10,135 research outputs found
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 -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 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 M 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
- …