697 research outputs found
Cluster versus POTENT Density and Velocity Fields: Cluster Biasing and Omega
The density and velocity fields as extracted from the Abell/ACO clusters are
compared to the corresponding fields recovered by the POTENT method from the
Mark~III peculiar velocities of galaxies. In order to minimize non-linear
effects and to deal with ill-sampled regions we smooth both fields using a
Gaussian window with radii ranging between 12 - 20\hmpc. The density and
velocity fields within 70\hmpc exhibit similarities, qualitatively consistent
with gravitational instability theory and a linear biasing relation between
clusters and mass. The random and systematic errors are evaluated with the help
of mock catalogs. Quantitative comparisons within a volume containing
independent samples yield
\betac\equiv\Omega^{0.6}/b_c=0.22\pm0.08, where is the cluster biasing
parameter at 15\hmpc. If , as indicated by the cluster
correlation function, our result is consistent with .Comment: 18 pages, latex, 2 ps figures 6 gif figures. Accepted for
pubblications in MNRA
Cosmological Parameters from Velocities, CMB and Supernovae
We compare and combine likelihood functions of the cosmological parameters
Omega_m, h and sigma_8, from peculiar velocities, CMB and type Ia supernovae.
These three data sets directly probe the mass in the Universe, without the need
to relate the galaxy distribution to the underlying mass via a "biasing"
relation. We include the recent results from the CMB experiments BOOMERANG and
MAXIMA-1. Our analysis assumes a flat Lambda CDM cosmology with a
scale-invariant adiabatic initial power spectrum and baryonic fraction as
inferred from big-bang nucleosynthesis. We find that all three data sets agree
well, overlapping significantly at the 2 sigma level. This therefore justifies
a joint analysis, in which we find a joint best fit point and 95 per cent
confidence limits of Omega_m=0.28 (0.17,0.39), h=0.74 (0.64,0.86), and
sigma_8=1.17 (0.98,1.37). In terms of the natural parameter combinations for
these data sigma_8 Omega_m^0.6 = 0.54 (0.40,0.73), Omega_m h = 0.21
(0.16,0.27). Also for the best fit point, Q_rms-ps = 19.7 muK and the age of
the universe is 13.2 Gyr.Comment: 8 pages, 5 figures. Submitted to MNRA
Cluster versus POTENT density and velocity fields:cluster biasing and Omega
The density and velocity fields as extracted from the Abell/ACO clusters are compared with the corresponding fields recovered by the POTENT method from the Mark III peculiar velocities of galaxies. In order to minimize non-linear effects and to deal with ill-sampled regions, we smooth both fields using a Gaussian window with radii ranging between 12 and 20 h(-1) Mpc. The density and velocity fields within 70 h(-1) Mpc exhibit similarities, qualitatively consistent with gravitational instability theory and a linear biasing relation between clusters and mass. The random and systematic errors are evaluated with the help of mock catalogues. Quantitative comparisons within a volume containing similar to 12 independent samples yield beta(c)=Omega(0.6)/b(c)=0.22 +/- 0.08, where b(c) is the cluster biasing parameter at 15 h(-1) Mpc. If b(c)similar to 4.5, as indicated by the cluster correlation function, our result is consistent with Omega similar to 1
Large Scale Power Spectrum from Peculiar Velocities Via Likelihood Analysis
The power spectrum (PS) of mass density fluctuations, independent of
`biasing', is estimated from the Mark III catalog of peculiar velocities using
Bayesian statistics. A parametric model is assumed for the PS, and the free
parameters are determined by maximizing the probability of the model given the
data. The method has been tested using detailed mock catalogs. It has been
applied to generalized CDM models with and without COBE normalization.
The robust result for all the models is a relatively high PS, with at . An
extrapolation to smaller scales using the different CDM models yields . The peak is weakly constrained to the range
. These results are consistent with a direct
computation of the PS (Kolatt & Dekel 1996). When compared to galaxy-density
surveys, the implied values for () are of order
unity to within 25%.
The parameters of the COBE-normalized, flat CDM model are confined by a 90%
likelihood contour of the sort , where
and for models with and without tensor
fluctuations respectively. For open CDM the powers are and (no tensor fluctuations). A -shape model free of COBE
normalization yields only a weak constraint: .Comment: 19 pages, 8 figures, 2 tables. Accepted for publication in The
Astrophysical Journa
Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS
In the Directed Feedback Vertex Set (DFVS) problem, we are given as input a directed graph D and an integer k, and the objective is to check whether there exists a set S of at most k vertices such that F=D-S is a directed acyclic graph (DAG). Determining whether DFVS admits a polynomial kernel (parameterized by the solution size) is one of the most important open problems in parameterized complexity. In this article, we give a polynomial kernel for DFVS parameterized by the solution size plus the size of any treewidth-eta modulator, for any positive integer eta. We also give a polynomial kernel for the problem, which we call Vertex Deletion to treewidth-eta DAG, where given as input a directed graph D and a positive integer k, the objective is to decide whether there exists a set of at most k vertices, say S, such that D-S is a DAG and the treewidth of D-S is at most eta
Matrix Rigidity from the Viewpoint of Parameterized Complexity
The rigidity of a matrix A for a target rank r over a field F is the minimum Hamming distance between A and a matrix of rank at most r. Rigidity is a classical concept in Computational Complexity Theory: constructions of rigid matrices are known to imply lower bounds of significant importance relating to arithmetic circuits. Yet, from the viewpoint of Parameterized Complexity, the study of central properties of matrices in general, and of the rigidity of a matrix in particular, has been neglected. In this paper, we conduct a comprehensive study of different aspects of the computation of the rigidity of general matrices in the framework of Parameterized Complexity. Naturally, given parameters r and k, the Matrix Rigidity problem asks whether the rigidity of A for the target rank r is at most k. We show that in case F equals the reals or F is any finite field, this problem is fixed-parameter tractable with respect to k+r. To this end, we present a dimension reduction procedure, which may be a valuable primitive in future studies of problems of this nature. We also employ central tools in Real Algebraic Geometry, which are not well known in Parameterized Complexity, as a black box. In particular, we view the output of our dimension reduction procedure as an algebraic variety. Our main results are complemented by a W[1]-hardness result and a subexponential-time parameterized algorithm for a special case of Matrix Rigidity, highlighting the different flavors of this problem
Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA
We allow for nonlinear effects in the likelihood analysis of galaxy peculiar
velocities, and obtain ~35%-lower values for the cosmological density parameter
Om and the amplitude of mass-density fluctuations. The power spectrum in the
linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only
Om as a free parameter. Since the likelihood is driven by the nonlinear regime,
we "break" the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b.
This allows for independent matching of the nonlinear behavior and an unbiased
fit in the linear regime. The analysis assumes Gaussian fluctuations and
errors, and a linear relation between velocity and density. Tests using proper
mock catalogs demonstrate a reduced bias and a better fit. We find for the
Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with
sigma_8*Om^0.6 = 0.49+-0.06 and 0.63+-0.08, in agreement with constraints from
other data. The quoted 90% errors include cosmic variance. The improvement in
likelihood due to the nonlinear correction is very significant for Mark3 and
moderately so for SFI. When allowing deviations from LCDM, we find an
indication for a wiggle in the power spectrum: an excess near k=0.05 and a
deficiency at k=0.1 (cold flow). This may be related to the wiggle seen in the
power spectrum from redshift surveys and the second peak in the CMB anisotropy.
A chi^2 test applied to modes of a Principal Component Analysis (PCA) shows
that the nonlinear procedure improves the goodness of fit and reduces a spatial
gradient of concern in the linear analysis. The PCA allows addressing spatial
features of the data and fine-tuning the theoretical and error models. It shows
that the models used are appropriate for the cosmological parameter estimation
performed. We address the potential for optimal data compression using PCA.Comment: 18 pages, LaTex, uses emulateapj.sty, ApJ in press (August 10, 2001),
improvements to text and figures, updated reference
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