The Boundary Value Problem of the Equations with Nonnegative Characteristic Form

We study the generalized Keldys-Fichera boundary value problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Hölder inequalities and Young inequalities we discuss the existence of the weak solution. Then by using the inverse Hölder inequalities, we obtain the regularity of the weak solution in the anisotropic Sobolev space

Spatiotemporal patterns and determinants of renewable energy innovation: Evidence from a province-level analysis in China

China’s renewable energy innovation is essential for realizing its carbon neutrality targets and the low-carbon transition, but few studies have spatially examined its characteristics and spillover effects. To fill the research gap, this study investigates its distribution and trends from a spatiotemporal dimension and focuses on the spatial effects of the influencing factors to identify those that have a significant impact on renewable energy innovation by using China’s provincial panel data from 2006 to 2019. The results show the following findings. (1) Renewable energy innovation shows distinct spatial differences across China’s provinces such that it is high in the east and south and low in the west and north, which exhibits spatial locking and path-dependence. (2) There is a positive spatial correlation with renewable energy innovation. (3) R&D investment and GDP per capita significantly promote renewable energy innovation, but the former effect is mainly observed in the local area, whereas the latter shows spatial effects. More market-oriented policies should be taken for the improvement of renewable energy innovation and the establishment of regional coordination mechanisms are proposed

A Family of GFP-like Proteins with Different Spectral Properties in Lancelet Branchiostoma Floridae

Background: Members of the green fluorescent protein (GFP) family share sequence similarity and the 11-stranded β-barrel fold. Fluorescence or bright coloration, observed in many members of this family, is enabled by the intrinsic properties of the polypeptide chain itself, without the requirement for cofactors. Amino acid sequence of fluorescent proteins can be altered by genetic engineering to produce variants with different spectral properties, suitable for direct visualization of molecular and cellular processes. Naturally occurring GFP-like proteins include fluorescent proteins from cnidarians of the Hydrozoa and Anthozoa classes, and from copepods of the Pontellidae family, as well as non-fluorescent proteins from Anthozoa. Recently, an mRNA encoding a fluorescent GFP-like protein AmphiGFP, related to GFP from Pontellidae, has been isolated from the lancelet Branchiostoma floridae, a cephalochordate (Deheyn et al., Biol Bull, 2007 213:95). Results: We report that the nearly-completely sequenced genome of Branchiostoma floridae encodes at least 12 GFP-like proteins. The evidence for expression of six of these genes can be found in the EST databases. Phylogenetic analysis suggests that a gene encoding a GFP-like protein was present in the common ancestor of Cnidaria and Bilateria. We synthesized and expressed two of the lancelet GFP-like proteins in mammalian cells and in bacteria. One protein, which we called LanFP1, exhibits bright green fluorescence in both systems. The other protein, LanFP2, is identical to AmphiGFP in amino acid sequence and is moderately fluorescent. Live imaging of the adult animals revealed bright green fluorescence at the anterior end and in the basal region of the oral cirri, as well as weaker green signals throughout the body of the animal. In addition, red fluorescence was observed in oral cirri, extending to the tips. Conclusion GFP-like proteins may have been present in the primitive Metazoa. Their evolutionary history includes losses in several metazoan lineages and expansion in cephalochordates that resulted in the largest repertoire of GFP-like proteins known thus far in a single organism. Lancelet expresses several of its GFP-like proteins, which appear to have distinct spectral properties and perhaps diverse functions. Reviewers: This article was reviewed by Shamil Sunyaev, Mikhail Matz (nominated by I. King Jordan) and L. Aravind

A new perspective on building efficient and expressive 3D equivariant graph neural networks

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these networks through a local-to-global analysis lacks today. In this paper, we propose a local hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs and investigate the process of representing global geometric information from local patches. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs; namely local substructure encoding (LSE) and frame transition encoding (FTE). To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules and achieves state-of-the-art performance on both scalar-valued and vector-valued molecular property prediction tasks. We further point out the design space for future developments of equivariant graph neural networks. Our codes are available at \url{https://github.com/yuanqidu/LeftNet}

Learning to Fuse Multiple Brain Functional Networks for Automated Autism Identification

Functional connectivity network (FCN) has become a popular tool to identify potential biomarkers for brain dysfunction, such as autism spectrum disorder (ASD). Due to its importance, researchers have proposed many methods to estimate FCNs from resting-state functional MRI (rs-fMRI) data. However, the existing FCN estimation methods usually only capture a single relationship between brain regions of interest (ROIs), e.g., linear correlation, nonlinear correlation, or higher-order correlation, thus failing to model the complex interaction among ROIs in the brain. Additionally, such traditional methods estimate FCNs in an unsupervised way, and the estimation process is independent of the downstream tasks, which makes it difficult to guarantee the optimal performance for ASD identification. To address these issues, in this paper, we propose a multi-FCN fusion framework for rs-fMRI-based ASD classification. Specifically, for each subject, we first estimate multiple FCNs using different methods to encode rich interactions among ROIs from different perspectives. Then, we use the label information (ASD vs. healthy control (HC)) to learn a set of fusion weights for measuring the importance/discrimination of those estimated FCNs. Finally, we apply the adaptively weighted fused FCN on the ABIDE dataset to identify subjects with ASD from HCs. The proposed FCN fusion framework is straightforward to implement and can significantly improve diagnostic accuracy compared to traditional and state-of-the-art methods