The Expected Perimeter in Eden and Related Growth Processes

Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem in Statistical Mechanics, we show that the average perimeter of the lattice animals resulting from a very natural family of "growth histories" does not obey a similar bound.Comment: 11 page

Observational Evidence for an Age Dependence of Halo Bias

We study the dependence of the cross-correlation between galaxies and galaxy groups on group properties. Confirming previous results, we find that the correlation strength is stronger for more massive groups, in good agreement with the expected mass dependence of halo bias. We also find, however, that for groups of the same mass, the correlation strength depends on the star formation rate (SFR) of the central galaxy: at fixed mass, the bias of galaxy groups decreases as the SFR of the central galaxy increases. We discuss these findings in light of the recent findings by Gao et al (2005) that halo bias depends on halo formation time, in that halos that assemble earlier are more strongly biased. We also discuss the implication for galaxy formation, and address a possible link to galaxy conformity, the observed correlation between the properties of satellite galaxies and those of their central galaxy.Comment: 4 pages, 4 figures, Accepted for publication in ApJ Letters. Figures 3 and 4 replaced. The bias dependence on the central galaxy luminosity is omitted due to its sensitivity to the mass mode

Permanent structures for irrigation farms

With the close of the irrigation season many farmers have put away their shovels with sighs of relief. Now no doubt they have forgotten, due to the passage of time, the many battles with unruly water. Perhaps they have even forgotten the arduous hours of shovelling and the attendant backaches

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Meta-Learning for Phonemic Annotation of Corpora

We apply rule induction, classifier combination and meta-learning (stacked classifiers) to the problem of bootstrapping high accuracy automatic annotation of corpora with pronunciation information. The task we address in this paper consists of generating phonemic representations reflecting the Flemish and Dutch pronunciations of a word on the basis of its orthographic representation (which in turn is based on the actual speech recordings). We compare several possible approaches to achieve the text-to-pronunciation mapping task: memory-based learning, transformation-based learning, rule induction, maximum entropy modeling, combination of classifiers in stacked learning, and stacking of meta-learners. We are interested both in optimal accuracy and in obtaining insight into the linguistic regularities involved. As far as accuracy is concerned, an already high accuracy level (93% for Celex and 86% for Fonilex at word level) for single classifiers is boosted significantly with additional error reductions of 31% and 38% respectively using combination of classifiers, and a further 5% using combination of meta-learners, bringing overall word level accuracy to 96% for the Dutch variant and 92% for the Flemish variant. We also show that the application of machine learning methods indeed leads to increased insight into the linguistic regularities determining the variation between the two pronunciation variants studied.Comment: 8 page

Properties of Galaxy Groups in the SDSS: II.- AGN Feedback and Star Formation Truncation

Successfully reproducing the galaxy luminosity function and the bimodality in the galaxy distribution requires a mechanism that can truncate star formation in massive haloes. Current models of galaxy formation consider two such truncation mechanisms: strangulation, which acts on satellite galaxies, and AGN feedback, which predominantly affects central galaxies. The efficiencies of these processes set the blue fraction of galaxies as function of galaxy luminosity and halo mass. In this paper we use a galaxy group catalogue extracted from the Sloan Digital Sky Survey (SDSS) to determine these fractions. To demonstrate the potential power of this data as a benchmark for galaxy formation models, we compare the results to the semi-analytical model for galaxy formation of Croton et al. (2006). Although this model accurately fits the global statistics of the galaxy population, as well as the shape of the conditional luminosity function, there are significant discrepancies when the blue fraction of galaxies as a function of mass and luminosity is compared between the observations and the model. In particular, the model predicts (i) too many faint satellite galaxies in massive haloes, (ii) a blue fraction of satellites that is much too low, and (iii) a blue fraction of centrals that is too high and with an inverted luminosity dependence. In the same order, we argue that these discrepancies owe to (i) the neglect of tidal stripping in the semi-analytical model, (ii) the oversimplified treatment of strangulation, and (iii) improper modeling of dust extinction and/or AGN feedback. The data presented here will prove useful to test and calibrate future models of galaxy formation and in particular to discriminate between various models for AGN feedback and other star formation truncation mechanisms.Comment: 16 pages, 5 figures, submitted to MNRA

The cross-correlation between galaxies of different luminosities and Colors

We study the cross-correlation between galaxies of different luminosities and colors, using a sample selected from the SDSS Dr 4. Galaxies are divided into 6 samples according to luminosity, and each of these samples is divided into red and blue subsamples. Projected auto-correlation and cross-correlation is estimated for these subsample. At projected separations r_p > 1\mpch, all correlation functions are roughly parallel, although the correlation amplitude depends systematically on luminosity and color. On r_p < 1\mpch, the auto- and cross-correlation functions of red galaxies are significantly enhanced relative to the corresponding power laws obtained on larger scales. Such enhancement is absent for blue galaxies and in the cross-correlation between red and blue galaxies. We esimate the relative bias factor on scales r > 1\mpch for each subsample using its auto-correlation function and cross-correlation functions. The relative bias factors obtained from different methods are similar. For blue galaxies the luminosity-dependence of the relative bias is strong over the luminosity range probed (-23.0<M_r < -18.0),but for red galaxies the dependence is weaker and becomes insignificant for luminosities below L^*. To examine whether a significant stochastic/nonlinear component exists in the bias relation, we study the ratio R_ij= W_{ii}W_{jj}/W_{ij}^2, where W_{ij} is the projected correlation between subsample i and j. We find that the values of R_ij are all consistent with 1 for all-all, red-red and blue-blue samples, however significantly larger than 1 for red-blue samples. For faint red - faint blue samples the values of R_{ij} are as high as ~ 2 on small scales r_p < 1 \mpch and decrease with increasing r_p.Comment: 25 pages, 18 figures, Accepted for publication in Ap