Nontrivial Periodic Solutions to Some Semilinear Sixth-Order Difference Equations

We establish some new criteria to guarantee nonexistence, existence, and multiplicity of nontrivial periodic solutions of some semilinear sixth-order difference equations by using minmax method, Z2 index theory, and variational technique. Our results only make some assumptions on the period T, which are very easy to verify and rather relaxed

Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations

In this paper, we investigate the existence and nonexistence of positive solutions to a class of nonlocal partial difference equations via a variant version of the mountain pass theorem. The conditions in our obtained results release the classical (AR) condition in some sense

Multiple nontrivial periodic solutions to a second-order partial difference equation

In this article, applying variational technique as well as critical point theory, we establish a series of criteria to ensure the existence and multiplicity of nontrivial periodic solutions to a second-order nonlinear partial difference equation. Our results generalize some known results. Moreover, numerical stimulations are presented to illustrate applications of our major findings

Single-cell RNA-seq data analysis using graph autoencoders and graph attention networks

With the development of high-throughput sequencing technology, the scale of single-cell RNA sequencing (scRNA-seq) data has surged. Its data are typically high-dimensional, with high dropout noise and high sparsity. Therefore, gene imputation and cell clustering analysis of scRNA-seq data is increasingly important. Statistical or traditional machine learning methods are inefficient, and improved accuracy is needed. The methods based on deep learning cannot directly process non-Euclidean spatial data, such as cell diagrams. In this study, we developed scGAEGAT, a multi-modal model with graph autoencoders and graph attention networks for scRNA-seq analysis based on graph neural networks. Cosine similarity, median L1 distance, and root-mean-squared error were used to measure the gene imputation performance of different methods for comparison with scGAEGAT. Furthermore, adjusted mutual information, normalized mutual information, completeness score, and Silhouette coefficient score were used to measure the cell clustering performance of different methods for comparison with scGAEGAT. Experimental results demonstrated promising performance of the scGAEGAT model in gene imputation and cell clustering prediction on four scRNA-seq data sets with gold-standard cell labels

Advanced progress on χ(3) nonlinearity in chip-scale photonic platforms

χ(3) nonlinearity enables ultrafast femtosecond scale light-to-light coupling and manipulation of intensity, phase, and frequency. χ(3) nonlinear functionality in micro-and nano-scale photonic waveguides can potentially replace bulky fiber platforms for many applications. In this Review, we summarize and comment on the progress on χ(3) nonlinearity in chip-scale photonic platforms, including several focused hot topics such as broadband and coherent sources in the new bands, nonlinear pulse shaping, and all-optical signal processing. An outlook of challenges and prospects on this hot research field is given at the end

RNA delivery by extracellular vesicles in mammalian cells and its applications.

The term 'extracellular vesicles' refers to a heterogeneous population of vesicular bodies of cellular origin that derive either from the endosomal compartment (exosomes) or as a result of shedding from the plasma membrane (microvesicles, oncosomes and apoptotic bodies). Extracellular vesicles carry a variety of cargo, including RNAs, proteins, lipids and DNA, which can be taken up by other cells, both in the direct vicinity of the source cell and at distant sites in the body via biofluids, and elicit a variety of phenotypic responses. Owing to their unique biology and roles in cell-cell communication, extracellular vesicles have attracted strong interest, which is further enhanced by their potential clinical utility. Because extracellular vesicles derive their cargo from the contents of the cells that produce them, they are attractive sources of biomarkers for a variety of diseases. Furthermore, studies demonstrating phenotypic effects of specific extracellular vesicle-associated cargo on target cells have stoked interest in extracellular vesicles as therapeutic vehicles. There is particularly strong evidence that the RNA cargo of extracellular vesicles can alter recipient cell gene expression and function. During the past decade, extracellular vesicles and their RNA cargo have become better defined, but many aspects of extracellular vesicle biology remain to be elucidated. These include selective cargo loading resulting in substantial differences between the composition of extracellular vesicles and source cells; heterogeneity in extracellular vesicle size and composition; and undefined mechanisms for the uptake of extracellular vesicles into recipient cells and the fates of their cargo. Further progress in unravelling the basic mechanisms of extracellular vesicle biogenesis, transport, and cargo delivery and function is needed for successful clinical implementation. This Review focuses on the current state of knowledge pertaining to packaging, transport and function of RNAs in extracellular vesicles and outlines the progress made thus far towards their clinical applications