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Zhiyuan Li

Publications and source records attributed to Zhiyuan Li.

At least 379 records · Page 21Linked to original sources
arXiv2019

Chandra Detection of Intra-cluster X-ray Sources in Fornax

Based on archival {\it Chandra} observations with a total exposure of 1.3 Ms, we study X-ray point sources in the Fornax cluster of galaxies, with the primary aim of searching for intra-cluster X-ray source populations. We detect 1177 point sources out to a projected radius of $\sim$30 arcmin ($\sim$180 kpc) from the cluster center and down to a limiting 0.5--8 keV luminosity of $\sim3\times10^{37}{\rm~erg~s^{-1}}$. We construct source surface density profile, after excluding sources associated with foreground stars, known globular clusters, ultra-compact dwarfs and galactic nuclei. From this profile we statistically identify $\sim$183 excess sources that are not associated with the bulk stellar content of the individual member galaxies of Fornax, nor with the cosmic X-ray background. Taking into account Poisson error and cosmic variance, the cumulative significance of this excess is at $\gtrsim 2\,σ$ level (with a maximum of 3.6\,$σ$) outside three effective radii of the central giant elliptical, NGC\,1399. The luminosity function of the excess sources is found to be significantly steeper than that of the GC-hosting sources (presumably low-mass X-ray binaries [LMXBs]), disfavoring the possibility that unidentified GCs are primarily responsible for the excess. We show that a large fraction of the excess can be related to the extended stellar halo of NGC\,1399 and/or the diffuse intra-cluster light, thus providing strong evidence for the presence of intra-cluster X-ray sources in Fornax, the second unambiguous case for a galaxy cluster after Virgo. Other possible origins of the excess, including supernova-kicked LMXBs and stripped nucleated dwarf galaxies are discussed.

astro-ph.GA↗
arXiv2018

JCMT Mapping of CO(3-2) in the Circumnuclear Region of M31

We present a survey of CO(3-2) molecular line emission in the circumnuclear region of M31 with the James Clerk Maxwell Telescope (JCMT), aiming to explore the physical conditions of the molecular gas. Significant CO(3-2) lines are detected primarily along the so-called nuclear spiral, out to a projected galactocentric radius of 700 pc at a linear resolution of ~50 pc. We find that the velocity field of the molecular gas is in rough agreement with that of the ionized gas previously determined from optical observations. Utilizing existed CO(2-1) and CO(1-0) measurements in selected regions of the nuclear spiral, we derive characteristic intensity ratios of CO(3-2)/CO(2-1) and CO(3-2)/CO(1-0), which are both close to unity and are significantly higher than the typical intensity ratios in the disk. Such line ratios suggest high kinetic temperatures of the gas, which might be due to strong interstellar shocks prevalent in the circumnuclear region.

astro-ph.GA↗
arXiv2018

Probabilistic Attribute Tree in Convolutional Neural Networks for Facial Expression Recognition

In this paper, we proposed a novel Probabilistic Attribute Tree-CNN (PAT-CNN) to explicitly deal with the large intra-class variations caused by identity-related attributes, e.g., age, race, and gender. Specifically, a novel PAT module with an associated PAT loss was proposed to learn features in a hierarchical tree structure organized according to attributes, where the final features are less affected by the attributes. Then, expression-related features are extracted from leaf nodes. Samples are probabilistically assigned to tree nodes at different levels such that expression-related features can be learned from all samples weighted by probabilities. We further proposed a semi-supervised strategy to learn the PAT-CNN from limited attribute-annotated samples to make the best use of available data. Experimental results on five facial expression datasets have demonstrated that the proposed PAT-CNN outperforms the baseline models by explicitly modeling attributes. More impressively, the PAT-CNN using a single model achieves the best performance for faces in the wild on the SFEW dataset, compared with the state-of-the-art methods using an ensemble of hundreds of CNNs.

cs.CV↗
arXiv2018

Theoretical Analysis of Auto Rate-Tuning by Batch Normalization

Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has been lacking. Here theoretical support is provided for one of its conjectured properties, namely, the ability to allow gradient descent to succeed with less tuning of learning rates. It is shown that even if we fix the learning rate of scale-invariant parameters (e.g., weights of each layer with BN) to a constant (say, $0.3$), gradient descent still approaches a stationary point (i.e., a solution where gradient is zero) in the rate of $T^{-1/2}$ in $T$ iterations, asymptotically matching the best bound for gradient descent with well-tuned learning rates. A similar result with convergence rate $T^{-1/4}$ is also shown for stochastic gradient descent.

cs.LG↗
arXiv2018

Deep Template Matching for Offline Handwritten Chinese Character Recognition

Just like its remarkable achievements in many computer vision tasks, the convolutional neural networks (CNN) provide an end-to-end solution in handwritten Chinese character recognition (HCCR) with great success. However, the process of learning discriminative features for image recognition is difficult in cases where little data is available. In this paper, we propose a novel method for learning siamese neural network which employ a special structure to predict the similarity between handwritten Chinese characters and template images. The optimization of siamese neural network can be treated as a simple binary classification problem. When the training process has been finished, the powerful discriminative features help us to generalize the predictive power not just to new data, but to entirely new classes that never appear in the training set. Experiments performed on the ICDAR-2013 offline HCCR datasets have shown that the proposed method has a very promising generalization ability to the new classes that never appear in the training set.

cs.CV↗
arXiv2018

Searching for GeV gamma-ray emission from the bulge of M31

The three major large-scale, diffuse $γ$-ray structures of the Milky Way are the Galactic disk, a bulge-like GeV excess towards the Galactic center, and the Fermi bubble. Whether such structures can also be present in other normal galaxies remains an open question. M31, as the nearest massive normal galaxy, holds promise for spatially-resolving the $γ$-ray emission. Based on more than 8 years of Fermi-LAT observations, we use (1) disk, (2) bulge, and (3) disk-plus-bulge templates to model the spatial distribution of the $γ$-ray emission from M31. Among these, the disk-plus-bulge template delivers the best-fit, in which the bulge component has a TS value 25.7 and a photon-index of $2.57\pm0.17$, providing strong evidence for a centrally-concentrated gamma-ray emission from M31, that is analogous to the Galactic center excess. The total 0.2-300 GeV gamma-ray luminosity from this bulge component is $(1.16\pm0.14)\times10^{38} erg s^{-1}$, which would require $\sim1.5\times10^5$ millisecond pulsars, if they were the dominant source. We also search for a Fermi bubble-like structure in M31 using the full dataset (pass8), but no significant evidence is found. In addition, a likelihood analysis using only photons with the most accurate reconstructed direction (i.e., PSF3-only data) reveals a 4.8 $σ$ point-like source located at $\sim$ 10kpc to the northwest of the M31 disk, with a luminosity of $(0.97\pm0.27)\times10^{38} erg s^{-1}$ and a photon-index of $2.31\pm0.18$. Lacking of a counterpart on the southeast side of the disk, the relation between this point-like source and a bubble-like structure remains elusive.

astro-ph.HE↗
arXiv2018

A Chandra Survey of Milky Way Globular Clusters II: Testing the Hills-Heggie Law

Binary-single and binary-binary encounters play a pivotal role in the evolution of star clusters, as they may lead to the disruption or hardening of binaries, a novel prediction of the Hills-Heggie law. Based on our recent {\it Chandra} survey of Galactic globular clusters (GCs), we revisit the role of stellar dynamical interactions in GCs, focusing on main-sequence (MS) binary encounters as a potential formation channel of the observed X-ray sources in GCs. We show that the cumulative X-ray luminosity ($L_X$), a proxy of the total number of X-ray-emitting binaries (primarily cataclysmic variables and coronally active binaries) in a given GC, is highly correlated with the MS binary encounter rate ($Γ_{b}$), as $L_X \propto Γ_{b}^{0.77\pm0.11}$. We further test the Hills-Heggie law against the {\it binary hardness ratio}, defined as the relative number of X-ray-emitting hard binaries to MS binaries and approximated by $L_{X}/(L_{K}f_{b})$, with $L_{K}$ being the GC K-band luminosity and $f_b$ the MS binary fraction. We demonstrate that the binary hardness ratio of most GCs is larger than that of the Solar neighborbood stars, and exhibits a positive correlation with the cluster specific encounter rate ($γ$), as $L_{X}/(L_{K}f_{b}) \propto γ^{0.65\pm0.12}$. We also find a strong correlation between the binary hardness ratio and cluster velocity dispersion ($σ$), with $L_{X}/(L_{K}f_{b}) \propto σ^{1.71\pm0.48}$, which is consistent with the Hills-Heggie law. We discuss the role of binary encounters in the context of the Nuclear Star Cluster, arguing that the X-ray-emitting, close binaries detected therein could have been predominatly formed in GCs that later inspiralled to the Galactic center.

astro-ph.HE↗
arXiv2018

Probing the dynamical state, baryon content, and multiphase nature of galaxy clusters with bright background QSOs

We have initiated a programme to study the physical/dynamical state of gas in galaxy clusters and the impact of the cluster environment on gaseous halos of individual galaxies using X-ray imaging and UV absorption line spectroscopy of background QSOs. Here we report results from the analysis Chandra and XMM-Newton archival data of five galaxy clusters with such QSOs, one of which has an archival UV spectrum. We characterize the gravitational masses and dynamical states, as well as the hot intracluster medium (ICM) properties of these clusters. Most clusters are dynamically disturbed clusters based on the X-ray morphology parameters, the X-ray temperature profiles, the large offset between X-ray peak and brightest cluster galaxy (BCG). The baryon contents in the hot ICM and stars of these clusters within $r_{500}$ are lower than the values expected from the gravitational masses, according to the standard cosmology. We also estimate column densities of the hot ICM along the sightlines toward the background QSOs as well as place upper limits on the warm-hot phase for the one sightline with existing UV observations. These column densities, compared with those of the warm and warm-hot ICM to be measured with UV absorption line spectroscopy, will enable us to probe the relationship among various gaseous phases and their connection to the heating/cooling and dynamical processes of the clusters. Furthermore, our analysis of the archival QSO spectrum probing one cluster underscores the need for high quality, targeted UV observations to robustly constrain the 10$^{5-6}$ K gas phase.

astro-ph.GA↗
arXiv2018

An inverse problem for distributed order time-fractional diffusion equations

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the distributed order time-fractional diffusion equation by means of eigenfunction expansion, which ensure that the weak solution has the classical derivatives. We next give a Harnack type inequality of the solution in the frequency domain under the Laplace transform, from which we further show a uniqueness result for an inverse problem in determining the weight function in the distributed order time derivative from point observation.

math.AP↗
arXiv2018

Unique continuation principle for the one-dimensional time-fractional diffusion equation

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order $α\in(0,1)$. Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

math.AP↗
arXiv2018

Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks

Despite existing work on ensuring generalization of neural networks in terms of scale sensitive complexity measures, such as norms, margin and sharpness, these complexity measures do not offer an explanation of why neural networks generalize better with over-parametrization. In this work we suggest a novel complexity measure based on unit-wise capacities resulting in a tighter generalization bound for two layer ReLU networks. Our capacity bound correlates with the behavior of test error with increasing network sizes, and could potentially explain the improvement in generalization with over-parametrization. We further present a matching lower bound for the Rademacher complexity that improves over previous capacity lower bounds for neural networks.

cs.LG↗
arXiv2018

Planetary Nebulae in the Circumnuclear Region of M31: A Spectroscopic Sample

Planetary nebulae (PNe) are an important tool for studying the dynamics and chemical evolution of galaxies in the Local Universe, given their characteristic, bright emission line spectra. The Andromeda Galaxy (M31) provides a unique laboratory for studying PNe in the circumnuclear region, thanks to its proximity and almost uniformly low line-of-sight extinction that ensures observations with high resolution and sensitivity. Using the WIYN/Hydra multi-fiber spectrograph, we have obtained optical (4119--6882Å) spectra of 77 PN candidates selected from Hubble Space Telescope narrow-band imaging, which are located within the central $\sim$500pc region of M31. Among these candidates, 49 (64%) are spectroscopically observed for the first time. The spectra of 300 previously known PNe and H II regions, which primarily reside in the disk, are also taken for comparison. All 77 circumnuclear PN candidates exhibit prominent emission lines, including [O III] $λ$5007, [N II] $λ$6583, H$α$ and H$β$, strongly suggesting that they are genuine PNe. We measured the line fluxes, radial velocities and line widths for all objects, and found that the radial velocities of the circumnuclear PNe generally trace rotation of the inner bulge. We also estimated a dynamical mass of $\sim$6.4$\pm$0.5$\times$10$^{9}$$M_{\odot}$ enclosed within an effective galactocentric radius of 340pc, which is compatible with the previously estimated total stellar mass in this region.

astro-ph.GA↗
arXiv2018

Deep Chandra observations of X-ray point sources in M87

We present a study of X-ray source populations in M87, the cD galaxy of the Virgo cluster, using 12 archival {\it Chandra} observations with a total exposure of $\sim$680 ks spanning about a decade. A total of 346 point-like sources are detected down to a limiting 0.5--8 keV luminosity of $4\times10^{37}{\rm~erg~s^{-1}}$ and out to a galactocentric radius of $\sim$40 kpc. We cross-correlate the X-ray sources with published catalogs of globular clusters (GCs), derived from the ACS Virgo Cluster Survey and the Next Generation Virgo Cluster Survey. This results in 122 matches, making it one of the largest samples of GC-hosting X-ray sources in an external galaxy. These sources, most likely low-mass X-ray binaries (LMXBs), correspond to $\sim$5\% of all known GCs within the {\it Chandra} field-of-view. Conversely, $\sim$50\% of the detected X-ray sources are found in a GC. Moreover, red (metal-rich) GCs are $\sim$2.2 times more likely to host an X-ray source than blue (metal-poor) GCs. We also examine 76 currently known ultra-compact dwarf galaxies around M87, but find no significant X-ray counterparts. After statistically accounting for the cosmic X-ray background, we identify $\sim$110 field-LMXBs. The GC-LMXBs and field-LMXBs differ in their luminosity function and radial distribution, which indicates that the latter cannot be primarily originated from GCs. Using another set of deep {\it Chandra} observations toward $\sim$100 kpc northwest of the M87 center, we statistically constrain the abundance of field-LMXBs in the stellar halo, which is consistent with that found in the central region. We also identify 40 variable X-ray sources, among which one source is likely a black hole binary residing in a GC.

astro-ph.HE↗
arXiv2018

The Star Formation History in the M31 Bulge

We present the study of stellar populations in the central 5.5' (~1.2 kpc) of the M31 bulge by using the optical color magnitude diagram derived from HST ACS WFC/HRC observations. In order to enhance image quality and then obtain deeper photometry, we construct Nyquist-sampled images and use a deconvolution method to detect sources and measure their photometry. We demonstrate that our method performs better than DOLPHOT in the extremely crowded region. The resolved stars in the M31 bulge have been divided into nine annuli and the color magnitude diagram fitting is performed for each of them. We confirm that the majority of stars (> 70%) in the M31 bulge are indeed very old (>5 Gyr) and metal-rich ([Fe/H] > 0.3). At later times, the star formation rate decreased and then experienced a significant rise around 1 Gyr ago, which pervaded the entire M31 bulge. After that, stars formed at less than 500 Myr ago in the central 130". Through simulation, we find that these intermediate-age stars cannot be the artifacts introduced by the blending effect. Our results suggest that although the majority of the M31 bulge are very old, the secular evolutionary process still continuously builds up the M31 bulge slowly. We compare our star formation history with an older analysis derived from the spectral energy distribution fitting, which suggests that the latter one is still a reasonable tool for the study of stellar populations in remote galaxies.

astro-ph.GA↗
arXiv2018

Online Improper Learning with an Approximation Oracle

We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and require only poly-logarithmically many calls to the approximation oracle per iteration. Furthermore, these algorithms apply to the more general improper learning problems. In the bandit setting, our algorithm also significantly improves the best previously known oracle complexity while maintaining the same regret.

cs.LG↗
arXiv2018

Building Efficient CNN Architecture for Offline Handwritten Chinese Character Recognition

Deep convolutional networks based methods have brought great breakthrough in images classification, which provides an end-to-end solution for handwritten Chinese character recognition(HCCR) problem through learning discriminative features automatically. Nevertheless, state-of-the-art CNNs appear to incur huge computation cost, and require the storage of a large number of parameters especially in fully connected layers, which is difficult to deploy such networks into alternative hardware device with the limit of computation amount. To solve the storage problem, we propose a novel technique called Global Weighted Arverage Pooling for reducing the parameters in fully connected layer without loss in accuracy. Besides, we implement a cascaded model in single CNN by adding mid output layer to complete recognition as early as possible, which reduces average inference time significantly. Experiments were performed on the ICDAR-2013 offline HCCR dataset, and it is found that the proposed approach only needs 6.9ms for classfying a chracter image on average, and achieves the state-of-the-art accuracy of 97.1% while requiring only 3.3MB for storage.

cs.CV↗
arXiv2018

A Chandra Study of The Stellar X-ray Emissivity of Globular Clusters in M\,31 Bulge

The X-ray emissivity (i.e., luminosity per unit stellar mass) of globular clusters are an important indicator of their dynamical evolution history. Based on deep archival \textit{Chandra} observations, we report a stacking analysis of 44 globular clusters (GCs) with 0.5-8 keV luminosities $L_{\rm X} \lesssim 10^{35} {\rm~erg~s^{-1}}$ in the M\,31 bulge, which are supposed to be dominated by cataclysmic variables (CVs) and coronally active binaries (ABs). We obtain a significant detection at $5σ$ level in 0.5-8 keV band. The average X-ray luminosity per GC and the average X-ray emissivity are determined to be $5.3 \pm 1.6\times10^{33}\rm~erg~s^{-1}$ and $13.2\pm4.3\times10^{27}\rm~erg~{\rm s^{-1}~M^{-1}_{\odot}}$, respectively. Both of these values are consistent with those of MW GCs. What's more, the measured emissivity of M31 GCs is also consistent with that of the MW field stars. Massive GCs have X-ray luminosities which are marginally higher with less massive ones. Massive GCs also show a lower emissivity ($4.5\pm 2.4\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$) than less massive ones ($15.0\pm 7.8\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$), which is consistent with the scenario that the (progenitors of) CVs and ABs were more efficiently destructed via stellar encounters in the more massive GCs. No dependence of the X-ray emissivity on GC color or on the projected galactocentric distance of GCs were found.

astro-ph.HE↗