6,854 research outputs found
An -Regularization Approach to High-Dimensional Errors-in-variables Models
Several new estimation methods have been recently proposed for the linear
regression model with observation error in the design. Different assumptions on
the data generating process have motivated different estimators and analysis.
In particular, the literature considered (1) observation errors in the design
uniformly bounded by some , and (2) zero mean independent
observation errors. Under the first assumption, the rates of convergence of the
proposed estimators depend explicitly on , while the second
assumption has been applied when an estimator for the second moment of the
observational error is available. This work proposes and studies two new
estimators which, compared to other procedures for regression models with
errors in the design, exploit an additional -norm regularization.
The first estimator is applicable when both (1) and (2) hold but does not
require an estimator for the second moment of the observational error. The
second estimator is applicable under (2) and requires an estimator for the
second moment of the observation error. Importantly, we impose no assumption on
the accuracy of this pilot estimator, in contrast to the previously known
procedures. As the recent proposals, we allow the number of covariates to be
much larger than the sample size. We establish the rates of convergence of the
estimators and compare them with the bounds obtained for related estimators in
the literature. These comparisons show interesting insights on the interplay of
the assumptions and the achievable rates of convergence
Is 4U 0114+65 an eclipsing HMXB?
We present the pulsation and spectral characteristics of the HMXB 4U 0114+65
during a \emph{Suzaku} observation covering the part of the orbit that included
the previously known low intensity emission of the source (dip) and the egress
from this state. This dip has been interpreted in previous works as an X-ray
eclipse. Notably, in this Suzaku observation, the count rate during and outside
the dip vary by a factor of only 2-4 at odds with the eclipses of other HMXBs,
where the intensity drops upto two orders of magnitude. The orbital intensity
profile of 4U 0114+65 is characterized by a narrow dip in the RXTE-ASM (2-12
\rm{keV}) light curve and a shallower one in the Swift-BAT (15-50 \rm{keV}),
which is different from eclipse ingress/egress behaviour of other HMXBs. The
time-resolved spectral analysis reveal moderate absorption column density
(N - 2-20 atoms ) and a relatively low
equivalent width ( 30 \rm{eV} \& 12 \rm{eV} of the iron K and
K lines respectively) as opposed to the typical X-ray spectra of HMXBs
during eclipse where the equivalent width is 1 \rm{keV}. Both XIS and
PIN data show clear pulsations during the dip, which we have further confirmed
using the entire archival data of the IBIS/ISGRI and JEM-X instruments onboard
\emph{INTEGRAL}. The results we presented question the previous interpretation
of the dip in the light curve of 4U 0114+65 as an X-ray eclipse. We thus
discuss alternative interpretations of the periodic dip in the light curve of
4U 0114+65.Comment: 16 pages, 7 figures, 1 table, Accepted in MNRA
Low Luminosity States of the Black Hole Candidate GX~339--4. II. Timing Analysis
Here we present timing analysis of a set of eight Rossi X-ray Timing Explorer
(RXTE) observations of the black hole candidate GX 339-4 that were taken during
its hard/low state. On long time scales, the RXTE All Sky Monitor data reveal
evidence of a 240 day periodicity, comparable to timescales expected from
warped, precessing accretion disks. On short timescales all observations save
one show evidence of a persistent f approximately equal to 0.3 Hz QPO. The
broad band (10^{-3}-10^2 Hz) power appears to be dominated by two independent
processes that can be modeled as very broad Lorentzians with Q approximately
less than 1. The coherence function between soft and hard photon variability
shows that if these are truly independent processes, then they are individually
coherent, but they are incoherent with one another. This is evidenced by the
fact that the coherence function between the hard and soft variability is near
unity between 0.005-10 Hz but shows evidence of a dip at f approximately equal
to 1 Hz. This is the region of overlap between the broad Lorentzian fits to the
PSD. Similar to Cyg X-1, the coherence also drops dramatically at frequencies
approximately greater than 10 Hz. Also similar to Cyg X-1, the hard photon
variability is seen to lag the soft photon variability with the lag time
increasing with decreasing Fourier frequency. The magnitude of this time lag
appears to be positively correlated with the flux of GX 339-4. We discuss all
of these observations in light of current theoretical models of both black hole
spectra and temporal variability.Comment: To Appear in the AStrophysical Journa
Pivotal estimation in high-dimensional regression via linear programming
We propose a new method of estimation in high-dimensional linear regression
model. It allows for very weak distributional assumptions including
heteroscedasticity, and does not require the knowledge of the variance of
random errors. The method is based on linear programming only, so that its
numerical implementation is faster than for previously known techniques using
conic programs, and it allows one to deal with higher dimensional models. We
provide upper bounds for estimation and prediction errors of the proposed
estimator showing that it achieves the same rate as in the more restrictive
situation of fixed design and i.i.d. Gaussian errors with known variance.
Following Gautier and Tsybakov (2011), we obtain the results under weaker
sensitivity assumptions than the restricted eigenvalue or assimilated
conditions
Evidence for reduced magnetic braking in polars from binary population models
We present the first population synthesis of synchronous magnetic cataclysmic variables, called polars, taking into account the effect of the white dwarf (WD) magnetic field on angular momentum loss. We implemented the reduced magnetic braking (MB) model proposed by Li, Wu & Wickramasinghe into the Binary Stellar Evolution (BSE) code recently calibrated for cataclysmic variable (CV) evolution. We then compared separately our predictions for polars and non-magnetic CVs with a large and homogeneous sample of observed CVs from the Sloan Digital Sky Survey. We found that the predicted orbital period distributions and space densities agree with the observations if period bouncers are excluded. For polars, we also find agreement between predicted and observed mass transfer rates, while the mass transfer rates of non-magnetic CVs with periods ≳3 h drastically disagree with those derived from observations. Our results provide strong evidence that the reduced MB model for the evolution of highly magnetized accreting WDs can explain the observed properties of polars. The remaining main issues in our understanding of CV evolution are the origin of the large number of highly magnetic WDs, the large scatter of the observed mass transfer rates for non-magnetic systems with periods ≳3 h, and the absence of period bouncers in observed samples
Origin of the X-ray Quasi-Periodic Oscillations and Identification of a Transient Ultraluminous X-Ray Source in M82
The starburst galaxy M82 contains two ultraluminous X-ray sources (ULXs),
CXOM82 J095550.2+694047 (=X41.4+60) and CXOM82 J095551.1+694045 (=X42.3+59),
which are unresolved by XMM-Newton. We revisited the two XMM-Newton
observations of M82 and analyzed the surface brightness profiles using the
known Chandra source positions. We show that the quasi-periodic oscillations
(QPOs) detected with XMM-Newton originate from X41.4+60, the brightest X-ray
source in M82. Correcting for the contributions of the unresolved sources, the
QPO at a frequency of 55.8+/-1.3 mHz on 2001 May 06 had a fractional rms
amplitude of 32%, and the QPO at 112.9+/-1.3 mHz on 2004 April 21 had an
amplitude of 21%. The QPO frequency may possibly be correlated with the source
flux, similar to the type C QPOs in XTE 1550-564 and GRS 1915+105, but at
luminosities two orders of magnitude higher. X42.3+59, the second brightest
source in M82, displayed a strikingly high flux of 1.4E-11 ergs/cm^2/s in the
2-10 keV band on 2001 May 6. A seven-year light curve of X42.3+59 shows extreme
variability over a factor of 1000; the source is not detected in several
Chandra observations. This transient behavior suggests accretion from an
unstable disk. If the companion star is massive, as might be expected in the
young stellar environment, then the compact object would likely be an IMBH.Comment: 9 pages, 6 figures, submitted to ApJ on May 08, 200
Discovery of two simultaneous non-harmonically related Quasi-Periodic Oscillations in the 2005 outburst of the black-hole binary GRO J1655-40
We studied the low-frequency quasi-periodic oscillations (LFQPOs) in the
black hole GRO J1655-40 during the 2005 outburst, using data from the Rossi
X-ray Timing Explorer. All LFQPOs could be identified as either type B or type
C using previously proposed classification schemes. In the soft state of the
outburst the type-C LFQPOs reached frequencies that are among the highest ever
seen for LFQPOs in black holes. At the peak of the outburst, in the
ultra-luminous state, the power spectrum showed two simultaneous,
non-harmonically related peaks which we identified as a type-B and a type-C
QPO. The simultaneous presence of a type-C and type-B QPO shows that at least
two of the three known LFQPO types are intrinsically different and likely the
result of distinct physical mechanisms. We also studied the properties of a
broad peaked noise component in the power spectra of the ultra-luminous state.
This noise component becomes more coherent with count rate and there are strong
suggestions that it evolves into a type-B QPO at the highest observed count
rates.Comment: 14 pages, 6 figures, 2 tables, accepted for publication in MNRA
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