Recent advancements in spatial transcriptomics(ST)technologies offer unprecedented opportunities to unveil the spatial heterogeneity of gene expression and cell states within tissues.Despite these capabilities of the ...Recent advancements in spatial transcriptomics(ST)technologies offer unprecedented opportunities to unveil the spatial heterogeneity of gene expression and cell states within tissues.Despite these capabilities of the ST data,accurately dissecting spatiotemporal structures(e.g.,spatial domains,temporal trajectories,and functional interactions)remains challenging.Here,we introduce a computational framework,PearlST(partial differential equation[PDE]-enhanced adversarial graph autoencoder of ST),for accurate inference of spatiotemporal structures from the ST data using PDE-enhanced adversarial graph autoencoder.PearlST employs contrastive learning to extract histological image features,integrates a PDE-based diffusion model to enhance characterization of spatial features at domain boundaries,and learns the latent low-dimensional embeddings via Wasserstein adversarial regularized graph autoencoders.Comparative analyses across multiple ST datasets with varying resolutions demonstrate that PearlST outperforms existing methods in spatial clustering,trajectory inference,and pseudotime analysis.Furthermore,PearlST elucidates functional regulations of the latent features by linking intercellular ligand-receptor interactions to most contributing genes of the low-dimensional embeddings,as illustrated in a human breast cancer dataset.Overall,PearlST proves to be a powerful tool for extracting interpretable latent features and dissecting intricate spatiotemporal structures in ST data across various biological contexts.展开更多
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ...A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.展开更多
A honeycomb-Kagome hexagonal superlattice pattern with dark discharges is observed in a dielectric barrier discharge system for the first time.The spatiotemporal structure of the honeycomb-Kagome hexagonal superlattic...A honeycomb-Kagome hexagonal superlattice pattern with dark discharges is observed in a dielectric barrier discharge system for the first time.The spatiotemporal structure of the honeycomb-Kagome hexagonal superlattice pattern with dark discharges is investigated by an intensified charge-coupled device and the photomultipliers show that it is an interleaving of three different sub-lattices,which are bright-spot,invisible honeycomb lattice,and Kagome lattice with invisible frameworks and dim-spots,respectively.The invisible honeycomb lattices and Kagome lattices are actually composed of dark discharges.By using the optical emission spectra method,it is found that the plasma parameters of the three different sub-lattices are different.The influence of the dark discharges on pattern formation is discussed.The results may have significance for the investigation of the dark discharges and will accelerate the development of self-organized pattern dynamics.展开更多
基金supported by grants from the National Key R&D Program of China(2021YFF1200903)the National Natural Science Foundation of China(62273364,11931019,11871070,and 62362062)+2 种基金the Guangdong Basic and Applied Basic Research Foundation(2020B1515020047)Fundamental Research Funds for the Central Universities,Sun Yat-sen University(231lgbj025)the open fund of Information Materials and Intelligent Sensing Laboratory of Anhui Province(grant no.IMIS202105).
文摘Recent advancements in spatial transcriptomics(ST)technologies offer unprecedented opportunities to unveil the spatial heterogeneity of gene expression and cell states within tissues.Despite these capabilities of the ST data,accurately dissecting spatiotemporal structures(e.g.,spatial domains,temporal trajectories,and functional interactions)remains challenging.Here,we introduce a computational framework,PearlST(partial differential equation[PDE]-enhanced adversarial graph autoencoder of ST),for accurate inference of spatiotemporal structures from the ST data using PDE-enhanced adversarial graph autoencoder.PearlST employs contrastive learning to extract histological image features,integrates a PDE-based diffusion model to enhance characterization of spatial features at domain boundaries,and learns the latent low-dimensional embeddings via Wasserstein adversarial regularized graph autoencoders.Comparative analyses across multiple ST datasets with varying resolutions demonstrate that PearlST outperforms existing methods in spatial clustering,trajectory inference,and pseudotime analysis.Furthermore,PearlST elucidates functional regulations of the latent features by linking intercellular ligand-receptor interactions to most contributing genes of the low-dimensional embeddings,as illustrated in a human breast cancer dataset.Overall,PearlST proves to be a powerful tool for extracting interpretable latent features and dissecting intricate spatiotemporal structures in ST data across various biological contexts.
文摘A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.
基金supported by National Natural Science Foundation of China(No.12075075)Natural Science Foundation of Hebei Province,China(Nos.2020201016 and A2018201154).
文摘A honeycomb-Kagome hexagonal superlattice pattern with dark discharges is observed in a dielectric barrier discharge system for the first time.The spatiotemporal structure of the honeycomb-Kagome hexagonal superlattice pattern with dark discharges is investigated by an intensified charge-coupled device and the photomultipliers show that it is an interleaving of three different sub-lattices,which are bright-spot,invisible honeycomb lattice,and Kagome lattice with invisible frameworks and dim-spots,respectively.The invisible honeycomb lattices and Kagome lattices are actually composed of dark discharges.By using the optical emission spectra method,it is found that the plasma parameters of the three different sub-lattices are different.The influence of the dark discharges on pattern formation is discussed.The results may have significance for the investigation of the dark discharges and will accelerate the development of self-organized pattern dynamics.
