A physical interpretation of Hubble's law and the cosmological redshift from the perspective of a static observer

We derive explicit and exact expressions for the physical velocity of a free particle comoving with the Hubble flow as measured by a static observer, and for the frequency shift of light emitted by a comoving source and received, again, by a static observer. The expressions make it clear that an interpretation of the redshift as a kind of Doppler effect only makes sense when the distance between the observer and the source vanishes exactly.Comment: 5 pages, added references; accepted for publication in General Relativity and Gravitatio

Do Slotting Allowances Harm Retail Competition?

Slotting allowances are fees paid by manufacturers to get access to retailers’ shelf space. Both in the USA and Europe, the use of slotting allowances has attracted attention in the general press as well as among policy makers and economists. One school of thought claims that slotting allowances are efficiency enhancing, while another school of thought maintains that slotting allowances are used in an anti-competitive manner. In this paper, we argue that this controversy is partially caused by inadequate assumptions of how the retail market is structured and organized. Using a formal model, we show that there are good reasons to expect anti-competitive effects of slotting allowances. We further point out that competition authorities tend to use an unsatisfactory basis for comparison when analyzing welfare consequences of slotting allowances.slotting allowances, retail competition, anti-trust policy

Revised WMAP constraints on neutrino masses and other extensions of the minimal Λ\LambdaCDM model

Recently, two issues concerning the three-year WMAP likelihood code were pointed out. On large angular scales ($l \lesssim 30$), a sub-optimal likelihood approximation resulted in a small power excess. On small angular scales ($l \gtrsim 300$), over-subtraction of unresolved point sources produced a small power deficit. For a minimal six-parameter cosmological model, these two effects conspired to decrease the value of $n_s$ by $\sim 0.7 \sigma$. In this paper, we study the change in preferred parameter ranges for more extensive cosmological models, including running of $n_s$, massive neutrinos, curvature, and the equation of state for dark energy. We also include large-scale structure and supernova data in our analysis. We find that the parameter ranges for $\alpha_s$, $\Omega_k$ and $w$ are not much altered by the modified analysis. For massive neutrinos the upper limit on the sum of the neutrino masses decreases from $M_\nu < 1.90$eV to $M_\nu < 1.57$eV when using the modified WMAP code and WMAP data only. We also find that the shift of $n_s$ to higher values is quite robust to these extensions of the minimal cosmological model.Comment: 7 pages. Matching version published in Physical Review D. Figures changed, references added, additional comment

Where do Women Give Birth in Rural Tanzania?

Skilled birth attendance is one of the key factors in improving maternal and neonatal health but coverage is frequently less than 50% in many African and Asian countries, especially in rural areas. This article reports the findings on skilled birth attendance in a remote area with a large nomadic population in northern Tanzania. In a secondary analysis of data from a retrospective study on immunisation rates, data were compiled on the rates of skilled birth attendance at 8 mobile reproductive and child health clinics run by a rural first-referral hospital in the Mbulu area, covering the years 1998, 1999, 2006 and 2007. These data were analysed according to tribal affiliation and distance from health institutions with obstetric services. Based on 3851 data sets, average rates of skilled birth attendance were 27%, 24%, 28% and 30% in 1998, 1999, 2006 and 2007, respectively (p = 0.02). At individual clinics, rates could be as low as 5-10%. Only at one clinic, significant improvement occurred over time (p< 0.01). In the univariate analysis, affiliation to the Iraqw tribe was a strong predictor of higher rates of skilled birth attendance in comparison with the nomadic Datoga tribe for all years combined (odds ratio [OR] 2.43 [95% confidence interval {CI} 1.92-3.07]), whereas distance showed only a minor influence (OR 1.02 [95% CI 1.01-1.02]). In the multivariate analysis, only tribal affiliation in 2007 (OR 2.69 [95% CI 1.12-6.46]) and for all years combined (OR 1.65 [95% CI 1.04-2.61]) was a significant factor. This study documented lower than the national average rates of skilled birth attendance in a rural area in Tanzania, especially among the nomadic Datoga tribe, over several years. The effect of distance was not consistent. To increase rates of women giving birth with skilled attendance in rural, remote settings and in populations with large proportions of nomadic people, a multi-facetted approach involving education in and sensitisation for pregnancy- and delivery-related issues, support for planned and emergency transportation, and improved quality of obstetric and neonatal services needs to be explored

Dimensions, Maximal Growth Sites and Optimization in the Dielectric Breakdown Model

We study the growth of fractal clusters in the Dielectric Breakdown Model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent $\alpha_{min}$) as a function of the growth exponent $\eta$ of the DBM model. We do not find evidence for a phase transition from fractal to non-fractal growth for a finite $\eta$-value. Simultaneously, we observe that the limit of non-fractal growth ($D\to 1$) is consistent with $\alpha_{min} \to 1/2$. Finally, using an optimization principle, we give a recipe on how to estimate the effective value of $\eta$ from temporal growth data of fractal aggregates.Comment: 5 pages, 7 figures; v2: extra figures and new data adde

Diameters in graphs

AbstractA diameter critical graph has the property that the addition of any edge decreases the diameter. All such graphs are determined for a given vertex connectivity and the edge number is given