Three editions of the Star Catalogue of Tycho Brahe

Tycho Brahe completed his catalogue with the positions and magnitudes of 1004 fixed stars in 1598. This catalogue circulated in manuscript form. Brahe edited a shorter version with 777 stars, printed in 1602, and Kepler edited the full catalogue of 1004 stars, printed in 1627. We provide machine-readable versions of the three versions of the catalogue, describe the differences between them and briefly discuss their accuracy on the basis of comparison with modern data from the Hipparcos Catalogue. We also compare our results with earlier analyses by Dreyer (1916) and Rawlins (1993), finding good overall agreement. The magnitudes given by Brahe correlate well with modern values, his longitudes and latitudes have error distributions with widths of about 2 arcmin, with excess numbers of stars with larger errors (as compared to Gaussian distributions), in particular for the faintest stars. Errors in positions larger than 10 arcmin, which comprise about 15 per cent of the entries, are likely due to computing or copying errors.Comment: Accepted by Astronomy and Astrophysics; 24 pages; 63 figures; 3 machine readable tables made available at CD

Re-making urban segregation: processes of income sorting and neighbourhood change

Segregation studies have mainly focused on urban structures as a whole or have discussed specific (gentrifying or renewing) neighbourhoods. The literature suggests that changes in segregation occur primarily through selective migration. In this paper, we follow up on recent work that has questioned these orthodoxies, suggesting that in situ social mobility, and entries to and exits from the city population should be taken into account as well, and that dynamics in all neighbourhoods should be considered. The paper traces the processes by which segregation changes for the cities of Amsterdam and The Hague for 1999–2006, using a longitudinal individual-level database covering the entire population. It extends previous work by looking at income rather than socio-economic status and by drilling down to the neighbourhood level. Applying an existing measure of segregation (Delta) in a novel way, the analysis focuses on changes in the spatial distribution of household income, measuring the relative contribution of a range of processes to changes in segregation. Results show that segregation rises in both cities but that different processes drive changes in each case. Furthermore, the aggregate change in segregation for each city masks a diversity of changes at the neighbourhood level, some of which tend to increase segregation while others tend to reduce it. Mapping these changes and the individual processes contributing to them shows that they have a distinct geography, which seems to be structured by historically specific trends in state and housing market context.

Trying again to fail-first

For constraint satisfaction problems (CSPs), Haralick and Elliott [1] introduced the Fail-First Principle and defined in it terms of minimizing branch depth. By devising a range of variable ordering heuristics, each in turn trying harder to fail first, Smith and Grant [2] showed that adherence to this strategy does not guarantee reduction in search effort. The present work builds on Smith and Grant. It benefits from the development of a new framework for characterizing heuristic performance that defines two policies, one concerned with enhancing the likelihood of correctly extending a partial solution, the other with minimizing the effort to prove insolubility. The Fail-First Principle can be restated as calling for adherence to the second, fail-first policy, while discounting the other, promise policy. Our work corrects some deficiencies in the work of Smith and Grant, and goes on to confirm their finding that the Fail-First Principle, as originally defined, is insufficient. We then show that adherence to the fail-first policy must be measured in terms of size of insoluble subtrees, not branch depth. We also show that for soluble problems, both policies must be considered in evaluating heuristic performance. Hence, even in its proper form the Fail-First Principle is insufficient. We also show that the “FF” series of heuristics devised by Smith and Grant is a powerful tool for evaluating heuristic performance, including the subtle relations between heuristic features and adherence to a policy

No evidence for an early seventeenth-century Indian sighting of Keplers supernova (SN1604)

In a recent paper Sule et al. (Astronomical Notes, vol. 332 (2011), 655) argued that an early 17th-century Indian mural of the constellation Sagittarius with a dragon-headed tail indicated that the bright supernova of 1604 was also sighted by Indian astronomers. In this paper it will be shown that this identification is based on a misunderstanding of traditional Islamic astrological iconography and that the claim that the mural represents an early 17th-century Indian sighting of the supernova of 1604 has to be rejected.Comment: 7 pages, 6 figures. To appear in Astronomical Notes, vol. 334, issue 5 (2013), DOI number 1172

Long-term variations of turbulent transport coefficients in a solar-like convective dynamo simulation

The Sun, aside from its eleven year sunspot cycle is additionally subject to long term variation in its activity. In this work we analyse a solar-like convective dynamo simulation, containing approximately 60 magnetic cycles, exhibiting equatorward propagation of the magnetic field, multiple frequencies, and irregular variability, including a missed cycle and complex parity transitions between dipolar and quadrupolar modes. We compute the turbulent transport coefficients, describing the effects of the turbulent velocity field on the mean magnetic field, using the test-field method. The test-field analysis provides a plausible explanation of the missing cycle in terms of the reduction of $\alpha_{\phi\phi}$ in advance of the reduced surface activity, and enhanced downward turbulent pumping during the event to confine some of the magnetic field at the bottom of the convection zone, where local maximum of magnetic energy is observed during the event. At the same time, however, a quenching of the turbulent magnetic diffusivities is observed, albeit differently distributed in depth compared to the other transport coefficients. Therefore, dedicated mean-field modelling is required for verification.Comment: 11 pages, 12 figures, accepted by AN for 14th Potsdam Thinksho

A comparison of limited-stretch models of rubber elasticity

In this paper we describe various limited-stretch models of non-linear rubber elasticity, each dependent on only the first invariant of the left Cauchy-Green strain tensor and having only two independent material constants. The models are described as limited-stretch, or restricted elastic, because the strain energy and stress response become infinite at a finite value of the first invariant. These models describe well the limited stretch of the polymer chains of which rubber is composed. We discuss Gent's model which is the simplest limited-stretch model and agrees well with experiment. Various statistical models are then described: the one-chain, three-chain, four-chain and Arruda-Boyce eight-chain models, all of which involve the inverse Langevin function. A numerical comparison between the three-chain and eight-chain models is provided. Next, we compare various models which involve approximations to the inverse Langevin function with the exact inverse Langevin function of the eight-chain model. A new approximate model is proposed that is as simple as Cohen's original model but significantly more accurate. We show that effectively the eight-chain model may be regarded as a linear combination of the neo-Hookean and Gent models. Treloar's model is shown to have about half the percentage error of our new model but it is much more complicated. For completeness a modified Treloar model is introduced but this is only slightly more accurate than Treloar's original model. For the deformations of uniaxial tension, biaxial tension, pure shear and simple shear we compare the accuracy of these models, and that of Puso, with the eight-chain model by means of graphs and a table. Our approximations compare extremely well with models frequently used and described in the literature, having the smallest mean percentage error over most of the range of the argument

Finding problems in knowledge bases using modal logics

In this paper I propose that it is suitable to consider some statements that an expert makes during knowledge elicitation as being statements in a modal logic. This approach gives us several advantages in finding inconsistencies between a knowledge base and an expert's intuition in her field. I illustrate this approach by using the modal logic VC, a logic of counterfactual conditionals. In an appendix, I give brief details of theorem proving in VC