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Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for -- its applications on those scales being largely based on extrapolation and its validity sometimes questioned in the shadow of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of $N$-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel estimators beyond linear redshift distortions in two well-studied modified gravity models, chameleon $f(R)$ gravity and a braneworld model, and the potential of testing these deviations from GR using DESI. These estimators employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI., Comment: 69 pages, 36 figures, 6 tables; accepted for publication in JCAP. The modified gravity HOD galaxy catalogues used in this paper can be downloaded from http://icc.dur.ac.uk/data/, by searching for the title of this paper from the dataset table

Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann and $n$-exact categories in the sense of Jasso. In this article, we show that an $n$-exangulated category has the structure of an $(n+2)$-angulated category if and only if for any object $X$ in the category, the morphism $0\to X$ is a trivial deflation and the morphism $X\to 0$ is a trivial inflation., Comment: 17 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2006.02223, arXiv:2007.01716, arXiv:1909.13284

With the unprecedented developments in deep learning, automatic segmentation of main abdominal organs seems to be a solved problem as state-of-the-art (SOTA) methods have achieved comparable results with inter-rater variability on many benchmark datasets. However, most of the existing abdominal datasets only contain single-center, single-phase, single-vendor, or single-disease cases, and it is unclear whether the excellent performance can generalize on diverse datasets. This paper presents a large and diverse abdominal CT organ segmentation dataset, termed AbdomenCT-1K, with more than 1000 (1K) CT scans from 12 medical centers, including multi-phase, multi-vendor, and multi-disease cases. Furthermore, we conduct a large-scale study for liver, kidney, spleen, and pancreas segmentation and reveal the unsolved segmentation problems of the SOTA methods, such as the limited generalization ability on distinct medical centers, phases, and unseen diseases. To advance the unsolved problems, we further build four organ segmentation benchmarks for fully supervised, semi-supervised, weakly supervised, and continual learning, which are currently challenging and active research topics. Accordingly, we develop a simple and effective method for each benchmark, which can be used as out-of-the-box methods and strong baselines. We believe the AbdomenCT-1K dataset will promote future in-depth research towards clinical applicable abdominal organ segmentation methods. The datasets, codes, and trained models are publicly available at https://github.com/JunMa11/AbdomenCT-1K., Comment: 20 pages

We investigate the transverse modes of the gravitational and velocity fields in $\Lambda$CDM, based on a high-resolution simulation performed using the adaptive-mesh refinement general-relativistic $N$-body code GRAMSES. We study the generation of vorticity in the dark matter velocity field at low redshift, providing fits to the shape and evolution of its power spectrum over a range of scales. By analysing the gravitomagnetic vector potential, which is absent in Newtonian simulations, in dark matter haloes with masses ranging from $\sim10^{12.5}~h^{-1}{M}_{\odot}$ to $\sim10^{15}~h^{-1}{M}_{\odot}$, we find that its magnitude correlates with the halo mass, peaking in the inner regions. Nevertheless, on average, its ratio against the scalar gravitational potential remains fairly constant, below percent level, decreasing roughly linearly with redshift and showing a weak dependence on halo mass. Furthermore, we show that the gravitomagnetic acceleration in haloes peaks towards the core and reaches almost $10^{-10}$ $h$ cm/s$^2$ in the most massive halo of the simulation. However, regardless of the halo mass, the ratio between the magnitudes of the gravitomagnetic force and the standard gravitational force is typically at around the $10^{-5}$ level inside the haloes, again without significant radius dependence. This result confirms that the gravitomagnetic effects have a negligible impact on structure formation, even for the most massive structures, although its behaviour in low density regions remains to be explored. Likewise, the impact on observations remains to be understood in the future., Comment: Fixed Newtonian force results. Figs. 5, 9 and 10 updated. Matches accepted version

The unreliable service and the unstable operation of a high frequency bus line are shown as bus bunching and the uneven distribution of headways along the bus line. Although many control strategies, such as the static and dynamic holding strategies, have been proposed to solve the above problems, many of them take on some oversimplified assumptions about the real bus line operation. So it is hard for them to continuously adapt to the evolving complex system. In view of this dynamic setting, we present an adaptive holding method which combines the classic approximate dynamic programming (ADP) with the multi-stage look-ahead mechanism. The holding time, that is the only control means used in this study, will be determined by estimating its impact on the operation stability of the bus line system in the remained observation period. The multi-stage look-ahead mechanism introduced into the classic Q-learning algorithm of the ADP model makes the algorithm get through its earlier unstable phase more quickly and easily. During the implementation of the new holding approach, the past experiences of holding operations can be cumulated effectively into an artificial neural network used to approximate the unavailable Q-factor. The use of a detailed simulation system in the new approach makes it possible to take into accounts most of the possible causes of instability. The numerical experiments show that the new holding approach can stabilize the system by producing evenly distributed headway and removing bus bunching thoroughly. Comparing with the terminal station holding strategies, the new method brings a more reliable bus line with shorter waiting times for passengers.

We present the first numerical simulations of gravitational waves (GWs) passing through a potential well generated by a compact object in 3-D space, with a realistic source waveform derived from numerical relativity for the merger of two black holes. Unlike the previous work, our analyses focus on the time-domain, in which the propagation of GWs is a well-posed "initial-value" problem for the hyperbolic equations with rigorous rooting in mathematics and physics. Based on these simulations, we investigate for the first time in realistic 3-D space how the wave nature of GWs affects the speed and waveform of GWs in a potential well. We find that GWs travel faster than the prediction of the Shapiro time-delay in the geometric limit due to the effects of diffraction and wavefront geometry. As the wave speed of GWs is closely related to the locality and wavefront geometry of GWs, which are inherently difficult to be addressed in the frequency-domain, our analyses in the time-domain, therefore, provide the first robust analyses to date on this issue based on solid physics. Moreover, we also investigate, for the first time, the interference between the incident and the scattered waves (the "echoes" of the incident waves). We find that such interference makes the total lensed waveforms dramatically different from those of the original incident ones not only in the amplitude but also in the phase and pattern, especially for signals near the merger of the two back holes., Comment: 5 pages, 5 figures

Purpose: Accurate segmentation of lung and infection in COVID-19 CT scans plays an important role in the quantitative management of patients. Most of the existing studies are based on large and private annotated datasets that are impractical to obtain from a single institution, especially when radiologists are busy fighting the coronavirus disease. Furthermore, it is hard to compare current COVID-19 CT segmentation methods as they are developed on different datasets, trained in different settings, and evaluated with different metrics. Methods: To promote the development of data-efficient deep learning methods, in this paper, we built three benchmarks for lung and infection segmentation based on 70 annotated COVID-19 cases, which contain current active research areas, e.g., few-shot learning, domain generalization, and knowledge transfer. For a fair comparison among different segmentation methods, we also provide standard training, validation and testing splits, evaluation metrics and, the corresponding code. Results: Based on the state-of-the-art network, we provide more than 40 pre-trained baseline models, which not only serve as out-of-the-box segmentation tools but also save computational time for researchers who are interested in COVID-19 lung and infection segmentation. We achieve average Dice Similarity Coefficient (DSC) scores of 97.3\%, 97.7\%, and 67.3\% and average Normalized Surface Dice (NSD) scores of 90.6\%, 91.4\%, and 70.0\% for left lung, right lung, and infection, respectively. Conclusions: To the best of our knowledge, this work presents the first data-efficient learning benchmark for medical image segmentation and the largest number of pre-trained models up to now. All these resources are publicly available, and our work lays the foundation for promoting the development of deep learning methods for efficient COVID-19 CT segmentation with limited data., Comment: accepted for publication in Medical Physics

Cluster of viral pneumonia occurrences during a short period of time may be a harbinger of an outbreak or pandemic, like SARS, MERS, and recent COVID-19. Rapid and accurate detection of viral pneumonia using chest X-ray can be significantly useful in large-scale screening and epidemic prevention, particularly when other chest imaging modalities are less available. Viral pneumonia often have diverse causes and exhibit notably different visual appearances on X-ray images. The evolution of viruses and the emergence of novel mutated viruses further result in substantial dataset shift, which greatly limits the performance of classification approaches. In this paper, we formulate the task of differentiating viral pneumonia from non-viral pneumonia and healthy controls into an one-class classification-based anomaly detection problem, and thus propose the confidence-aware anomaly detection (CAAD) model, which consists of a shared feature extractor, an anomaly detection module, and a confidence prediction module. If the anomaly score produced by the anomaly detection module is large enough or the confidence score estimated by the confidence prediction module is small enough, we accept the input as an anomaly case (i.e., viral pneumonia). The major advantage of our approach over binary classification is that we avoid modeling individual viral pneumonia classes explicitly and treat all known viral pneumonia cases as anomalies to reinforce the one-class model. The proposed model outperforms binary classification models on the clinical X-VIRAL dataset that contains 5,977 viral pneumonia (no COVID-19) cases, 18,619 non-viral pneumonia cases, and 18,774 healthy controls., Comment: Accepted to IEEE Trans. Medical Imaging. 12 pages

We investigate the wave effects of gravitational waves (GWs) using numerical simulations with the finite element method (FEM) based on the publicly available code {\it deal.ii}. We robustly test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree very well with the analytical predictions. Based on our code, we study the scattering of GWs by compact objects. Using monochromatic waves as the input source, we find that if the wavelength of GWs is much larger than the Schwarzschild radius of the compact object, the amplitude of the total scattered GWs does not change appreciably due to the strong diffraction effect, for an observer far away from the scatterer. This finding is consistent with the results reported in the literature. However, we also find that, near the scatterer, not only the amplitude of the scattered waves is very large, comparable to that of the incident waves, but also the phase of the GWs changes significantly due to the interference between the scattered and incident waves. As the evolution of the phase of GWs plays a crucial role in the matched filtering technique in extracting GW signals from the noisy background, our findings suggest that wave effects should be taken into account in the data analysis in the future low-frequency GW experiments, if GWs are scattered by nearby compact objects in our local environment., Comment: 15 pages, 8 figures