User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.Comment: 56 pages, 2 figure

Morphological Dependence of Star Formation Properties for the Galaxies in the Merging Galaxy Cluster A2255

The merging cluster of galaxies A2255 is covered by the Sloan Digital Sky Survey (SDSS) survey. In this paper we perform a morphological classification on the basis of the SDSS imaging and spectral data, and investigate the morphological dependence of the star formation rates (SFRs) for these member galaxies. As we expect, a tight correlation between the normalized SFR by stellar mass (SFR/M$_*$) and the H$\alpha$ equivalent width is found for the late-type galaxies in A2255. The correlation of SFR/M$_*$ with the continuum break strength at 4000 \AA is also confirmed. The SFR/M$_*$ - M$_*$ correlation is found for both the early- and late-type galaxies, indicating that the star formation activity tends to be suppressed when the assembled stellar mass M$_*$) increases, and this correlation is tighter and steeper for the late-type cluster galaxies. Compared with the mass range of field spiral galaxies, only two massive late-type galaxies with M$_*>10^{11}$ M$_{\odot}$ are survived in A2255, suggesting that the gas disks of massive spiral galaxies could have been tidally stripped during cluster formation. Additionally, the SFR variation with the projected radial distance are found to be heavily dependent upon galaxy morphology: the early-type galaxies have a very weak inner decrease in SFR/M$_*$, while the inner late-type galaxies tend to have higher SFR/M$_*$ values than the outer late-types. This may suggest that the galaxy-scale turbulence stimulated by the merging of subclusters might have played different roles on early- and late-type galaxies, which leads to a suppression of the star formation activity for E/S0 galaxies and a SFR enhancement for spiral and irregular galaxies.Comment: 21 pages, including 7 EPS figures and 1 tables, uses aastex.cls, Accepted by the A

Silicon nitride metalenses for unpolarized high-NA visible imaging

As one of nanoscale planar structures, metasurface has shown excellent superiorities on manipulating light intensity, phase and/or polarization with specially designed nanoposts pattern. It allows to miniature a bulky optical lens into the chip-size metalens with wavelength-order thickness, playing an unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and telephoto). However, a CMOS-compatible metalens has yet to be achieved in the visible region due to the limitation on material properties such as transmission and compatibility. Here, we experimentally demonstrate a divergent metalens based on silicon nitride platform with large numerical aperture (NA~0.98) and high transmission (~0.8) for unpolarized visible light, fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual focus spots are achieved within the visible region. Such metalens enables to shrink objects into a micro-scale size field of view as small as a single-mode fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also realized including over half billion nanoposts, showing a potential application of wide viewing-angle functionality. Thanks to the high-transmission and CMOS-compatibility of silicon nitride, our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, smart phones, aerial cameras, beam shaping, and other integrated on-chip devices.Comment: 16 pages, 7 figure

Zoom-VQA: Patches, Frames and Clips Integration for Video Quality Assessment

Video quality assessment (VQA) aims to simulate the human perception of video quality, which is influenced by factors ranging from low-level color and texture details to high-level semantic content. To effectively model these complicated quality-related factors, in this paper, we decompose video into three levels (\ie, patch level, frame level, and clip level), and propose a novel Zoom-VQA architecture to perceive spatio-temporal features at different levels. It integrates three components: patch attention module, frame pyramid alignment, and clip ensemble strategy, respectively for capturing region-of-interest in the spatial dimension, multi-level information at different feature levels, and distortions distributed over the temporal dimension. Owing to the comprehensive design, Zoom-VQA obtains state-of-the-art results on four VQA benchmarks and achieves 2nd place in the NTIRE 2023 VQA challenge. Notably, Zoom-VQA has outperformed the previous best results on two subsets of LSVQ, achieving 0.8860 (+1.0%) and 0.7985 (+1.9%) of SRCC on the respective subsets. Adequate ablation studies further verify the effectiveness of each component. Codes and models are released in https://github.com/k-zha14/Zoom-VQA.Comment: Accepted by CVPR 2023 Worksho

Dark Matter Spike surrounding Supermassive Black Holes Binary and the nanohertz Stochastic Gravitational Wave Background

Recently, the NANOGrav, PPTA, EPTA and CPTA collaborations reported compelling evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB). The amplitude and spectrum of this inferred gravitational-wave background align closely with the astrophysical predictions for a signal originating from the population of supermassive black-hole binaries. In light of these findings, we explore the possibility to detect dark matter spikes surrounding massive black holes, which could potentially impact the gravitational-wave waveform and modulate the SGWB. We demonstrate that the SMBH binary evolution induced by the combined effects of GW radiation and the dynamical friction of the dark matter spike exhibits detectable manifestations within the nHz frequency range of the SGWB.Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:1408.3534 by other author