Comment: 14 pages, LaTeX, with 9 included figures, to appear in MNRAS. Revised version includes updated references, some changes to section 4. Conclusions unchange

A Multi-Valued Logarithm on Time Scales

A new definition of a multi-valued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This new logarithm arises naturally from the definition of the cylinder transformation that is also at the heart of the definition of exponential functions on time scales. This definition will lead to a logarithm function on arbitrary time scales with familiar and useful properties that previous definitions in the literature lacked.Comment: Pre-print version 1, 17 page

Alp7/TACC-Alp14/TOG generates long-lived, fast-growing MTs by an unconventional mechanism

Alp14 is a TOG-family microtubule polymerase from S. pombe that tracks plus ends and accelerates their growth. To interrogate its mechanism, we reconstituted dynamically unstable single isoform S. pombe microtubules with full length Alp14/TOG and Alp7, the TACC-family binding partner of Alp14. We find that Alp14 can drive microtubule plus end growth at GTP-tubulin concentrations at least 10-fold below the usual critical concentration, at the expense of increased catastrophe. This reveals Alp14 to be a highly unusual enzyme that biases the equilibrium for the reaction that it catalyses. Alp7/TACC enhances the effectiveness of Alp14, by increasing its occupancy. Consistent with this, we show in live cells that Alp7 deletion produces very similar MT dynamics defects to Alp14 deletion. The ability of Alp7/14 to accelerate and bias GTP-tubulin exchange at microtubule plus ends allows it to generate long-lived, fast-growing microtubules at very low cellular free tubulin concentrations

Dispersed graph labellings

A $k$-dispersed labelling of a graph $G$ on $n$ vertices is a labelling of the vertices of $G$ by the integers $1, \dots , n$ such that $d(i,i+1) \geq k$ for $1 \leq i \leq n-1$. $DL(G)$ denotes the maximum value of $k$ such that $G$ has a $k$-dispersed labelling. In this paper, we study upper and lower bounds on $DL(G)$. Computing $DL(G)$ is NP-hard. However, we determine the exact values of $DL(G)$ for cycles, paths, grids, hypercubes and complete binary trees. We also give a product construction and we prove a degree-based bound.Comment: To be published in Australasian Journal of Combinatoric