Claus Beisbart

Luminosity- and Morphology-dependent Clustering of Galaxies

How does the clustering of galaxies depend on their inner properties like morphological type and luminosity? We address this question in the mathematical framework of marked point processes and clarify the notion of luminosity and morphological segregation. A number of test quantities such as conditional mark-weighted two-point correlation functions are introduced. These descriptors allow for a scale-dependent analysis of luminosity and morphology segregation. Moreover, they break the degeneracy between an inhomogeneous fractal point set and actual present luminosity segregation. Using the Southern Sky Redshift Survey 2, we find both luminosity and morphological segregation at a high level of significance, confirming claims by Benoist and colleagues in 1996 and Willmer and colleagues in 1998 using these data. Specifically, the average luminosity and the fluctuations in the luminosity of pairs of galaxies are enhanced out to separations of 15 h-1 Mpc. On scales smaller than 3 h-1 Mpc the luminosities on galaxy pairs show a tight correlation. A comparison with the random field model indicates that galaxy luminosities depend on the spatial distribution and galaxy-galaxy interactions. Early-type galaxies are also more strongly correlated, indicating morphological segregation. The galaxies in the PSCz catalog do not show significant luminosity segregation. This again illustrates that mainly early-type galaxies contribute to luminosity segregation. However, based on several independent investigations we show that the observed luminosity segregation cannot be explained by the morphology-density relation alone.

Morphological fluctuations of large{scale structure: The PSCz survey

In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the existence of significant fluctuations that are discernible in volume-limited samples out to 200Mpc/h. In contrast to earlier findings, comparisons with cosmological N-body simulations reveal that the observed fluctuations roughly agree with the cosmic variance found in corresponding mock samples. While two-point measures, e.g. the variance of count-in-cells, fluctuate only mildly, the fluctuations in the morphology on large scales indicate the presence of coherent structures that are at least as large as the sample.In a follow{up study to a previous analysis of the IRAS 1.2 Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We conrm the existence of signicant fluctuations that are discernible in volume{limited samples out to 200h 1 Mpc. In contrast to earlier ndings, comparisons with cosmological N{body simulations reveal that the observed fluctuations roughly agree with the cosmic variance found in corresponding mock samples. While two{point measures, e.g. the variance of count{in{cells, fluctuate only mildly, the fluctuations in the morphology on large scales indicate the presence of coherent structures that are at least as large as the sample.

A Utilitarian Assessment of Alternative Decision Rules in the Council of Ministers

We develop a utilitarian framework to assess different decision rules for the European Council of Ministers. The proposals to be decided on are conceptualized as utility vectors and a probability distribution is assumed over the utilities. We first show what decision rules yield the highest expected utilities for different means of the probability distribution. For proposals with high mean utility, simple benchmark rules (such as majority voting with proportional weights) tend to outperform rules that have been proposed in the political arena. For proposals with low mean utility, it is the other way round. We then compare the expected utilities for smaller and larger countries and look for Pareto-dominance relations. Finally, we provide an extension of the model, discuss its restrictions, and compare our approach with assessments of decision rules that are based on the Penrose measure of voting power.

Tensorial Minkowski functionals and anisotropy measures for planar patterns

Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor‐valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non‐equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores.

Welfarist evaluations of decision rules for boards of representatives

We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barberà and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power.

Vector- und Tensor-Valued Descriptors for Spatial Patterns

Higher-rank Minkowski valuations are efficient means of describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski functionals to vector- and tensor-valued measures. The versatility of these measures is demonstrated by using simple toy models as well as real data.

Why Monte Carlo Simulations Are Inferences and Not Experiments

Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations are analysed to identify the underlying inferences.

Morphometry of spatial patterns

Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape, and connectivity. Here we point out that these scalar descriptors can be complemented by vector-valued curvature measures also known as Quermas vectors. Using examples of galaxy clusters, we demonstrate that the Quermas vectors provide additional morphological information on directional features and symmetries displayed by spatial data.

The morphological and dynamical evolution of simulated galaxy clusters

We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental interest: 1. How does the average cluster morphology depend on the cosmological background model? 2. Is it possible to discriminate between dierent cosmological models using cluster substructure in a statistically signicant way? 3. How is the dynamical state of a cluster, especially its distance from a virial equilibrium, correlated to its visual substructure? To answer these questions, we quantify cluster substructure using a set of morphological order parameters constructed on the basis of the Minkowski valuations (MVs). The dynamical state of a cluster is described using global cluster parameters: in certain spaces of such parameters fundamental band-like structures are forming indicating the emergence of a virial equilibrium. We nd that the average distances from these fundamental structures are correlated to the average amount of cluster substructure for our cluster samples during the time evolution. Furthermore, signicant dierences show up between the high- and the low-m models. We pay special attention to the redshift evolution of morphological characteristics and nd large dierences between the cosmological models even for higher redshifts.

Welfarist evaluations of decision rules under interstate utility dependencies

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards, viz. that the expected average utility for a person in the federation be maximized or that the expected utilities for the different people be equal. We discuss an analytical result that characterizes the decision rule with maximum expected average utility, set up a class of models that display interstate dependencies and run simulations for different dependency scenarios in the European Union. We find that the results that Beisbart and Bovens (Soc Choice Welf 29:581–608, 2007) established for two types of models without interstate dependencies are fairly stable if interstate dependencies are switched on. There are exceptions, though: sometimes the way in which alternative decision rules shape the welfare distribution is significantly affected by such dependencies. These exceptions particularly include cases in which the interests of people from different states are partly anti-correlated.