2,061 research outputs found
Electrostatic Field Classifier for Deficient Data
This paper investigates the suitability of recently developed models based on the physical
field phenomena for classification problems with incomplete datasets. An original approach
to exploiting incomplete training data with missing features and labels, involving extensive use
of electrostatic charge analogy, has been proposed. Classification of incomplete patterns has been
investigated using a local dimensionality reduction technique, which aims at exploiting all available
information rather than trying to estimate the missing values. The performance of all proposed
methods has been tested on a number of benchmark datasets for a wide range of missing data scenarios
and compared to the performance of some standard techniques. Several modifications of the
original electrostatic field classifier aiming at improving speed and robustness in higher dimensional
spaces are also discussed
X-ray Lighthouses of the High-Redshift Universe. II. Further Snapshot Observations of the Most Luminous z>4 Quasars with Chandra
We report on Chandra observations of a sample of 11 optically luminous
(Mb<-28.5) quasars at z=3.96-4.55 selected from the Palomar Digital Sky Survey
and the Automatic Plate Measuring Facility Survey. These are among the most
luminous z>4 quasars known and hence represent ideal witnesses of the end of
the "dark age ''. Nine quasars are detected by Chandra, with ~2-57 counts in
the observed 0.5-8 keV band. These detections increase the number of X-ray
detected AGN at z>4 to ~90; overall, Chandra has detected ~85% of the
high-redshift quasars observed with snapshot (few kilosecond) observations. PSS
1506+5220, one of the two X-ray undetected quasars, displays a number of
notable features in its rest-frame ultraviolet spectrum, the most prominent
being broad, deep SiIV and CIV absorption lines. The average optical-to-X-ray
spectral index for the present sample (=-1.88+/-0.05) is steeper than
that typically found for z>4 quasars but consistent with the expected value
from the known dependence of this spectral index on quasar luminosity.
We present joint X-ray spectral fitting for a sample of 48 radio-quiet
quasars in the redshift range 3.99-6.28 for which Chandra observations are
available. The X-ray spectrum (~870 counts) is well parameterized by a power
law with Gamma=1.93+0.10/-0.09 in the rest-frame ~2-40 keV band, and a tight
upper limit of N_H~5x10^21 cm^-2 is obtained on any average intrinsic X-ray
absorption. There is no indication of any significant evolution in the X-ray
properties of quasars between redshifts zero and six, suggesting that the
physical processes of accretion onto massive black holes have not changed over
the bulk of cosmic time.Comment: 15 pages, 7 figures, accepted for publication in A
Statistical significance of communities in networks
Nodes in real-world networks are usually organized in local modules. These
groups, called communities, are intuitively defined as sub-graphs with a larger
density of internal connections than of external links. In this work, we
introduce a new measure aimed at quantifying the statistical significance of
single communities. Extreme and Order Statistics are used to predict the
statistics associated with individual clusters in random graphs. These
distributions allows us to define one community significance as the probability
that a generic clustering algorithm finds such a group in a random graph. The
method is successfully applied in the case of real-world networks for the
evaluation of the significance of their communities.Comment: 9 pages, 8 figures, 2 tables. The software to calculate the C-score
can be found at http://filrad.homelinux.org/cscor
The Time Machine: A Simulation Approach for Stochastic Trees
In the following paper we consider a simulation technique for stochastic
trees. One of the most important areas in computational genetics is the
calculation and subsequent maximization of the likelihood function associated
to such models. This typically consists of using importance sampling (IS) and
sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating
the tree, backward in time from observed data, to a most recent common ancestor
(MRCA). However, in many cases, the computational time and variance of
estimators are often too high to make standard approaches useful. In this paper
we propose to stop the simulation, subsequently yielding biased estimates of
the likelihood surface. The bias is investigated from a theoretical point of
view. Results from simulation studies are also given to investigate the balance
between loss of accuracy, saving in computing time and variance reduction.Comment: 22 Pages, 5 Figure
Pareto versus lognormal: a maximum entropy test
It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units
Testing linear hypotheses in high-dimensional regressions
For a multivariate linear model, Wilk's likelihood ratio test (LRT)
constitutes one of the cornerstone tools. However, the computation of its
quantiles under the null or the alternative requires complex analytic
approximations and more importantly, these distributional approximations are
feasible only for moderate dimension of the dependent variable, say .
On the other hand, assuming that the data dimension as well as the number
of regression variables are fixed while the sample size grows, several
asymptotic approximations are proposed in the literature for Wilk's \bLa
including the widely used chi-square approximation. In this paper, we consider
necessary modifications to Wilk's test in a high-dimensional context,
specifically assuming a high data dimension and a large sample size .
Based on recent random matrix theory, the correction we propose to Wilk's test
is asymptotically Gaussian under the null and simulations demonstrate that the
corrected LRT has very satisfactory size and power, surely in the large and
large context, but also for moderately large data dimensions like or
. As a byproduct, we give a reason explaining why the standard chi-square
approximation fails for high-dimensional data. We also introduce a new
procedure for the classical multiple sample significance test in MANOVA which
is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages
and 2 table
Quantum theory of incompatible observations
Maximum likelihood principle is shown to be the best measure for relating the
experimental data with the predictions of quantum theory.Comment: 3 page
Quantum homodyne tomography with a priori constraints
I present a novel algorithm for reconstructing the Wigner function from
homodyne statistics. The proposed method, based on maximum-likelihood
estimation, is capable of compensating for detection losses in a numerically
stable way.Comment: 4 pages, REVTeX, 2 figure
Iterative algorithm for reconstruction of entangled states
An iterative algorithm for the reconstruction of an unknown quantum state
from the results of incompatible measurements is proposed. It consists of
Expectation-Maximization step followed by a unitary transformation of the
eigenbasis of the density matrix. The procedure has been applied to the
reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake
correcte
Host Galaxy Evolution in Radio-Loud AGN
We investigate the luminosity evolution of the host galaxies of radio-loud
AGN through Hubble Space Telescope imaging of 72 BL Lac objects, including new
STIS imaging of nine z > 0.6 BL Lacs. With their intrinsically low accretion
rates and their strongly beamed jets, BL Lacs provide a unique opportunity to
probe host galaxy evolution independent of the biases and ambiguities implicit
in quasar studies. We find that the host galaxies of BL Lacs evolve strongly,
consistent with passive evolution from a period of active star formation in the
range 0.5 <~ z <~ 2.5, and inconsistent with either passive evolution from a
high formation redshift or a non-evolving population. This evolution is broadly
consistent with that observed in the hosts of other radio-loud AGN, and
inconsistent with the flatter luminosity evolution of quiescent early types and
radio-quiet hosts. This indicates that active star formation, and hence galaxy
interactions, are associated with the formation for radio-loud AGN, and that
these host galaxies preferentially accrete less material after their formation
epoch than galaxies without powerful radio jets. We discuss possible
explanations for the link between merger history and the incidence of a radio
jet.Comment: 37 pages, 8 figures, accepted for publication in ApJ, for full PDF
incl. figures see
http://www.ph.unimelb.edu.au/~modowd/papers/odowdurry2005.pd
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