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The youngest Galactic supernova remnant G1.9+0.3 shows a discrete feature between its radio and X-ray morphologies. The observed radio morphology features a single maximum in the north, while the X-ray observation shows two opposite 'ears' on the east and west sides. Using 3D magneto hydrodynamical simulations, we investigate the formation of the discrete feature of the remnant. We have tested different parameters for better simulation and reproduced similar discrete features under an environment with density gradient and an environment with clump, which provides a possible explanation of the observation., Comment: 7 pages, 3 figures, accepted for publication in ApJ

The study on the dynamic evolution of young supernova remnants (SNRs) is an important way to understand the density structure of the progenitor's circumstellar medium. We have reported the acceleration or deceleration, proper motion and brightness changes of 260 compact radio features in the second youngest known SNR Cas A at 5\,GHz based on the VLA data of five epochs from 1987 to 2004. The radio expansion center locates at $\alpha(1950)=23^{\rm h}21^{\rm m}9^{\rm s}_{\cdot}7 \pm 0^{\rm s}_{\cdot}29, \delta(1950)=+58^{\circ}32^{\prime}25^{\prime\prime}_{\cdot}2 \pm 2^{\prime\prime}_{\cdot}2$. Three-quarters of the compact knots are decelerating, this suggests that there are significant density fluctuations in the stellar winds of the remnant's progenitor. We have verified that the acceleration or deceleration of compact knots are not related with the distribution of brightness. The brightening, fading, disappearing or new appearing of compact radio features in Cas A suggests that the magnetic field in the remnant is changing rapidly., Comment: 20 pages,9 figures, ApJ accepted

We find several missing one-loop-order contributions in previous considerations about secondary gravitational waves induced at nonlinear order in cosmological perturbations. We consider a consistent perturbative expansion to third-order in cosmological perturbations, including higher-order interactions and iterative solutions ignored in the previous literature. Tensor fluctuations induced by the source with two scalar and one tensor perturbations are correlated with the first-order tensor fluctuation and thus give a one-loop-order correction to the tensor power spectrum. The missing loop correction is \textit{scale-invariant} and \textit{negative} in the superhorion region, which secondarily reduces the initial primordial tensor power spectrum prior to the horizon re-entry. Such an IR behavior is very different from the auto-spectrum of second-order induced tensor modes discussed in the previous literature and can be important for the actual gravitational wave measurements. For a sharp peak of scalar fluctuations with $A_\zeta=10^{-2}$ at $k_*=10^{5}h/{\rm Mpc}$ motivated by the LIGO/Virgo events, we show that the tensor power spectrum at the cosmic microwave background scale reduces by at most 35%. Hence, the polarization B-mode might not be seen because of the reduction of the original tensor spectrum due to the secondary effect of primordial black hole formation., Comment: 13 pages, 6 figures

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization.The code is available at \url{https://github.com/zhuhui100/FASUNet}., Comment: 18 pages

Automated social behaviour analysis of mice has become an increasingly popular research area in behavioural neuroscience. Recently, pose information (i.e., locations of keypoints or skeleton) has been used to interpret social behaviours of mice. Nevertheless, effective encoding and decoding of social interaction information underlying the keypoints of mice has been rarely investigated in the existing methods. In particular, it is challenging to model complex social interactions between mice due to highly deformable body shapes and ambiguous movement patterns. To deal with the interaction modelling problem, we here propose a Cross-Skeleton Interaction Graph Aggregation Network (CS-IGANet) to learn abundant dynamics of freely interacting mice, where a Cross-Skeleton Node-level Interaction module (CS-NLI) is used to model multi-level interactions (i.e., intra-, inter- and cross-skeleton interactions). Furthermore, we design a novel Interaction-Aware Transformer (IAT) to dynamically learn the graph-level representation of social behaviours and update the node-level representation, guided by our proposed interaction-aware self-attention mechanism. Finally, to enhance the representation ability of our model, an auxiliary self-supervised learning task is proposed for measuring the similarity between cross-skeleton nodes. Experimental results on the standard CRMI13-Skeleton and our PDMB-Skeleton datasets show that our proposed model outperforms several other state-of-the-art approaches., Comment: Accepted to IEEE Transactions on Image Processing