On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group $\Gamma$, will construct explicit finite models for the skeleta of $K(\Gamma,1)$ and hence compute the integral homology and cohomology of $\Gamma$.Comment: 21 pages, 4 figure

Infinite groups with fixed point properties

We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first examples of infinite finitely generated groups $Q$ with the property that for any action of $Q$ on any $X\in \mathcal{X}_{ac}$, there is a global fixed point. Moreover, $Q$ may be chosen to be simple and to have Kazhdan's property (T). We construct a finitely presented infinite group $P$ that admits no non-trivial action by diffeomorphisms on any smooth manifold in $\mathcal{X}_{ac}$. In building $Q$, we exhibit new families of hyperbolic groups: for each $n\geq 1$ and each prime $p$, we construct a non-elementary hyperbolic group $G_{n,p}$ which has a generating set of size $n+2$, any proper subset of which generates a finite $p$-group.Comment: Version 2: 29 pages. This is the final published version of the articl

Building audiences: Aboriginal and Torres Strait Islander arts

Building Audiences examines the barriers to and the strategies for increasing audiences in the Aboriginal and Torres Strait Islander arts sector. This research investigates the attitudes, beliefs and behaviours of current and potential audiences. What is in the report? The findings reveal the key barriers facing audience attendance include: uncertainty about how to behave at cultural events and fear of offending lack of awareness with audiences not actively seeking information about Indigenous arts and outdated perceptions of the sector – that it is only perceived as ‘serious or educational’. Building Audiences also considered several strategies to build audiences for Indigenous arts: providing skills development, advice and resourcing to Indigenous practitioners within the arts sector; increasing representation of Indigenous artists in the main programing of arts companies by including more Indigenous people in decision making roles; promoting relationships between Indigenous arts and non-Indigenous companies to present their work to wider audiences; introducing children and young people to Indigenous arts through schools and extracurricular activities; allowing audiences to feel comfortable engaging by creating accessible experiences; implementing long-term strategies to change negative perceptions of Indigenous arts. The project was commissioned by the Australia Council for the Arts and funding partners include Australia Council for the Arts; Faculty of Business and Law and Institute of Koorie Education, Deakin University; Melbourne Business School, The University of Melbourne

Strongly bounded groups and infinite powers of finite groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman. Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups with Property (FH)". To appear in Comm. Algebr

High Performance Algorithms for Counting Collisions and Pairwise Interactions

The problem of counting collisions or interactions is common in areas as computer graphics and scientific simulations. Since it is a major bottleneck in applications of these areas, a lot of research has been carried out on such subject, mainly focused on techniques that allow calculations to be performed within pruned sets of objects. This paper focuses on how interaction calculation (such as collisions) within these sets can be done more efficiently than existing approaches. Two algorithms are proposed: a sequential algorithm that has linear complexity at the cost of high memory usage; and a parallel algorithm, mathematically proved to be correct, that manages to use GPU resources more efficiently than existing approaches. The proposed and existing algorithms were implemented, and experiments show a speedup of 21.7 for the sequential algorithm (on small problem size), and 1.12 for the parallel proposal (large problem size). By improving interaction calculation, this work contributes to research areas that promote interconnection in the modern world, such as computer graphics and robotics.Comment: Accepted in ICCS 2019 and published in Springer's LNCS series. Supplementary content at https://mjsaldanha.com/articles/1-hpc-ssp

Diacetyl in Australian dry red wines and its significance in wine quality

The diacetyl content of 466 Australian dry red table wines ranged from less than 0.1 ppm to 7.5 ppm with a mean of 2.4 ppm. Malo-lactic fermentation had occurred in 71 per cent of the wines, which had a mean diacetyl level of 2.8 ppm. In wines which had not undergone malo-lactic fermentation the mean diacetyl level 1.3 ppm.Taste threshold tests showed that a difference of as little as 1 ppm could be detected in a light dry red wine containing 0.3 ppm diacetyl. In a full flavoured darker wine of higher quality containing 3 ppm the minimum detectable addition was 1.3 ppm.It is considered that diacetyl in amounts up to 2 to 4 ppm, depending on the wine, improved quality by adding complexity to the flavour. Above these levels the aroma of diacetyl became identifiable as such and resulted in a reduction in quality. The diacetyl content of a range of red table wines stored at 15° C showed a mean decrease of 19 per cent in diacetyl content in 4 months, 22 per cent in 8 months, 26 per cent in 12 months and 28 per c ent in 18 months

On residualizing homomorphisms preserving quasiconvexity

H is called a G-subgroup of a hyperbolic group G if for any finite subset M G there exists a homomorphism from G onto a non-elementary hyperbolic group G_1 that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. Here we show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity

Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page