A fourth-order unfitted characteristic finite element method for solving the advection-diffusion equation on time-varying domains

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for interface tracking, the fourth-order backward differentiation formula for temporal integration, and an unfitted finite element method for spatial discretization. Our convergence analysis includes errors of discretely representing the moving boundary, tracing boundary markers, and the spatial discretization and the temporal integration of the governing equation. Numerical experiments are performed on a rotating domain and a severely deformed domain to verify our theoretical results and to demonstrate the optimal convergence of the proposed method

MDFL: Multi-domain Diffusion-driven Feature Learning

High-dimensional images, known for their rich semantic information, are widely applied in remote sensing and other fields. The spatial information in these images reflects the object's texture features, while the spectral information reveals the potential spectral representations across different bands. Currently, the understanding of high-dimensional images remains limited to a single-domain perspective with performance degradation. Motivated by the masking texture effect observed in the human visual system, we present a multi-domain diffusion-driven feature learning network (MDFL) , a scheme to redefine the effective information domain that the model really focuses on. This method employs diffusion-based posterior sampling to explicitly consider joint information interactions between the high-dimensional manifold structures in the spectral, spatial, and frequency domains, thereby eliminating the influence of masking texture effects in visual models. Additionally, we introduce a feature reuse mechanism to gather deep and raw features of high-dimensional data. We demonstrate that MDFL significantly improves the feature extraction performance of high-dimensional data, thereby providing a powerful aid for revealing the intrinsic patterns and structures of such data. The experimental results on three multi-modal remote sensing datasets show that MDFL reaches an average overall accuracy of 98.25%, outperforming various state-of-the-art baseline schemes. The code will be released, contributing to the computer vision community

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example

Trust in China: A Cross-Regional Analysis

Using the cross-regional data, this paper shows that trust has a strong effect on uneven development of economy in China. As is discovered in many studies, it is found that trust affects the growth of economy, size distribution of enterprise, and FDI inflow and so on. We also find that cross-regional differences of trust in China are reflections of the regional diversities of education, marketization of economies, urbanization, population density and transportation facilities. Although not statistically significant, “too many officials” may damage social trust. The paper demonstrates that trust cannot simply be taken as a cultural heritage. The paper also argues that sustainability of further economic development of China much depends on how fast China can build trust-facilitating institution, and that the most fundamental institution for trust is the property right.http://deepblue.lib.umich.edu/bitstream/2027.42/39972/3/wp586.pd

Guided Hybrid Quantization for Object detection in Multimodal Remote Sensing Imagery via One-to-one Self-teaching

Considering the computation complexity, we propose a Guided Hybrid Quantization with One-to-one Self-Teaching (GHOST}) framework. More concretely, we first design a structure called guided quantization self-distillation (GQSD), which is an innovative idea for realizing lightweight through the synergy of quantization and distillation. The training process of the quantization model is guided by its full-precision model, which is time-saving and cost-saving without preparing a huge pre-trained model in advance. Second, we put forward a hybrid quantization (HQ) module to obtain the optimal bit width automatically under a constrained condition where a threshold for distribution distance between the center and samples is applied in the weight value search space. Third, in order to improve information transformation, we propose a one-to-one self-teaching (OST) module to give the student network a ability of self-judgment. A switch control machine (SCM) builds a bridge between the student network and teacher network in the same location to help the teacher to reduce wrong guidance and impart vital knowledge to the student. This distillation method allows a model to learn from itself and gain substantial improvement without any additional supervision. Extensive experiments on a multimodal dataset (VEDAI) and single-modality datasets (DOTA, NWPU, and DIOR) show that object detection based on GHOST outperforms the existing detectors. The tiny parameters (<9.7 MB) and Bit-Operations (BOPs) (<2158 G) compared with any remote sensing-based, lightweight or distillation-based algorithms demonstrate the superiority in the lightweight design domain. Our code and model will be released at https://github.com/icey-zhang/GHOST.Comment: This article has been delivered to TRGS and is under revie