The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices

Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic (geometric) mean of weight vectors, calculated from all spanning trees, is proved to be optimal to the (logarithmic) least squares problem, not only for complete, as it was recently shown in Lundy, M., Siraj, S., Greco, S. (2017): The mathematical equivalence of the "spanning tree" and row geometric mean preference vectors and its implications for preference analysis, European Journal of Operational Research 257(1) 197-208, but for incomplete matrices as well. Unlike the complete case, where an explicit formula, namely the row arithmetic/geometric mean of matrix elements, exists for the (logarithmic) least squares problem, the incomplete case requires a completely different and new proof. Finally, Kirchhoff's laws for the calculation of potentials in electric circuits is connected to our results.Comment: 21 pages, 6 figure

Nazi Punks Folk Off: Leisure, Nationalism, Cultural Identity and the Consumption of Metal and Folk Music

Far-right activists have attempted to infiltrate and use popular music scenes to propagate their racialised ideologies. This paper explores attempts by the far right to co-opt two particular music scenes: black metal and English folk. Discourse tracing is used to explore online debates about boundaries, belonging and exclusion in the two scenes, and to compare such online debates with ethnographic work and previous research. It is argued that both scenes have differently resisted the far right through the policing of boundaries and communicative choices, but both scenes are compromised by their relationship to myths of whiteness and the instrumentality of the pop music industry

Shepard avocado maturity consumer sensory research

Dry matter content (DM) of avocados represents the amount of carbohydrates and nutrients that have been transported from the tree into the fruit. The longer the avocado remains on the tree, the higher the dry matter, and consequently, %DM is used by growers to decide when avocados are ready to harvest. In the current study, 112 consumers tasted ‘Shepard’, a variety of avocado that can be harvested early in the season. The avocados were collected from a range of locations in Northern Queensland in order to ensure that fruit of varying maturity (%DM) were available for tasting at the same time. Consumers’ liking of flavour increased progressively as the DM content of avocados increased from 18% to 23% but then reached a plateau, where further increases in DM did not result in corresponding increases in liking. The immature (lower DM) avocados were frequently described as having ‘bland/tasteless’ or ‘watery’ flavour as well as being less liked than other avocados. Following tasting, consumers were asked about their experience with avocados and the extent that a quality guarantee offering to refund or replace damaged fruit might increase purchasing. Consumers continued to report a high incidence and severity of damage in the avocados they purchased for consumption at home. The study indicated that consumers’ willingness to buy avocados increased as a consequence of the quality guarantee

The unstable coastline: navigating dispossession and belonging in Colombo

This article explores how residents of a small coastal fishing enclave in Colombo live with cumulative waves of dispossession brought on by exclusionary projects of urban development. Drawing on ethnographic fieldwork, I introduce the analytic of navigation to describe how people move, plan and live with both present and future threats of dispossession. Navigation offers a unique perspective on questions of agency and resistance in oppressive conditions. Rather than framing subjects as “resisting” projects of world-class city-making, this analysis shows that urban residents instead engage in complex and occasionally contradictory modes of living with uncertainty. I complicate existing understandings of the term “navigation” by describing how questions of nation and belonging are crucial to comprehending how people navigate. Ultimately, I suggest that expressions of belonging and obligation to an imagined community might not only be strategic, but instead reflect some of the broader social forces which structure possibilities for action

Justifying the Special Theory of Relativity with Unconceived Methods

Many realists argue that present scientific theories will not follow the fate of past scientific theories because the former are more successful than the latter. Critics object that realists need to show that present theories have reached the level of success that warrants their truth. I reply that the special theory of relativity has been repeatedly reinforced by unconceived scientific methods, so it will be reinforced by infinitely many unconceived scientific methods. This argument for the special theory of relativity overcomes the critics’ objection, and has advantages over the no-miracle argument and the selective induction for it

Independent measurement of the Hoyle state β\beta feeding from 12B using Gammasphere

Using an array of high-purity Compton-suppressed germanium detectors, we performed an independent measurement of the $\beta$-decay branching ratio from $^{12}\mathrm{B}$ to the second-excited (Hoyle) state in $^{12}\mathrm{C}$. Our result is $0.64(11)\%$, which is a factor $\sim 2$ smaller than the previously established literature value, but is in agreement with another recent measurement. This could indicate that the Hoyle state is more clustered than previously believed. The angular correlation of the Hoyle state $\gamma$ cascade has also been measured for the first time. It is consistent with theoretical predictions