Lightweight remote sensing image super-resolution (RSISR) methods aim to reconstruct remote sensing images (RSIs) while reducing computational complexity. Previous lightweight model development has primarily focused on the design of convolutional neural networks (CNNs). While CNNs excel at capturing local features, they are limited in establishing long-range dependencies. Mamba, as a model for long-range modeling, has linear computational complexity, making it a viable option for lightweight models. Based on these considerations, this paper proposes an efficient mamba-attention network (EMAN) that can efficiently capture the intricate details and broader semantic information in RSIs. Specifically, we designed a multi-scale detail extraction unit (MDEU) and a multi-dimensional mamba-attention (MDMA). In MDEU, we introduced a multi-scale mechanism and local variance to focus on structural information in RSIs. In MDMA, we integrated spatial expansion and an atrous-based selective scan mechanism to design an efficient scanning method. This method ensures the lightweight nature of the model while establishing global correlations. Additionally, MDMA establishes inter-channel correlations to enhance information exchange. We conducted a comprehensive evaluation of the proposed method on two remote sensing datasets and five benchmark super-resolution (SR) datasets. Extensive experiments demonstrate that our method can achieve superior performance while maintaining a model complexity similar to other lightweight models.

In the field of remote sensing image super-resolution (RSISR), most methods based on convolutional neural networks (CNNs) tend to focus on high-weight features in the convolutional kernels, thus overlooking low-weight background features. This bias may result in the neglect of some important information in the background. To address this challenge, we propose a background-based multiscale feature enhancement network (BMFENet), which can extract and supplement missing features from different scale backgrounds to improve the reconstruction of remote sensing images (RSIs). Specifically, we constructed a large kernel feature supplement block (LFSB). The LFSB uses large kernel attention mechanism and multiscale mechanism to expand the receptive field, aggregating global information. Meanwhile, it generates background feature weights to increase the attention to neglected information, thereby reducing the distortion of detailed features. Furthermore, to enhance the nonlinear expression capability of the model, we designed a lattice gated unit (LGU). The LGU removes redundant information through a gating mechanism, efficiently aggregates useful channel information through interchannel interactions and attention mechanisms, and introduces directional convolution to make the model more adaptable to super-resolution (SR) tasks in complex scenes. We validated our method on two remote sensing and four SR benchmark datasets, and the results show that our approach achieves a good balance between performance and complexity.

We present a compendium of Hodge decompositions of vector fields on tetrahedral meshes embedded in the 3D Euclidean space. After describing the foundations of the Hodge decomposition in the continuous setting, we describe how to implement a five-component orthogonal decomposition that generically splits, for a variety of boundary conditions, any given discrete vector field expressed as discrete differential forms into two potential fields, as well as three additional harmonic components that arise from the topology or boundary of the domain. The resulting decomposition is proper and mimetic, in the sense that the theoretical dualities on the kernel spaces of vector Laplacians valid in the continuous case (including correspondences to cohomology and homology groups) are exactly preserved in the discrete realm. Such a decomposition only involves simple linear algebra with symmetric matrices, and can thus serve as a basic computational tool for vector field analysis in graphics, electromagnetics, fluid dynamics and elasticity.

Motivation: Protein pocket information is invaluable for drug target identification, agonist design, virtual screening and receptor-ligand binding analysis. A recent study indicates that about half holoproteins can simultaneously bind multiple interacting ligands in a large pocket containing structured sub-pockets. Although this hierarchical pocket and sub-pocket structure has a significant impact to multi-ligand synergistic interactions in the protein binding site, there is no method available for this analysis. This work introduces a computational tool based on differential geometry, algebraic topology and physics-based simulation to address this pressing issue. Results: We propose to detect protein pockets by evolving the convex hull surface inwards until it touches the protein surface everywhere. The governing partial differential equations (PDEs) include the mean curvature flow combined with the eikonal equation commonly used in the fast marching algorithm in the Eulerian representation. The surface evolution induced Morse function and Reeb graph are utilized to characterize the hierarchical pocket and sub-pocket structure in controllable detail. The proposed method is validated on PDBbind refined sets of 4414 protein-ligand complexes. Extensive numerical tests indicate that the proposed method not only provides a unique description of pocket-sub-pocket relations, but also offers efficient estimations of pocket surface area, pocket volume and pocket depth. Availability and implementation: Source code available at https://github.com/rdzhao/ProteinPocketDetection. Webserver available at http://weilab.math.msu.edu/PPD/.