Dynamics of tournaments: the soccer case

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.Comment: To appear in EPJ

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm

Gravitational Lensing at Millimeter Wavelengths

With today's millimeter and submillimeter instruments observers use gravitational lensing mostly as a tool to boost the sensitivity when observing distant objects. This is evident through the dominance of gravitationally lensed objects among those detected in CO rotational lines at z>1. It is also evident in the use of lensing magnification by galaxy clusters in order to reach faint submm/mm continuum sources. There are, however, a few cases where millimeter lines have been directly involved in understanding lensing configurations. Future mm/submm instruments, such as the ALMA interferometer, will have both the sensitivity and the angular resolution to allow detailed observations of gravitational lenses. The almost constant sensitivity to dust emission over the redshift range z=1-10 means that the likelihood for strong lensing of dust continuum sources is much higher than for optically selected sources. A large number of new strong lenses are therefore likely to be discovered with ALMA, allowing a direct assessment of cosmological parameters through lens statistics. Combined with an angular resolution <0.1", ALMA will also be efficient for probing the gravitational potential of galaxy clusters, where we will be able to study both the sources and the lenses themselves, free of obscuration and extinction corrections, derive rotation curves for the lenses, their orientation and, thus, greatly constrain lens models.Comment: 69 pages, Review on quasar lensing. Part of a LNP Topical Volume on "Dark matter and gravitational lensing", eds. F. Courbin, D. Minniti. To be published by Springer-Verlag 2002. Paper with full resolution figures can be found at ftp://oden.oso.chalmers.se/pub/tommy/mmviews.ps.g

Spectroscopic target selection for the Sloan Digital Sky Survey: The luminous red galaxy sample

We describe the target selection and resulting properties of a spectroscopic sample of luminous red galaxies (LRGs) from the imaging data of the Sloan Digital Sky Survey (SDSS). These galaxies are selected on the basis of color and magnitude to yield a sample of luminous intrinsically red galaxies that extends fainter and farther than the main flux-limited portion of the SDSS galaxy spectroscopic sample. The sample is designed to impose a passively evolving luminosity and rest-frame color cut to a redshift of 0.38. Additional, yet more luminous red galaxies are included to a redshift of ∼0.5. Approximately 12 of these galaxies per square degree are targeted for spectroscopy, so the sample will number over 100,000 with the full survey. SDSS commissioning data indicate that the algorithm efficiently selects luminous (M*g ≈ - 21.4) red galaxies, that the spectroscopic success rate is very high, and that the resulting set of galaxies is approximately volume limited out to z = 0.38. When the SDSS is complete, the LRG spectroscopic sample will fill over 1 h-3 Gpc3 with an approximately homogeneous population of galaxies and will therefore be well suited to studies of large-scale structure and clusters out to z = 0.5

Designing magnesium-selective ligands using coordination chemistry principles

Progress in the selective binding and detection of magnesium ions has been slower than other biologically important divalent metal ions like calcium and zinc. The most widely used ligands for Mg2+ are by no means optimal, as they are not selective for it. Nevertheless, Mg2+ is a major cation in all cells, with physiologically critical functions. There is a need for improved sensors for Mg2+. In this review, we consider how an appreciation of fundamental coordination chemistry principles may inform the development of new ligands for Mg2+. A number of representative examples of ligands of differing denticity are discussed in this context. Low-denticity ligands such as β-keto acids offer the best selectivities, but speciation is an issue as other polydentate ligands such as pyrophosphate may complete the coordination sphere. High-denticity ligands based on aminocarboxylates such as APTRA typically offer the highest stability constants, but they bind Ca2+ and Zn2+ more strongly than Mg2+. We highlight recent examples featuring related aminophosphinates, where the longer bonds and smaller bite angles favour selectivity towards Mg2+. Macrocyclic receptors for magnesium are not discussed explicitly