Search

For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity., Comment: submitted to some journal

Neural implicit representations are known to be more compact for depicting 3D shapes than traditional discrete representations. However, the neural representations tend to round sharp corners or edges and struggle to represent surfaces with open boundaries. Moreover, they are slow to train. We present a unified neural implicit representation, called Patch-Grid, that fits to complex shapes efficiently, preserves sharp features, and effectively models surfaces with open boundaries and thin geometric features. Our superior efficiency comes from embedding each surface patch into a local latent volume and decoding it using a shared MLP decoder, which is pretrained on various local surface geometries. With this pretrained decoder fixed, fitting novel shapes and local shape updates can be done efficiently. The faithful preservation of sharp features is enabled by adopting a novel merge grid to perform local constructive solid geometry (CSG) combinations of surface patches in the cells of an adaptive Octree, yielding better robustness than using a global CSG construction as proposed in the literature. Experiments show that our Patch-Grid method faithfully captures shapes with complex sharp features, open boundaries and thin structures, and outperforms existing learning-based methods in both efficiency and quality for surface fitting and local shape updates.

Magnetic racetrack memory has significantly evolved and developed since its first experimental verification and is considered as one of the most promising candidates for future high-density on-chip solid state memory. However, the lack of a fast and precise magnetic domain wall (DW) shifting mechanism and the required extremely high DW motion (DWM) driving current both make the racetrack difficult to commercialize. Here, we propose a method for coherent DWM that is free from above issues, which is driven by chirality switching (CS) and an ultralow spin-orbit-torque (SOT) current. The CS, as the driving force of DWM, is achieved by the sign change of DM interaction which is further induced by a ferroelectric switching voltage. The SOT is used to break the symmetry when the magnetic moment is rotated to the Bloch direction. We numerically investigate the underlying principle and the effect of key parameters on the DWM through micromagnetic simulations. Under the CS mechanism, a fast (102 m/s), ultralow energy (5 attojoule), and precisely discretized DWM can be achieved. Considering that skyrmions with topological protection and smaller size are also promising for future racetrack, we similarly evaluate the feasibility of applying such a CS mechanism to a skyrmion. However, we find that the CS only causes it to "breathe" instead of moving. Our results demonstrate that the CS strategy is suitable for future DW racetrack memory with ultralow power consumption and discretized DWM.

In this paper, we use Nash-Moser iteration method to study the local and global behaviours of positive solutions to the nonlinear elliptic equation $\Delta_pv +av^{q}=0$ defined on a complete Riemannian manifolds $(M,g)$ where $p>1$, $a$ and $q$ are constants. Under some assumptions on $a$, $p$ and $q$, we derive gradient estimates and Liouville type theorems for such positive solutions., Comment: some corrections

The artificial intelligence (AI) system has achieved expert-level performance in electrocardiogram (ECG) signal analysis. However, in underdeveloped countries or regions where the healthcare information system is imperfect, only paper ECGs can be provided. Analysis of real-world ECG images (photos or scans of paper ECGs) remains challenging due to complex environments or interference. In this study, we present an AI system developed to detect and screen cardiac abnormalities (CAs) from real-world ECG images. The system was evaluated on a large dataset of 52,357 patients from multiple regions and populations across the world. On the detection task, the AI system obtained area under the receiver operating curve (AUC) of 0.996 (hold-out test), 0.994 (external test 1), 0.984 (external test 2), and 0.979 (external test 3), respectively. Meanwhile, the detection results of AI system showed a strong correlation with the diagnosis of cardiologists (cardiologist 1 (R=0.794, p<1e-3), cardiologist 2 (R=0.812, p<1e-3)). On the screening task, the AI system achieved AUCs of 0.894 (hold-out test) and 0.850 (external test). The screening performance of the AI system was better than that of the cardiologists (AI system (0.846) vs. cardiologist 1 (0.520) vs. cardiologist 2 (0.480)). Our study demonstrates the feasibility of an accurate, objective, easy-to-use, fast, and low-cost AI system for CA detection and screening. The system has the potential to be used by healthcare professionals, caregivers, and general users to assess CAs based on real-world ECG images., Comment: 47 pages, 29 figures

The phenomenon originating from spin-orbit coupling (SOC) provides energy-efficient strategies for spin manipulation and device applications. The broken inversion symmetry interface and resulting electric field induce a Rashba-type spin-orbit field (SOF), which has been demonstrated to generate spin-orbit torque for data storage applications. In this study, we found that spin flipping can be achieved by the valley-Zeeman SOF in monolayer WSe2 at room temperature, which manifests as a negative magnetoresistance in the vertical spin valve. Quantum transmission calculations based on an effective model near the K valley of WSe2 confirm the precessional spin transport of carriers under the giant SOF, which is estimated to be 650 T. In particular, the valley-Zeeman SOF-induced spin dynamics was demonstrated to be tunable with the layer number and stacking phase of WSe2 as well as the gate voltage, which provides a novel strategy for spin manipulation and can benefit the development of ultralow-power spintronic devices., Comment: 7 pages,3 figures

With the development of deep learning-based methods, automated classification of electrocardiograms (ECGs) has recently gained much attention. Although the effectiveness of deep neural networks has been encouraging, the lack of information given by the outputs restricts clinicians' reexamination. If the uncertainty estimation comes along with the classification results, cardiologists can pay more attention to "uncertain" cases. Our study aims to classify ECGs with rejection based on data uncertainty and model uncertainty. We perform experiments on a real-world 12-lead ECG dataset. First, we estimate uncertainties using the Monte Carlo dropout for each classification prediction, based on our Bayesian neural network. Then, we accept predictions with uncertainty under a given threshold and provide "uncertain" cases for clinicians. Furthermore, we perform a simulation experiment using varying thresholds. Finally, with the help of a clinician, we conduct case studies to explain the results of large uncertainties and incorrect predictions with small uncertainties. The results show that correct predictions are more likely to have smaller uncertainties, and the performance on accepted predictions improves as the accepting ratio decreases (i.e. more rejections). Case studies also help explain why rejection can improve the performance. Our study helps neural networks produce more accurate results and provide information on uncertainties to better assist clinicians in the diagnosis process. It can also enable deep-learning-based ECG interpretation in clinical implementation.

Well-annotated medical images are costly and sometimes even impossible to acquire, hindering landmark detection accuracy to some extent. Semi-supervised learning alleviates the reliance on large-scale annotated data by exploiting the unlabeled data to understand the population structure of anatomical landmarks. The global shape constraint is the inherent property of anatomical landmarks that provides valuable guidance for more consistent pseudo labelling of the unlabeled data, which is ignored in the previously semi-supervised methods. In this paper, we propose a model-agnostic shape-regulated self-training framework for semi-supervised landmark detection by fully considering the global shape constraint. Specifically, to ensure pseudo labels are reliable and consistent, a PCA-based shape model adjusts pseudo labels and eliminate abnormal ones. A novel Region Attention loss to make the network automatically focus on the structure consistent regions around pseudo labels. Extensive experiments show that our approach outperforms other semi-supervised methods and achieves notable improvement on three medical image datasets. Moreover, our framework is flexible and can be used as a plug-and-play module integrated into most supervised methods to improve performance further., Comment: Accepted to Neurocomputing

In this short note, we use a unified method to consider the gradient estimates of the positive solution to the following nonlinear elliptic equation $\Delta u + au^{p+1}=0$ defined on a complete noncompact Riemannian manifold $(M, g)$ where $a > 0$ and $ p <\frac{4}{n}$ or $a < 0$ and $p >0$ are two constants. For the case $a>0$, this improves considerably the previous known results except for the cases $\dim(M)=4$ and supplements the results for the case $\dim(M)\leq 2$. For the case $a<0$ and $p>0$, we also improve considerably the previous related results. When the Ricci curvature of $(M,g)$ is nonnegative, we also obtain a Liouville-type theorem for the above equation.

In this paper, we consider the gradient estimates of the positive solutions to the following equation defined on a complete Riemannian manifold $(M, g)$ $$\Delta u + au(\log u)^{p}+bu=0,$$ where $a, b\in \mathbb{R}$ and $p$ is a rational number with $p=\frac{k_1}{2k_2+1}\geq2$ where $k_1$ and $k_2$ are positive integer numbers. we obtain the gradient bound of a positive solution to the equation which does not depend on the bounds of the solution and the Laplacian of the distance function on $(M, g)$. Our results can be viewed as a natural extension of Yau's estimates on positive harmonic function., Comment: arXiv admin note: text overlap with arXiv:2009.14566

In the first part of this paper, we prove the extensibility of an arbitrary boundary metric to a positive scalar curvature (PSC) metric inside for a compact manifold with boundary, which completely solves an open problem due to Gromov (see Question \ref{extension1}). Then we introduce a fill-in invariant (see Definition \ref{fillininvariant}) and discuss its relationship with the positive mass theorems for asymptotically flat (AF) and asymptotically hyperbolic (AH) manifolds. Moreover, we prove that the positive mass theorem for AH manifolds implies that for AF manifolds. In the end, we give some estimates for the fill-in invariant, which provide some partially affirmative answers to Gromov's conjectures formulated in \cite{Gro19} (see Conjecture \ref{conj0} and Conjecture \ref{conj1} below), Comment: 39 pages, all comments are welcome!

In the first part of this paper, we consider the problem of fill-in of nonnegative scalar curvature (NNSC) metrics for a triple of Bartnik data $(\Sigma,\gamma,H)$. We prove that given a metric $\gamma$ on $\mathbf{S}^{n-1}$ ($3\leq n\leq 7$), $(\mathbf{S}^{n-1},\gamma,H)$ admits no fill-in of NNSC metrics provided the prescribed mean curvature $H$ is large enough (Theorem \ref{Thm: no fillin nonnegative scalar 2}). Moreover, we prove that if $\gamma$ is a positive scalar curvature (PSC) metric isotopic to the standard metric on $\mathbf{S}^{n-1}$, then the much weaker condition that the total mean curvature $\int_{\mathbf S^{n-1}}H\,\mathrm d\mu_\gamma$ is large enough rules out NNSC fill-ins, giving an partially affirmative answer to a conjecture by Gromov (see P.\,23 in \cite{Gromov4}). In the second part of this paper, we investigate the $\theta$-invariant of Bartnik data and obtain some sufficient conditions for the existence of PSC fill-ins., Comment: 34 pages, all comments are welcome

Changing the interlayer exchange coupling between magnetic layers in-situ is a key issue of spintronics, as it allows for the optimization of properties that are desirable for applications, including magnetic sensing and memory. In this paper, we utilize the phase change material VO2 as a spacer layer to regulate the interlayer exchange coupling between ferromagnetic layers with perpendicular magnetic anisotropy. The successful growth of ultra-thin (several nanometres) VO2 films is realized by sputtering at room temperature, which further enables the fabrication of [Pt/Co]2/VO2/[Co/Pt]2 multilayers with distinct interfaces. Such a magnetic multilayer exhibits an evolution from antiferromagnetic coupling to ferromagnetic coupling as the VO2 undergoes a phase change. The underlying mechanism originates from the change in the electronic structure of the spacer layer from an insulating to a metallic state. As a demonstration of phase change spintronics, this work may reveal the great potential of material innovations for next-generation spintronics.

In this paper, we propose a general framework for image classification using the attention mechanism and global context, which could incorporate with various network architectures to improve their performance. To investigate the capability of the global context, we compare four mathematical models and observe the global context encoded in the category disentangled conditional generative model could give more guidance as "know what is task irrelevant will also know what is relevant". Based on this observation, we define a novel Category Disentangled Global Context (CDGC) and devise a deep network to obtain it. By attending CDGC, the baseline networks could identify the objects of interest more accurately, thus improving the performance. We apply the framework to many different network architectures and compare with the state-of-the-art on four publicly available datasets. Extensive results validate the effectiveness and superiority of our approach. Code will be made public upon paper acceptance., Comment: I have not gotten legal permission to post it on arXiv from the corresponding authors

We report the phase-transition controlled magnetic anisotropy modulation in the (Co/Pt)2/VO2 heterostructure, where VO2 is introduced into the system to applied an interfacial strain by its metal-insulator transition. A large reversible modulation of the perpendicular magnetic anisotropy (PMA) reaching 38 kJ/m3 is observed during this process. The calculated energy density variation of interfacial anisotropy reaches 100 mJ/m2, which shows significant advantage over traditional modulation strategies. Further experimental results including magnetization change versus temperature, strain buffered modulation and pre-strained sample comparison prove that the interfacial coupling between VO2 and PMA layers plays a crucial role in this modulation. This work, demonstrating the great potential of phase-transition material in efficient magnetic anisotropy modulation, would benefit the exploration for low-power consumption devices.

Optical methods for magnetism manipulation have been considered as a promising strategy for ultralow-power and ultrahigh-speed spin switches, which becomes a hot spot in the field of spintronics. However, a widely applicable and efficient method to combine optical operation with magnetic modulation is still highly desired. Here, the strongly correlated electron material VO2 is introduced to realize phase-transition based optical control of the magnetism in NiFe. The NiFe/VO2 bilayer heterostructure features appreciable modulations in electrical conductivity (55%), coercivity (60%), and magnetic anisotropy (33.5%). Further analyses indicate that interfacial strain coupling plays a crucial role in this modulation. Utilizing this optically controlled magnetism modulation feature, programmable Boolean logic gates (AND, OR, NAND, NOR, XOR, NXOR and NOT) for high-speed and low-power data processing are demonstrated based on this engineered heterostructure. As a demonstration of phase-transition spintronics, this work may pave the way for next-generation electronics in the post-Moore era.

In this paper, we consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.

In this paper, we firstly extend Theorem 5.1.1 in \cite {Helein} due to H\'elein to a rescaled branched conformal immersed sequence(c.f. Theorem 1.5). By virtue of this local convergence theorem, we study the blowup behavior of a sequence of branched conformal immersions of closed Riemannian surface in $\mathbb{R}^{n}$ with uniformly bounded areas and Willmore energies. Furthermore, we prove that the integral identity of Gauss curvature is true., Comment: some typos corrected; accepted for publication in SCIENCE CHINA Mathematics