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We show that the stable module -category of a finite group decomposes in three different ways as a limit of the stable module -categories of certain subgroups of . Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module -category to be defined for any -space, then showing that this extension only depends on the -equivariant homotopy type of a -space. The methods used are not specific to the stable module -category, so may also be applicable in other settings where an -category depends functorially on .

We show that the stable module -category of a finite group decomposes in three different ways as a limit of the stable module -categories of certain subgroups of . Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module -category to be defined for any -space, then showing that this extension only depends on the -equivariant homotopy type of a -space. The methods used are not specific to the stable module -category, so may also be applicable in other settings where an -category depends functorially on .

The New Zealand dairy industry produces approximately 4.2 million calves annually, of which about 30% are retained within the dairy industry, while a further 20% are utilised in the beef industry. The remainder are surplus to requirements, and the majority (1.7 million per annum) are processed in the low value bobby calf trade. This model appears sub-optimal, with an estimated opportunity cost in excess of NZD $1 billion annually, and numerous animal welfare and ethical issues. Farming surplus dairy calves in an accelerated-cycle beef production enterprise for slaughter prior to one-year of age, could generate favourable outcomes, and the current study aimed to investigate this opportunity. Experimental growth and carcass data for Hereford x Friesian-Jersey steers slaughtered at 8-, 10- and 12- months of age was obtained in a live-animal trial. Simulation models (referred to as NGB8, NGB10 and NGB12 where the figures refer to monthly ages at slaughter) utilising Microsoft EXCEL feed budgets, gross margin analysis and the OVERSEER nutrient budget model were developed from the experimental data to estimate the physical, financial, and environmental performance of accelerated-cycle beef production at each slaughter age. Results were compared to a simulated high and low performing bull- beef enterprise based on the literature, with slaughter occurring at 18- or 24-months, to determine the relative performance of accelerated-cycle beef production. The model comparators are referred to as Bull18 and Bull24. In the trial, the accelerated-cycle beef production (NGB) steers achieved slaughter weights of 252, 303 and 348 kg at 8-, 10- and 12-months of age (119, 146 and 174 kg carcass weight). The dressing out percentage was the same in the 8- and 10-month treatments (P>0.05) but increased in the 12-month treatment (P<0.001). Using the ‘prime’ beef price, NGB8 and NGB10 generated a loss, while NGB12 was profitable. To be financially competitive with Bull18 or Bull24, NGB produ

In the late 1920’s and early 1930’s, physicists applied group representation theory to the quantum mechanics of atomic spectra. At the same time, physicists developed an alternative approach to theoretical atomic spectra that avoids using group theory. These two approaches exhibit nontrivial intellectual differences: the group theoretic approach provides a deeper understanding of many phenomena in atomic spectra. By focusing on derivations of selection rules for atomic spectra, I explicate one case where group theory enhances understanding. I refer to the non-group theoretic approach as the commutator approach; it serves as a benchmark for comparison. This case study motivates a deflationary account of mathematical explanations in science. According to my account, both group theoretic and commutator derivations explain selection rules for atomic spectra. I use these derivations to problematize stronger accounts of mathematical explanation that rely on a notion of relevance. Arguing that selection rules are an example of universality, I also criticize a strong interpretation of Batterman and Rice’s minimal model account of explanations of universality. After examining these accounts of explanation, I argue that explanatory criteria do not distinguish the intellectual content of the group theoretic and commutator approaches. Instead, I develop an account of scientific understanding that distinguishes these approaches based on organizational differences. Adopting terminology from Manders, I argue that these organizational differences arise from differences in the approach’s expressive means. Group theory reorganizes selection rule derivations by re-expressing physical concepts more effectively than the commutator approach. I argue that this superior organizational structure accounts for how group theory provides a heightened understanding of selection rules.

In the late 1920’s and early 1930’s, physicists applied group representation theory to the quantum mechanics of atomic spectra. At the same time, physicists developed an alternative approach to theoretical atomic spectra that avoids using group theory. These two approaches exhibit nontrivial intellectual differences: the group theoretic approach provides a deeper understanding of many phenomena in atomic spectra. By focusing on derivations of selection rules for atomic spectra, I explicate one case where group theory enhances understanding. I refer to the non-group theoretic approach as the commutator approach; it serves as a benchmark for comparison. This case study motivates a deflationary account of mathematical explanations in science. According to my account, both group theoretic and commutator derivations explain selection rules for atomic spectra. I use these derivations to problematize stronger accounts of mathematical explanation that rely on a notion of relevance. Arguing that selection rules are an example of universality, I also criticize a strong interpretation of Batterman and Rice’s minimal model account of explanations of universality. After examining these accounts of explanation, I argue that explanatory criteria do not distinguish the intellectual content of the group theoretic and commutator approaches. Instead, I develop an account of scientific understanding that distinguishes these approaches based on organizational differences. Adopting terminology from Manders, I argue that these organizational differences arise from differences in the approach’s expressive means. Group theory reorganizes selection rule derivations by re-expressing physical concepts more effectively than the commutator approach. I argue that this superior organizational structure accounts for how group theory provides a heightened understanding of selection rules.

Daniel R McGrath1, Hamid Frydoonfar2, Joshua J Hunt3, Chris J Dunkley3, Allan D Spigelman41Ipswich Hospital, Ipswich, UK; 2Hunter Pathology Service, New South Wales; 3Royal Newcastle Centre, Newcastle; 4St Vincent’s Clinical School, Sydney, AustraliaBackground: Despite the well recognized protective effect of cruciferous vegetables against various cancers, including human colorectal cancers, little is known about how this effect is conferred. It is thought that some phytochemicals found only in these vegetables confer the protection. These compounds include the glucosinolates, of which indole-3-carbinol is one. They are known to induce carcinogen-metabolizing (phase II) enzymes, including the glutathione S-transferase (GST) family. Other effects in humans are not well documented. We wished to assess the effect of indole-3-carbinol on GST enzymes.Methods: We carried out a placebo-controlled human volunteer study. All patients were given 400 mg daily of indole-3-carbinol for three months, followed by placebo. Serum samples were tested for the GSTM1 genotype by polymerase chain reaction. Serum GST levels were assessed using enzyme-linked immunosorbent assay and Western Blot methodologies.Results: Forty-nine volunteers completed the study. GSTM1 genotypes were obtained for all but two volunteers. A slightly greater proportion of volunteers were GSTM1-positive, in keeping with the general population. GST was detected in all patients. Total GST level was not affected by indole-3-carbinol dosing compared with placebo. Although not statistically significant, the GSTM1 genotype affected the serum GST level response to indole-3-carbinol.Conclusion: Indole-3-carbinol does not alter total serum GST levels during prolonged dosing.Keywords: pilot study, colorectal cancer, glutathione transferase, human, indole-3-carbinol