Ground state solutions for diffusion system with superlinear nonlinearity

In this paper, we study the following diffusion system \begin{equation*} \begin{cases} \partial_{t}u-\Delta_{x} u +b(t,x)\cdot \nabla_{x} u +V(x)u=g(t,x,v),\\ -\partial_{t}v-\Delta_{x} v -b(t,x)\cdot \nabla_{x} v +V(x)v=f(t,x,u) \end{cases} \end{equation*} where $z=(u,v)\colon\mathbb{R}\times\mathbb{R}^{N}\rightarrow\mathbb{R}^{2}$, $b\in C^{1}(\mathbb{R}\times\mathbb{R}^{N}, \mathbb{R}^{N})$ and $V(x)\in C(\mathbb{R}^{N},\mathbb{R})$. Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth

A Group Symmetric Stochastic Differential Equation Model for Molecule Multi-modal Pretraining

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks

Exploring crowd persistent dynamism from pedestrian crossing perspective: An empirical study

Crowd studies have gained increasing relevance due to the recurring incidents of crowd crush accidents. In addressing the issue of the crowd's persistent dynamism, this paper explored the macroscopic and microscopic features of pedestrians crossing in static and dynamic contexts, employing a series of systematic experiments. Firstly, empirical evidence has confirmed the existence of crowd's persistent dynamism. Subsequently, the research delves into two aspects, qualitative and quantitative, to address the following questions:(1) Cross pedestrians tend to avoid high-density areas when crossing static crowds and particularly evade pedestrians in front to avoid deceleration, thus inducing the formation of cross-channels, a self-organization phenomenon.(2) In dynamic crowds, when pedestrian suffers spatial constrained, two patterns emerge: decelerate or detour. Research results indicate the differences in pedestrian crossing behaviors between static and dynamic crowds, such as the formation of crossing channels, backward detours, and spiral turning. However, the strategy of pedestrian crossing remains consistent: utilizing detours to overcome spatial constraints. Finally, the empirical results of this study address the final question: pedestrians detouring causes crowds' persistent collective dynamism. These findings contribute to an enhanced understanding of pedestrian dynamics in extreme conditions and provide empirical support for research on individual movement patterns and crowd behavior prediction.Comment: 31pages, 17figure

Mixed Pattern Matching-Based Traffic Abnormal Behavior Recognition

A motion trajectory is an intuitive representation form in time-space domain for a micromotion behavior of moving target. Trajectory analysis is an important approach to recognize abnormal behaviors of moving targets. Against the complexity of vehicle trajectories, this paper first proposed a trajectory pattern learning method based on dynamic time warping (DTW) and spectral clustering. It introduced the DTW distance to measure the distances between vehicle trajectories and determined the number of clusters automatically by a spectral clustering algorithm based on the distance matrix. Then, it clusters sample data points into different clusters. After the spatial patterns and direction patterns learned from the clusters, a recognition method for detecting vehicle abnormal behaviors based on mixed pattern matching was proposed. The experimental results show that the proposed technical scheme can recognize main types of traffic abnormal behaviors effectively and has good robustness. The real-world application verified its feasibility and the validity

Magnetization-tuned topological quantum phase transition in MnBi2Te4 devices

Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion insulator state, high-Chern-number and high-temperature Chern insulator states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Specifically, as the magnetic field is tilted away from the out-of-plane direction by around 40-60 degrees, the Hall resistance deviates from the quantization value and a colossal, anisotropic magnetoresistance is detected. The theoretical analyses based on modified Landauer-Buttiker formalism show that the field-tilt-driven switching from ferromagnetic state to canted antiferromagnetic state induces a topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Our work provides an efficient means for modulating topological quantum states and topological quantum phase transitions