arXiv subjects
Publications and source records attributed to Kai Zhang.
In 1957, De Giorgi [3] proved the Hölder continuity for elliptic equations in divergence form and Moser [7] gave a new proof in 1960. Next year, Moser [8] obtained the Harnack inequality. In this note, we point out that the Harnack inequality was hidden in [3].
In this paper, we generalize the $W^{2,p}$ interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli in [1]. The generalizations are carried out in two directions. One is that we relax the regularity requirement on the "constant coefficients" equations and the other one is that we broaden the range of $p$.
Poly($para$-phenylene) has been recognized as one important family of conducting polymers upon doping with donors or acceptors. This system possesses a chain-like structure with infinite benzene rings linked with the single C-C bond. Oligophenyls as models of poly($para$-phenylene) with short chains in the \emph{para} position were found to exhibit superconductivity at transition temperatures ranging from 3 K to 123 K upon dopant. Structural studies have revealed that there exist the order-disorder transitions in many \emph{p}-oligophenyls with almost doubled lattice constants in the \emph{b} and \emph{c} directions at low temperatures, seemingly supporting the formation of the charge-density-wave order. Such a transition is of relevance to the understanding of the emergence of novel quantum functionality where unconventional polaronic interactions are relevant for the new emerging theory of superconductivity in this system. However, the accurate temperatures for the order-disorder transitions amongst these \emph{p}-oligophenyls are still needed to be determined. The chain length effects on the order-disorder transitions in this system remain unknown. Here we report the systematic investigation of the evolution of vibrational properties of the crystalline \emph{p}-oligophenyls over a wide temperature range. The order-disorder transition is identified by three indicators, the lowest energy peak together with the intensity ratios between the 1280 cm$^{-1}$ and 1220 cm$^{-1}$ modes and between the two modes at around 1600 cm$^{-1}$. A phase diagram of the order-disorder transition temperature as well as the melting curve for \emph{p}-oligophenyls is thus established. The former is found to increase with the chain length and saturates at around 350 K for poly($para$-phenylene).
A new class of quiescent galaxies harboring possible AGN-driven winds has been discovered using spatially resolved optical spectroscopy from the ongoing SDSS-IV MaNGA survey. These galaxies, termed "red geysers", constitute $5-10\%$ of the local quiescent population and are characterized by narrow bisymmetric patterns in ionized gas emission features. Cheung et al. argued that these galaxies host large-scale AGN-driven winds that may play a role in suppressing star formation at late times. In this work, we test the hypothesis that AGN activity is ultimately responsible for the red geyser phenomenon. We compare the nuclear radio activity of the red geysers to a matched control sample with similar stellar mass, redshift, rest frame $NUV-r$ color, axis ratio and presence of ionized gas. We have used the 1.4 GHz radio continuum data from VLA FIRST survey to stack the radio flux from the red geyser and control samples. In addition to a 3 times higher FIRST detection rate, we find that red geysers have a 5$σ$ higher level of average radio flux than control galaxies. After restricting to rest-frame $NUV-r$ color $>$ 5 and checking mid-IR WISE photometry, we rule out star formation contamination and conclude that red geysers are associated with more active AGN. Red geysers and a possibly-related class with disturbed H$α$ emission account for 40\% of all radio-detected red galaxies with $\rm log~(M_\star/M_\odot) < 11$. Our results support a picture in which episodic AGN activity drives large-scale-relatively weak ionized winds that may provide a feedback mechanism for many early-type galaxies.
The InfraRed Imaging Spectrograph (IRIS) is the first-light client instrument for the Narrow Field Infrared Adaptive Optics System (NFIRAOS) on the Thirty Meter Telescope (TMT). IRIS includes three natural guide star (NGS) On-Instrument Wavefront Sensors (OIWFS) to measure tip/tilt and focus errors in the instrument focal plane. NFIRAOS also has an internal natural guide star wavefront sensor, and IRIS and NFIRAOS must precisely coordinate the motions of their wavefront sensor positioners to track the locations of NGSs while the telescope is dithering (offsetting the telescope to cover more area), to avoid a costly re-acquisition time penalty. First, we present an overview of the sequencing strategy for all of the involved subsystems. We then predict the motion of the telescope during dithers based on finite-element models provided by TMT, and finally analyze latency and jitter issues affecting the propagation of position demands from the telescope control system to individual motor controllers.
Infrared Imaging Spectrograph (IRIS) is the first light instrument for the Thirty Meter Telescope (TMT) that consists of a near-infrared (0.84 to 2.4 micron) imager and integral field spectrograph (IFS) which operates at the diffraction-limit utilizing the Narrow-Field Infrared Adaptive Optics System (NFIRAOS). The imager will have a 34 arcsec x 34 arcsec field of view with 4 milliarcsecond (mas) pixels. The IFS consists of a lenslet array and slicer, enabling four plate scales from 4 mas to 50 mas, multiple gratings and filters, which in turn will operate hundreds of individual modes. IRIS, operating in concert with NFIRAOS will pose many challenges for the data reduction system (DRS). Here we present the updated design of the real-time and post-processing DRS. The DRS will support two modes of operation of IRIS: (1) writing the raw readouts sent from the detectors and performing the sampling on all of the readouts for a given exposure to create a raw science frame; and (2) reduction of data from the imager, lenslet array and slicer IFS. IRIS is planning to save the raw readouts for a given exposure to enable sophisticated processing capabilities to the end users, such as the ability to remove individual poor seeing readouts to improve signal-to-noise, or from advanced knowledge of the point spread function (PSF). The readout processor (ROP) is a key part of the IRIS DRS design for writing and sampling of the raw readouts into a raw science frame, which will be passed to the TMT data archive. We discuss the use of sub-arrays on the imager detectors for saturation/persistence mitigation, on-detector guide windows, and fast readout science cases (< 1 second).
A variety of fabrication methods for van der Waals heterostructures have been demonstrated; however, their wafer-scale deposition remains a challenge. Here we report few-layer van der Waals PtS2/PtSe2 heterojunction photodiodes fabricated on a 2" SiO2/Si substrate that is only limited by the size of work chamber of the growth equipment, offering throughputs necessary for practical applications. Theoretical simulation results show that the bandgap of PtS2 is shrunk to half of its original size in the PtS2/PtSe2 heterostructures, while PtSe2 exhibits a limited response to the coupling. Both PtSe2 and PtS2 layers in the coupled system are still semiconductors. Dynamic photovoltaic switching in the heterojunctions is observed at zero-volt state under laser illuminations of 532 to 2200 nm wavelengths. The PtS2/PtSe2 photodiodes show excellent characteristics in terms of a high photoresponsivity of 361 mAW-1, an external quantum efficiency (EQE) of 84%, and a fast response speed (66 ms). The wafer-scale production of 2D photodiodes in this work accelerates the possibility of 2D materials for practical applications in the next-generation energy-efficient electronics.
The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sq deg will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope will deliver light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. We will describe the production and manufacturing processes developed for the 5000 fiber positioner robots mounted on the focal plane of the Mayall telescope.
Massively multiplexed spectroscopic stellar surveys such as MSE present enormous challenges in the spectrograph design. The combination of high multiplex, large telescope aperture, high resolution (R~40,000) and natural seeing implies that multiple spectrographs with large beam sizes, large grating angles, and fast camera speeds are required, with high cost and risk. An attractive option to reduce the beam size is to use Bragg-type gratings at much higher angles than hitherto considered. As well as reducing the spectrograph size and cost, this also allows the possibility of very high efficiency due to a close match of s and p-polarization Bragg efficiency peaks. The grating itself could be a VPH grating, but Surface Relief (SR) gratings offer an increasingly attractive alternative, with higher maximum line density and better bandwidth. In either case, the grating needs to be immersed within large prisms to get the light to and from the grating at the required angles. We present grating designs and nominal spectrograph designs showing the efficiency gains and size reductions such gratings might allow for the MSE high resolution spectrograph.
The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sq deg will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope will deliver light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. To achieve this goal, it is crucial to guarantee that fiber positioners work properly under the extremes of potential operating conditions, including the full range of temperatures, high speed wind disturbance etc. Thermal testing provides valuable insight into the functionality of the fiber positioners that can be used to help mitigate poor performance at extreme temperatures and wind disturbance test provide guidance to design of ventilation system. Here, we describe the thermal and wind disturbance tests for DESI fiber positioners and how the test results helped improve the robustness of the positioners.
The Maunakea Spectroscopic Explorer (MSE) project will transform the CFHT 3.6m optical telescope to a 10m class dedicated multi-object spectroscopic facility, with an ability to measure thousands of objects with three spectral resolution modes respectively low resolution of R~3,000, moderate resolution of R~6,000 and high resolution of R~40,000. Two identical multi-object high resolution spectrographs are expected to simultaneously produce 1084 spectra with high resolution of 40,000 at Blue (401-416nm) and Green (472-489nm) channels, and 20,000 at Red (626-674nm) channel. At the Conceptual Design Phase (CoDP), different optical schemes were proposed to meet the challenging requirements, especially a unique design with a novel transmission image slicer array, and another conventional design with oversize Volume Phase Holographic (VPH) gratings. It became clear during the CoDP that both designs presented problems of complexity or feasibility of manufacture, especially high line density disperser (general name for all kinds of grating, grism, prism). At the present, a new design scheme is proposed for investigating the optimal way to reduce technical risk and get more reliable estimation of cost and timescale. It contains new dispersers, F/2 fast collimator and so on. Therein, the disperser takes advantage of a special grism and a prism to reduce line density on grating surface, keep wide opening angle of optical path, and get the similar spectrum layout in all three spectral channels. For the fast collimator, it carefully compares on-axis and off-axis designs in throughput, interface to fiber assembly and technical risks. The current progress is more competitive and credible than the previous design, but it also indicates more challenging work will be done to improve its accessibility in engineering.
A large population of ultra-diffuse galaxies (UDGs) was recently discovered in the Coma cluster. Here we present optical spectra of three such UDGs, DF7, DF44 and DF17, which have central surface brightnesses of $μ_g \approx 24.4-25.1$ mag arcsec$^{-2}$. The spectra were acquired as part of an ancillary program within the SDSS-IV MaNGA Survey. We stacked 19 fibers in the central regions from larger integral field units (IFUs) per source. With over 13.5 hours of on-source integration we achieved a mean signal-to-noise ratio (S/N) in the optical of $9.5$Å$^{-1}$, $7.9$Å$^{-1}$ and $5.0$Å$^{-1}$, respectively, for DF7, DF44 and DF17. Stellar population models applied to these spectra enable measurements of recession velocities, ages and metallicities. The recession velocities of DF7, DF44 and DF17 are $6599^{+40}_{-25}$km/s, $6402^{+41}_{-39}$km/s and $8315^{+43}_{-43}$km/s, spectroscopically confirming that all of them reside in the Coma cluster. The stellar populations of these three galaxies are old and metal-poor, with ages of $7.9^{+3.6}_{-2.5}$Gyr, $8.9^{+4.3}_{-3.3}$Gyr and $9.1^{+3.9}_{-5.5}$Gyr, and iron abundances of $\mathrm{[Fe/H]}$ $-1.0^{+0.3}_{-0.4}$, $-1.3^{+0.4}_{-0.4}$ and $-0.8^{+0.5}_{-0.5}$, respectively. Their stellar masses are $3$-$6\times10^8 M_\odot$. The UDGs in our sample are as old or older than galaxies at similar stellar mass or velocity dispersion (only DF44 has an independently measured dispersion). They all follow the well-established stellar mass$-$stellar metallicity relation, while DF44 lies below the velocity dispersion-metallicity relation. These results, combined with the fact that UDGs are unusually large for their stellar mass, suggest that stellar mass plays a more important role in setting stellar population properties for these galaxies than either size or surface brightness.
Recent years have witnessed the unprecedented success of deep convolutional neural networks (CNNs) in single image super-resolution (SISR). However, existing CNN-based SISR methods mostly assume that a low-resolution (LR) image is bicubicly downsampled from a high-resolution (HR) image, thus inevitably giving rise to poor performance when the true degradation does not follow this assumption. Moreover, they lack scalability in learning a single model to non-blindly deal with multiple degradations. To address these issues, we propose a general framework with dimensionality stretching strategy that enables a single convolutional super-resolution network to take two key factors of the SISR degradation process, i.e., blur kernel and noise level, as input. Consequently, the super-resolver can handle multiple and even spatially variant degradations, which significantly improves the practicability. Extensive experimental results on synthetic and real LR images show that the proposed convolutional super-resolution network not only can produce favorable results on multiple degradations but also is computationally efficient, providing a highly effective and scalable solution to practical SISR applications.
The tradeoff between receptive field size and efficiency is a crucial issue in low level vision. Plain convolutional networks (CNNs) generally enlarge the receptive field at the expense of computational cost. Recently, dilated filtering has been adopted to address this issue. But it suffers from gridding effect, and the resulting receptive field is only a sparse sampling of input image with checkerboard patterns. In this paper, we present a novel multi-level wavelet CNN (MWCNN) model for better tradeoff between receptive field size and computational efficiency. With the modified U-Net architecture, wavelet transform is introduced to reduce the size of feature maps in the contracting subnetwork. Furthermore, another convolutional layer is further used to decrease the channels of feature maps. In the expanding subnetwork, inverse wavelet transform is then deployed to reconstruct the high resolution feature maps. Our MWCNN can also be explained as the generalization of dilated filtering and subsampling, and can be applied to many image restoration tasks. The experimental results clearly show the effectiveness of MWCNN for image denoising, single image super-resolution, and JPEG image artifacts removal.
Due to the fast inference and good performance, discriminative learning methods have been widely studied in image denoising. However, these methods mostly learn a specific model for each noise level, and require multiple models for denoising images with different noise levels. They also lack flexibility to deal with spatially variant noise, limiting their applications in practical denoising. To address these issues, we present a fast and flexible denoising convolutional neural network, namely FFDNet, with a tunable noise level map as the input. The proposed FFDNet works on downsampled sub-images, achieving a good trade-off between inference speed and denoising performance. In contrast to the existing discriminative denoisers, FFDNet enjoys several desirable properties, including (i) the ability to handle a wide range of noise levels (i.e., [0, 75]) effectively with a single network, (ii) the ability to remove spatially variant noise by specifying a non-uniform noise level map, and (iii) faster speed than benchmark BM3D even on CPU without sacrificing denoising performance. Extensive experiments on synthetic and real noisy images are conducted to evaluate FFDNet in comparison with state-of-the-art denoisers. The results show that FFDNet is effective and efficient, making it highly attractive for practical denoising applications.
In this paper, bilateral teleoperation of multiple slaves coupled to a single master under scheduling communication is investigated. The sampled-data transmission between the master and the multiple slaves is fulfilled over a delayed communication network, and at each sampling instant, only one slave is allowed to transmit its current information to the master side according to some scheduling protocols. To achieve the master-slave synchronization, Round-Robin scheduling protocol and Try-Once-Discard scheduling protocol are employed, respectively. By designing a scheduling-communication-based controller, some sufficient stability criteria related to the controller gain matrices, sampling intervals, and communication delays are obtained for the closed-loop teleoperation system under Round-Robin and Try-Once-Discard scheduling protocols, respectively. Finally, simulation studies are given to validate the effectiveness of the proposed results.
Current strategies for designing tunable locally resonant metamaterials are based on tuning the stiffness of the resonator; however, this approach presents a major shortcoming as the effective mass density is constant at high frequency. Here, this paper reports a type of tunable locally elastic metamaterial-'called tunable fluid-solid composite'-inspired by the functions of heart and vessels in animals and humans. The proposed metamaterial consists of several liquid or gas inclusions in a solid matrix, controlled through a pair of embedded pumps. Both the band gap and effective mass density at high frequency can be tuned by controlling the liquid distribution in the unit cell, as demonstrated through a combination of theoretical analysis, numerical simulation, and experimental testing. Finally, we show that the tunable fluid-solid metamaterial can be utilized to manipulate wave propagation over a broad frequency range, providing new avenues for vibration isolation and wave guiding.
Given a large number of low-level heterogeneous categorical alerts from an anomaly detection system, how to characterize complex relationships between different alerts, filter out false positives, and deliver trustworthy rankings and suggestions to end users? This problem is motivated by and generalized from applications in enterprise security and attack scenario reconstruction. While existing techniques focus on either reconstructing abnormal scenarios or filtering out false positive alerts, it can be more advantageous to consider the two perspectives simultaneously in order to improve detection accuracy and better understand anomaly behaviors. In this paper, we propose CAR, a collaborative alerts ranking framework that exploits both temporal and content correlations from heterogeneous categorical alerts. CAR first builds a tree-based model to capture both short-term correlations and long-term dependencies in each alert sequence, which identifies abnormal action sequences. Then, an embedding-based model is employed to learn the content correlations between alerts via their heterogeneous categorical attributes. Finally, by incorporating both temporal and content dependencies into one optimization framework, CAR ranks both alerts and their corresponding alert patterns. Our experiments, using real-world enterprise monitoring data and real attacks launched by professional hackers, show that CAR can accurately identify true positive alerts and successfully reconstruct attack scenarios at the same time.