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We consider the following anisotropic sinh-Poisson tpye equation with a Hardy or H\'{e}non term: $$-\mathrm{div} (a(x)\nabla u)+ a(x)u=\varepsilon^2a(x)|x-q|^{2\alpha}(e^u-e^{-u}) \quad\mathrm{in}\quad \Omega,$$ $$\frac{\partial u}{\partial n}=0,\quad \mathrm{on}\quad \partial\Omega,$$ where $\varepsilon>0$, $q\in \bar\Omega\subset \mathbb{R}^2$, $\alpha \in(-1,\infty)- \mathbb{N}$, $\Omega\subset \mathbb{R}^2$ is a smooth bounded domain, $n$ is the unit outward normal vector of $\partial \Omega$ and $a(x)$ is a smooth positive function defined on $\bar\Omega$. From finite dimensional reduction method, we proved that this problem has a sequence of sign-changing solutions with arbitrarily many interior spikes accumulating to $q$, provided $q\in \Omega$ is a local maximizer of $a(x)$. However, if $q\in \partial \Omega$ is a strict local maximum point of $a(x)$ and satisfies $\langle \nabla a(q),n \rangle=0$, we proved that this problem has a family of sign-changing solutions with arbitrarily many mixed interior and boundary spikes accumulating to $q$. Under the same condition, we could also construct a sequence of blow-up solutions for the following problem $$ -\mathrm{div} (a(x)\nabla u)+ a(x)u=\varepsilon^2a(x)|x-q|^{2\alpha}e^u\quad \mathrm{in} \quad\Omega,$$ $$\frac{\partial u}{\partial n}=0, \quad \mathrm{on}\quad \partial\Omega.$$, Comment: 54 pages

In this paper, a high noise immune time-domain inversion cascade network (TICaN) is proposed to reconstruct scatterers from the measured electromagnetic fields. The TICaN is comprised of a denoising block aiming at improving the signal-to-noise ratio, and an inversion block to reconstruct the electromagnetic properties from the raw time-domain measurements. The scatterers investigated in this study include complicated geometry shapes and high contrast, which cover the stratum layer, lossy medium and hyperfine structure, etc. After being well trained, the performance of the TICaN is evaluated from the perspective of accuracy, noise-immunity, computational acceleration, and generalizability. It can be proven that the proposed framework can realize high-precision inversion under high-intensity noise environments. Compared with traditional reconstruction methods, TICaN avoids the tedious iterative calculation by utilizing the parallel computing ability of GPU and thus significantly reduce the computing time. Besides, the proposed TICaN has certain generalization ability in reconstructing the unknown scatterers such as the famous Austria rings. Herein, it is confident that the proposed TICaN will serve as a new path for real-time quantitative microwave imaging for various practical scenarios., Comment: 9 pages, 11 figures

We present our progress on the Chroma interfaces of the twisted-mass, HISQ (highly improved staggered quark) and overlap fermion inverters using QUDA.

Increasing attention on microwave ultra-broadband metamaterial absorbers has been paid due to their promising applications. While most microwave ultra-broadband metamaterial absorbers developed so far are based on metallic resonant structures, dispersive dielectric water-based metamaterial opens a simpler and more versatile route for the construction of polarization- and angle- insensitive ultra-broadband absorption. Here, we review the recent progresses of water-based metamaterial absorber by providing an illustration of the mechanisms to realize ultra-broadband, tunable and multi-functional absorption. We also address the further development direction and some potential novel applications., Comment: 28 pages, 11 figures

Federated learning is a novel framework that enables resource-constrained edge devices to jointly learn a model, which solves the problem of data protection and data islands. However, standard federated learning is vulnerable to Byzantine attacks, which will cause the global model to be manipulated by the attacker or fail to converge. On non-iid data, the current methods are not effective in defensing against Byzantine attacks. In this paper, we propose a Byzantine-robust framework for federated learning via credibility assessment on non-iid data (BRCA). Credibility assessment is designed to detect Byzantine attacks by combing adaptive anomaly detection model and data verification. Specially, an adaptive mechanism is incorporated into the anomaly detection model for the training and prediction of the model. Simultaneously, a unified update algorithm is given to guarantee that the global model has a consistent direction. On non-iid data, our experiments demonstrate that the BRCA is more robust to Byzantine attacks compared with conventional methods