9,247 research outputs found
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
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