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 $h$ and for any density operator $\rho$ on a finite dimensional Hilbert space with the orthogonal projection $\Pi$ onto the range of $\rho$ there holds the estimate \Tr(\Pi \rme^{-\rmi ht}\rho \rme^{\rmi ht}) \geq\cos^{2}((\Delta h)_{\rho}t) for all real $t$ with $(\Delta h)_{\rho}| t| \leq\pi/2.$ We show that equality either holds for all $t\in\mathbb{R}$ or it does not hold for a single $t$ with $0<(\Delta h)_{\rho}| t| \leq\pi/2.$ All the density operators saturating the bound for all $t\in\mathbb{R},$ 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 $\gtrsim 160$ within a span of $\Delta$$t$/$t$ $\le$ 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 $10^{4-6}$ M$_{\odot}$. (2) We detect rapid ($\lesssim 500$ 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 $\lesssim 400$ 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 $63.4 \pm 4.5$ AU ($\sim 10^{15}$ cm) at all times during the outburst, the blackbody temperature drops significantly from $\sim$ 30,000 K at early times to a value of $\sim$ 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 $z=0.07897$. 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 $L_{\rm{peak}} \approx 1.5 \times 10^{44}$ erg/s. The inferred temperature from the optical and UV data shows a value of (3$-$5) $\times 10^4$ K. The transient is not detected in X-rays up to $L_X < 3 \times 10^{42}$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$\alpha$ 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 $N_{\rm{H}} > 10^{23}$ cm$^{-2}$. 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