1,378 research outputs found
Reconstructing Galaxy Spectral Energy Distributions from Broadband Photometry
We present a novel approach to photometric redshifts, one that merges the
advantages of both the template fitting and empirical fitting algorithms,
without any of their disadvantages. This technique derives a set of templates,
describing the spectral energy distributions of galaxies, from a catalog with
both multicolor photometry and spectroscopic redshifts. The algorithm is
essentially using the shapes of the templates as the fitting parameters. From
simulated multicolor data we show that for a small training set of galaxies we
can reconstruct robustly the underlying spectral energy distributions even in
the presence of substantial errors in the photometric observations. We apply
these techniques to the multicolor and spectroscopic observations of the Hubble
Deep Field building a set of template spectra that reproduced the observed
galaxy colors to better than 10%. Finally we demonstrate that these improved
spectral energy distributions lead to a photometric-redshift relation for the
Hubble Deep Field that is more accurate than standard template-based
approaches.Comment: 23 pages, 8 figures, LaTeX AASTeX, accepted for publication in A
Decomposing data sets into skewness modes
We derive the nonlinear equations satisfied by the coefficients of linear
combinations that maximize their skewness when their variance is constrained to
take a specific value. In order to numerically solve these nonlinear equations
we develop a gradient-type flow that preserves the constraint. In combination
with the Karhunen-Lo\`eve decomposition this leads to a set of orthogonal modes
with maximal skewness. For illustration purposes we apply these techniques to
atmospheric data; in this case the maximal-skewness modes correspond to
strongly localized atmospheric flows. We show how these ideas can be extended,
for example to maximal-flatness modes.Comment: Submitted for publication, 12 pages, 4 figure
A Robust Classification of Galaxy Spectra: Dealing with Noisy and Incomplete Data
Over the next few years new spectroscopic surveys (from the optical surveys
of the Sloan Digital Sky Survey and the 2 degree Field survey through to
space-based ultraviolet satellites such as GALEX) will provide the opportunity
and challenge of understanding how galaxies of different spectral type evolve
with redshift. Techniques have been developed to classify galaxies based on
their continuum and line spectra. Some of the most promising of these have used
the Karhunen and Loeve transform (or Principal Component Analysis) to separate
galaxies into distinct classes. Their limitation has been that they assume that
the spectral coverage and quality of the spectra are constant for all galaxies
within a given sample. In this paper we develop a general formalism that
accounts for the missing data within the observed spectra (such as the removal
of sky lines or the effect of sampling different intrinsic rest wavelength
ranges due to the redshift of a galaxy). We demonstrate that by correcting for
these gaps we can recover an almost redshift independent classification scheme.
From this classification we can derive an optimal interpolation that
reconstructs the underlying galaxy spectral energy distributions in the regions
of missing data. This provides a simple and effective mechanism for building
galaxy spectral energy distributions directly from data that may be noisy,
incomplete or drawn from a number of different sources.Comment: 20 pages, 8 figures. Accepted for publication in A
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
Spectral Templates from Multicolor Redshift Surveys
Understanding how the physical properties of galaxies (e.g. their spectral
type or age) evolve as a function of redshift relies on having an accurate
representation of galaxy spectral energy distributions. While it has been known
for some time that galaxy spectra can be reconstructed from a handful of
orthogonal basis templates, the underlying basis is poorly constrained. The
limiting factor has been the lack of large samples of galaxies (covering a wide
range in spectral type) with high signal-to-noise spectrophotometric
observations. To alleviate this problem we introduce here a new technique for
reconstructing galaxy spectral energy distributions directly from samples of
galaxies with broadband photometric data and spectroscopic redshifts.
Exploiting the statistical approach of the Karhunen-Loeve expansion, our
iterative training procedure increasingly improves the eigenbasis, so that it
provides better agreement with the photometry. We demonstrate the utility of
this approach by applying these improved spectral energy distributions to the
estimation of photometric redshifts for the HDF sample of galaxies. We find
that in a small number of iterations the dispersion in the photometric
redshifts estimator (a comparison between predicted and measured redshifts) can
decrease by up to a factor of 2.Comment: 25 pages, 9 figures, LaTeX AASTeX, accepted for publication in A
An extension of Wiener integration with the use of operator theory
With the use of tensor product of Hilbert space, and a diagonalization
procedure from operator theory, we derive an approximation formula for a
general class of stochastic integrals. Further we establish a generalized
Fourier expansion for these stochastic integrals. In our extension, we
circumvent some of the limitations of the more widely used stochastic integral
due to Wiener and Ito, i.e., stochastic integration with respect to Brownian
motion. Finally we discuss the connection between the two approaches, as well
as a priori estimates and applications.Comment: 13 page
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
A multifrequency analysis of radio variability of blazars
We have carried out a multifrequency analysis of the radio variability of
blazars, exploiting the data obtained during the extensive monitoring programs
carried out at the University of Michigan Radio Astronomy Observatory (UMRAO,
at 4.8, 8, and 14.5 GHz) and at the Metsahovi Radio Observatory (22 and 37
GHz). Two different techniques detect, in the Metsahovi light curves, evidences
of periodicity at both frequencies for 5 sources (0224+671, 0945+408, 1226+023,
2200+420, and 2251+158). For the last three sources consistent periods are
found also at the three UMRAO frequencies and the Scargle (1982) method yields
an extremely low false-alarm probability. On the other hand, the 22 and 37 GHz
periodicities of 0224+671 and 0945+408 (which were less extensively monitored
at Metsahovi and for which we get a significant false-alarm probability) are
not confirmed by the UMRAO database, where some indications of ill-defined
periods about a factor of two longer are retrieved. We have also investigated
the variability index, the structure function, and the distribution of
intensity variations of the most extensively monitored sources. We find a
statistically significant difference in the distribution of the variability
index for BL Lac objects compared to flat-spectrum radio quasars (FSRQs), in
the sense that the former objects are more variable. For both populations the
variability index steadily increases with increasing frequency. The
distribution of intensity variations also broadens with increasing frequency,
and approaches a log-normal shape at the highest frequencies. We find that
variability enhances by 20-30% the high frequency counts of extragalactic
radio-sources at bright flux densities, such as those of the WMAP and Planck
surveys.Comment: A&A accepted. 12 pages, 16 figure
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