375 research outputs found
Efficient Estimation of Heat Kernel PageRank for Local Clustering
Given an undirected graph G and a seed node s, the local clustering problem
aims to identify a high-quality cluster containing s in time roughly
proportional to the size of the cluster, regardless of the size of G. This
problem finds numerous applications on large-scale graphs. Recently, heat
kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs,
is applied to this problem and found to be more efficient compared with prior
methods. However, existing solutions for computing HKPR either are
prohibitively expensive or provide unsatisfactory error approximation on HKPR
values, rendering them impractical especially on billion-edge graphs.
In this paper, we present TEA and TEA+, two novel local graph clustering
algorithms based on HKPR, to address the aforementioned limitations.
Specifically, these algorithms provide non-trivial theoretical guarantees in
relative error of HKPR values and the time complexity. The basic idea is to
utilize deterministic graph traversal to produce a rough estimation of exact
HKPR vector, and then exploit Monte-Carlo random walks to refine the results in
an optimized and non-trivial way. In particular, TEA+ offers practical
efficiency and effectiveness due to non-trivial optimizations. Extensive
experiments on real-world datasets demonstrate that TEA+ outperforms the
state-of-the-art algorithm by more than four times on most benchmark datasets
in terms of computational time when achieving the same clustering quality, and
in particular, is an order of magnitude faster on large graphs including the
widely studied Twitter and Friendster datasets.Comment: The technical report for the full research paper accepted in the
SIGMOD 201
Fleming's bound for the decay of mixed states
Fleming's inequality is generalized to the decay function of mixed states. We
show that for any symmetric hamiltonian and for any density operator
on a finite dimensional Hilbert space with the orthogonal projection onto
the range of there holds the estimate \Tr(\Pi \rme^{-\rmi ht}\rho
\rme^{\rmi ht}) \geq\cos^{2}((\Delta h)_{\rho}t) for all real with
We show that equality either holds for all
or it does not hold for a single with All the density operators saturating the bound for
all i.e. the mixed intelligent states, are determined.Comment: 12 page
Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra
We create classical (non-quantum) dynamic data structures supporting queries
for recommender systems and least-squares regression that are comparable to
their quantum analogues. De-quantizing such algorithms has received a flurry of
attention in recent years; we obtain sharper bounds for these problems. More
significantly, we achieve these improvements by arguing that the previous
quantum-inspired algorithms for these problems are doing leverage or
ridge-leverage score sampling in disguise; these are powerful and standard
techniques in randomized numerical linear algebra. With this recognition, we
are able to employ the large body of work in numerical linear algebra to obtain
algorithms for these problems that are simpler or faster (or both) than
existing approaches.Comment: Adding new numerical experiment
A Case Study of On-the-Fly Wide-Field Radio Imaging Applied to the Gravitational-wave Event GW 151226
We apply a newly-developed On-the-Fly mosaicing technique on the NSF's Karl
G. Jansky Very Large Array (VLA) at 3 GHz in order to carry out a sensitive
search for an afterglow from the Advanced LIGO binary black hole merger event
GW 151226. In three epochs between 1.5 and 6 months post-merger we observed a
100 sq. deg region, with more than 80% of the survey region having a RMS
sensitivity of better than 150 uJy/beam, in the northern hemisphere having a
merger containment probability of 10%. The data were processed in
near-real-time, and analyzed to search for transients and variables. No
transients were found but we have demonstrated the ability to conduct blind
searches in a time-frequency phase space where the predicted afterglow signals
are strongest. If the gravitational wave event is contained within our survey
region, the upper limit on any late-time radio afterglow from the merger event
at an assumed mean distance of 440 Mpc is about 1e29 erg/s/Hz. Approximately
1.5% of the radio sources in the field showed variability at a level of 30%,
and can be attributed to normal activity from active galactic nuclei. The low
rate of false positives in the radio sky suggests that wide-field imaging
searches at a few Gigahertz can be an efficient and competitive search
strategy. We discuss our search method in the context of the recent afterglow
detection from GW 170817 and radio follow-up in future gravitational wave
observing runs.Comment: 11 pages. 6 figures. 1 table. Accepted for publication in ApJ Letter
How Baryonic Processes affect Strong Lensing properties of Simulated Galaxy Clusters
The observed abundance of giant arcs produced by galaxy cluster lenses and
the measured Einstein radii have presented a source of tension for LCDM.
Previous cosmological tests for high-redshift clusters (z>0.5) have suffered
from small number statistics in the simulated sample and the implementation of
baryonic physics is likely to affect the outcome. We analyse zoomed-in
simulations of a fairly large sample of cluster-sized objects, with Mvir >
3x10^14 Msun/h, identified at z=0.25 and z=0.5, for a concordance LCDM
cosmology. We start with dark matter only simulations, and then add gas
hydrodynamics, with different treatments of baryonic processes: non-radiative
cooling, radiative cooling with star formation and galactic winds powered by
supernova explosions, and finally including the effect of AGN feedback. We find
that the addition of gas in non-radiative simulations does not change the
strong lensing predictions significantly, but gas cooling and star formation
together significantly increase the number of expected giant arcs and the
Einstein radii, particularly for lower redshift clusters and lower source
redshifts. Further inclusion of AGN feedback reduces the predicted strong
lensing efficiencies such that the lensing probability distributions becomes
closer to those obtained for simulations including only dark matter. Our
results indicate that the inclusion of baryonic physics in simulations will not
solve the arc-statistics problem at low redshifts, when the physical processes
included provide a realistic description of cooling in the central regions of
galaxy clusters. [Abridged]Comment: 19 pages, 18 figures, 1 table, Accepted for publication in MNRA
3C 220.3: a radio galaxy lensing a submillimeter galaxy
Herschel Space Observatory photometry and extensive multiwavelength followup
have revealed that the powerful radio galaxy 3C 220.3 at z=0.685 acts as a
gravitational lens for a background submillimeter galaxy (SMG) at z=2.221. At
an observed wavelength of 1mm, the SMG is lensed into three distinct images. In
the observed near infrared, these images are connected by an arc of 1.8" radius
forming an Einstein half-ring centered near the radio galaxy. In visible light,
only the arc is apparent. 3C 220.3 is the only known instance of strong
galaxy-scale lensing by a powerful radio galaxy not located in a galaxy cluster
and therefore it offers the potential to probe the dark matter content of the
radio galaxy host. Lens modeling rejects a single lens, but two lenses centered
on the radio galaxy host A and a companion B, separated by 1.5", provide a fit
consistent with all data and reveal faint candidates for the predicted fourth
and fifth images. The model does not require an extended common dark matter
halo, consistent with the absence of extended bright X-ray emission on our
Chandra image. The projected dark matter fractions within the Einstein radii of
A (1.02") and B (0.61") are about 0.4 +/- 0.3 and 0.55 +/- 0.3. The mass to
i-band light ratios of A and B, M/L ~ 8 +/- 4 Msun/Lsun, appear comparable to
those of radio-quiet lensing galaxies at the same redshift in the CASTLES, LSD,
and SL2S samples. The lensed SMG is extremely bright with observed f(250um) =
440mJy owing to a magnification factor mu~10. The SMG spectrum shows luminous,
narrow CIV 154.9nm emission, revealing that the SMG houses a hidden quasar in
addition to a violent starburst. Multicolor image reconstruction of the SMG
indicates a bipolar morphology of the emitted ultraviolet (UV) light suggestive
of cones through which UV light escapes a dust-enshrouded nucleus.Comment: 17 pages, 14 Figures, accepted for publication in Ap
Seminal plasma and prostaglandin E2 up-regulate fibroblast growth factor 2 expression in endometrial adenocarcinoma cells via E-series prostanoid-2 receptor-mediated transactivation of the epidermal growth factor receptor and extracellular signal-regulated kinase pathway
We report a multiwavelength (X-ray, ultraviolet/optical/infrared, radio)
analysis of the relativistic tidal disruption event candidate Sw J2058+05 from
3 months to 3 yr post-discovery in order to study its properties and compare
its behavior with that of Sw J1644+57. Our main results are as follows. (1) The
long-term X-ray light curve of Sw J2058+05 shows a remarkably similar trend to
that of Sw J1644+57. After a prolonged power-law decay, the X-ray flux drops
off rapidly by a factor of within a span of /
0.95. Associating this sudden decline with the transition from super-Eddington
to sub-Eddington accretion, we estimate the black hole mass to be in the range
of M. (2) We detect rapid ( s) X-ray
variability before the dropoff, suggesting that, even at late times, the X-rays
originate from close to the black hole (ruling out a forward-shock origin). (3)
We confirm using HST and VLBA astrometry that the location of the source
coincides with the galaxy's center to within pc (in projection).
(4) We modeled Sw J2058+05's ultraviolet/optical/infrared spectral energy
distribution with a single-temperature blackbody and find that while the radius
remains more or less constant at a value of AU (
cm) at all times during the outburst, the blackbody temperature drops
significantly from 30,000 K at early times to a value of 15,000 K
at late times (before the X-ray dropoff). Our results strengthen Sw J2058+05's
interpretation as a tidal disruption event similar to Sw J1644+57.Comment: Replaced with the published version of the manuscrip
The Broad Absorption Line Tidal Disruption Event iPTF15af: Optical and Ultraviolet Evolution
We present multi-wavelength observations of the tidal disruption event (TDE)
iPTF15af, discovered by the intermediate Palomar Transient Factory (iPTF)
survey at redshift . The optical and ultraviolet (UV) light curves
of the transient show a slow decay over five months, in agreement with previous
optically discovered TDEs. It also has a comparable black-body peak luminosity
of erg/s. The inferred temperature
from the optical and UV data shows a value of (35) K. The
transient is not detected in X-rays up to erg/s within
the first five months after discovery. The optical spectra exhibit two distinct
broad emission lines in the He II region, and at later times also H
emission. Additionally, emission from [N III] and [O III] is detected, likely
produced by the Bowen fluorescence effect. UV spectra reveal broad emission and
absorption lines associated with high-ionization states of N V, C IV, Si IV,
and possibly P V. These features, analogous to those of broad absorption line
quasars (BAL QSOs), require an absorber with column densities cm. This optically thick gas would also explain the
non-detection in soft X-rays. The profile of the absorption lines with the
highest column density material at the largest velocity is opposite that of BAL
QSOs. We suggest that radiation pressure generated by the TDE flare at early
times could have provided the initial acceleration mechanism for this gas.
Spectral UV line monitoring of future TDEs could test this proposal.Comment: 20 pages, 12 figures, published in Ap
Estimating Nuisance Parameters in Inverse Problems
Many inverse problems include nuisance parameters which, while not of direct
interest, are required to recover primary parameters. Structure present in
these problems allows efficient optimization strategies - a well known example
is variable projection, where nonlinear least squares problems which are linear
in some parameters can be very efficiently optimized. In this paper, we extend
the idea of projecting out a subset over the variables to a broad class of
maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with
nuisance parameters, such as variance or degrees of freedom. As a result, we
are able to incorporate nuisance parameter estimation into large-scale
constrained and unconstrained inverse problem formulations. We apply the
approach to a variety of problems, including estimation of unknown variance
parameters in the Gaussian model, degree of freedom (d.o.f.) parameter
estimation in the context of robust inverse problems, automatic calibration,
and optimal experimental design. Using numerical examples, we demonstrate
improvement in recovery of primary parameters for several large- scale inverse
problems. The proposed approach is compatible with a wide variety of algorithms
and formulations, and its implementation requires only minor modifications to
existing algorithms.Comment: 16 pages, 5 figure
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