Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data

Multidimensional scaling (MDS) is often used for the analysis of correlation matrices of items generated by a facet theory design. The emphasis of the analysis is on regional hypotheses on the location of the items in the MDS solution. An important regional hypothesis is the axial constraint where the items from different levels of a facet are assumed to be located in different parallel slices. The simplest approach is to do an MDS and draw the parallel lines separating the slices as good as possible by hand. Alternatively, Borg and Shye (1995) propose to automate the second step. Borg and Groenen (1997, 2005) proposed a simultaneous approach for ordered facets when the number of MDS dimensions equals the number of facets. In this paper, we propose a new algorithm that estimates an MDS solution subject to axial constraints without the restriction that the number of facets equals the number of dimensions. The algorithm is based on constrained iterative majorization of De Leeuw and Heiser (1980) with special constraints. This algorithm is applied to Levi’s (1983) data on political protests.Axial Partitioning;Constrained Estimation;Facet Theory;Iterative Majorization;Multidimensional Scaling;Regional Restrictions

Borg’s Minimalism and the Problem of Paradox

According to Emma Borg, minimalism is (roughly) the view that natural language sentences have truth conditions, and that these truth conditions are fully determined by syntactic structure and lexical content. A principal motivation for her brand of minimalism is that it coheres well with the popular view that semantic competence is underpinned by the cognition of a minimal semantic theory. In this paper, I argue that the liar paradox presents a serious problem for this principal motivation. Two lines of response to the problem are discussed, and difficulties facing those responses are raised. I close by issuing a challenge: to construe the principal motivation for Borg’s version of minimalism in such a way so as to avoid the problem of paradox

A spectroscopically confirmed z=1.327 galaxy-scale deflector magnifying a z~8 Lyman-Break galaxy in the Brightest of Reionizing Galaxies survey

We present a detailed analysis of an individual case of gravitational lensing of a $z\sim8$ Lyman-Break galaxy (LBG) in a blank field, identified in Hubble Space Telescope imaging obtained as part of the Brightest of Reionizing Galaxies survey. To investigate the close proximity of the bright ($m_{AB}=25.8$) $Y_{098}$-dropout to a small group of foreground galaxies, we obtained deep spectroscopy of the dropout and two foreground galaxies using VLT/X-Shooter. We detect H-$\alpha$, H-$\beta$, [OIII] and [OII] emission in the brightest two foreground galaxies (unresolved at the natural seeing of $0.8$ arcsec), placing the pair at $z=1.327$. We can rule out emission lines contributing all of the observed broadband flux in $H_{160}$ band at $70\sigma$, allowing us to exclude the $z\sim8$ candidate as a low redshift interloper with broadband photometry dominated by strong emission lines. The foreground galaxy pair lies at the peak of the luminosity, redshift and separation distributions for deflectors of strongly lensed $z\sim8$ objects, and we make a marginal detection of a demagnified secondary image in the deepest ($J_{125}$) filter. We show that the configuration can be accurately modelled by a singular isothermal ellipsoidal deflector and a S\'{e}rsic source magnified by a factor of $\mu=4.3\pm0.2$. The reconstructed source in the best-fitting model is consistent with luminosities and morphologies of $z\sim8$ LBGs in the literature. The lens model yields a group mass of $9.62\pm0.31\times10^{11} M_{\odot}$ and a stellar mass-to-light ratio for the brightest deflector galaxy of $M_{\star}/L_{B}=2.3^{+0.8}_{-0.6} M_{\odot}/L_{\odot}$ within its effective radius. The foreground galaxies' redshifts would make this one of the few strong lensing deflectors discovered at $z>1$.Comment: Accepted for publication in MNRAS. 16 pages, 11 figures, 3 table

Self-Reported Upper Body Discomfort due to Driving: Effect of Driving Experience, Gender and Automobile Age

This study investigated the human upper body discomfort caused by automobile driving. Both global and local discomfort estimates were achieved by means of a self-administered questionnaire. The questionnaire used a Borg CR10 scale to evaluate human discomfort, and contained sections to gather information regarding the driving experience, gender and most frequently used automobile of the respondent. The geographic area surveyed was the city of Turin, Italy, and data from a total of 269 drivers was analysed. For all subgroups analysed, the back region was reported to suffer the greatest discomfort, followed in order of decreasing discomfort by the neck, shoulder, arm, hand-wrist, forearm, head, chest and mandible. Generally, female drivers provided higher discomfort responses than male drivers. Subdividing the data according to driving experience lead to large and statistically significant (a<0.05) differences inboth global and local discomfort. Subdividing by gender suggested some significant differences, while subdividing by automobile age produced few differences. The results suggest the usefulness of controlling for test subject driving experience and gender when performing subjective evaluations of automobiles. Further, comparison of the global and the local discomfort responses suggested that individuals were able to form a stable estimate of global discomfort based on the sensations perceived in each of the individual body regions involved. This suggests the interesting possibility that global evaluations may not always provide an accurate understanding of human discomfort since situations can be imagined in which different distributions of upper body discomfort might produce the same, global, response