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

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

The signature of the first stars in atomic hydrogen at redshift 20

Dark and baryonic matter moved at different velocities in the early Universe, which strongly suppressed star formation in some regions. This was estimated to imprint a large-scale fluctuation signal of about 2 mK in the 21-cm spectral line of atomic hydrogen associated with stars at a redshift of 20, although this estimate ignored the critical contribution of gas heating due to X-rays and major enhancements of the suppression. A large velocity difference reduces the abundance of halos and requires the first stars to form in halos of about a million solar masses, substantially greater than previously expected. Here we report a simulation of the distribution of the first stars at z=20 (cosmic age of ~180 Myr), incorporating all these ingredients within a 400 Mpc box. We find that the 21-cm signature of these stars is an enhanced (10 mK) fluctuation signal on the 100-Mpc scale, characterized by a flat power spectrum with prominent baryon acoustic oscillations. The required sensitivity to see this signal is achievable with an integration time of a thousand hours with an instrument like the Murchison Wide-field Array or the Low Frequency Array but designed to operate in the range of 50-100 MHz.Comment: 27 pages, 5 figures, close (but not exact) match to accepted version. Basic results unchanged from first submitted version, but justification strengthened, title and abstract modified, and substantial Supplementary Material added. Originally first submitted for publication on Oct. 12, 201