Nonradial solutions for semilinear Schrödinger equations with sign-changing potential

In this paper, we investigate the existence of infinite nonradial solutions for the Schrödinger equations \begin{equation*} \begin{cases} -\triangle u+b(|x|)u=f(|x|, u), &\quad x\in {\mathbb{R}}^{N},\\ u\in H^{1}({\mathbb{R}}^{N}), \end{cases} \end{equation*} where $b$ is allowed to be sign-changing. Under some assumptions on $b\in C([0,\infty),\mathbb{R})$ and $f\in C([0,\infty)\times\mathbb{R}^{N},\mathbb{R})$, we obtain that the above system possesses infinitely many nonradial solutions. The method of proof relies on critical point theorem

Existence of Periodic Solutions for the Duffing Equation with Impulses

Peer reviewe

Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations

We study the existence of periodic solutions for third-order nonlinear differential equations. The method of proof relies on Schauder’s fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results

Long-Range Grouping Transformer for Multi-View 3D Reconstruction

Nowadays, transformer networks have demonstrated superior performance in many computer vision tasks. In a multi-view 3D reconstruction algorithm following this paradigm, self-attention processing has to deal with intricate image tokens including massive information when facing heavy amounts of view input. The curse of information content leads to the extreme difficulty of model learning. To alleviate this problem, recent methods compress the token number representing each view or discard the attention operations between the tokens from different views. Obviously, they give a negative impact on performance. Therefore, we propose long-range grouping attention (LGA) based on the divide-and-conquer principle. Tokens from all views are grouped for separate attention operations. The tokens in each group are sampled from all views and can provide macro representation for the resided view. The richness of feature learning is guaranteed by the diversity among different groups. An effective and efficient encoder can be established which connects inter-view features using LGA and extract intra-view features using the standard self-attention layer. Moreover, a novel progressive upsampling decoder is also designed for voxel generation with relatively high resolution. Hinging on the above, we construct a powerful transformer-based network, called LRGT. Experimental results on ShapeNet verify our method achieves SOTA accuracy in multi-view reconstruction. Code will be available at https://github.com/LiyingCV/Long-Range-Grouping-Transformer.Comment: Accepted to ICCV 202

Expressive Whole-Body Control for Humanoid Robots

Can we enable humanoid robots to generate rich, diverse, and expressive motions in the real world? We propose to learn a whole-body control policy on a human-sized robot to mimic human motions as realistic as possible. To train such a policy, we leverage the large-scale human motion capture data from the graphics community in a Reinforcement Learning framework. However, directly performing imitation learning with the motion capture dataset would not work on the real humanoid robot, given the large gap in degrees of freedom and physical capabilities. Our method Expressive Whole-Body Control (Exbody) tackles this problem by encouraging the upper humanoid body to imitate a reference motion, while relaxing the imitation constraint on its two legs and only requiring them to follow a given velocity robustly. With training in simulation and Sim2Real transfer, our policy can control a humanoid robot to walk in different styles, shake hands with humans, and even dance with a human in the real world. We conduct extensive studies and comparisons on diverse motions in both simulation and the real world to show the effectiveness of our approach.Comment: Website: https://expressive-humanoid.github.i

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

This paper is concerned about the existence of extreme solutions of multipoint boundary value problem for a class of second-order impulsive functional differential equations. We introduce a new concept of lower and upper solutions. Then, by using the method of upper and lower solutions introduced and monotone iterative technique, we obtain the existence results of extreme solutions

GARNet: Global-Aware Multi-View 3D Reconstruction Network and the Cost-Performance Tradeoff

Deep learning technology has made great progress in multi-view 3D reconstruction tasks. At present, most mainstream solutions establish the mapping between views and shape of an object by assembling the networks of 2D encoder and 3D decoder as the basic structure while they adopt different approaches to obtain aggregation of features from several views. Among them, the methods using attention-based fusion perform better and more stable than the others, however, they still have an obvious shortcoming -- the strong independence of each view during predicting the weights for merging leads to a lack of adaption of the global state. In this paper, we propose a global-aware attention-based fusion approach that builds the correlation between each branch and the global to provide a comprehensive foundation for weights inference. In order to enhance the ability of the network, we introduce a novel loss function to supervise the shape overall and propose a dynamic two-stage training strategy that can effectively adapt to all reconstructors with attention-based fusion. Experiments on ShapeNet verify that our method outperforms existing SOTA methods while the amount of parameters is far less than the same type of algorithm, Pix2Vox++. Furthermore, we propose a view-reduction method based on maximizing diversity and discuss the cost-performance tradeoff of our model to achieve a better performance when facing heavy input amount and limited computational cost

Unify, Align and Refine: Multi-Level Semantic Alignment for Radiology Report Generation

Automatic radiology report generation has attracted enormous research interest due to its practical value in reducing the workload of radiologists. However, simultaneously establishing global correspondences between the image (e.g., Chest X-ray) and its related report and local alignments between image patches and keywords remains challenging. To this end, we propose an Unify, Align and then Refine (UAR) approach to learn multi-level cross-modal alignments and introduce three novel modules: Latent Space Unifier (LSU), Cross-modal Representation Aligner (CRA) and Text-to-Image Refiner (TIR). Specifically, LSU unifies multimodal data into discrete tokens, making it flexible to learn common knowledge among modalities with a shared network. The modality-agnostic CRA learns discriminative features via a set of orthonormal basis and a dual-gate mechanism first and then globally aligns visual and textual representations under a triplet contrastive loss. TIR boosts token-level local alignment via calibrating text-to-image attention with a learnable mask. Additionally, we design a two-stage training procedure to make UAR gradually grasp cross-modal alignments at different levels, which imitates radiologists' workflow: writing sentence by sentence first and then checking word by word. Extensive experiments and analyses on IU-Xray and MIMIC-CXR benchmark datasets demonstrate the superiority of our UAR against varied state-of-the-art methods.Comment: 8 pages,6 figures,4 table