Adaptive grid generation based onthe least-squares finite-element method

AbstractApproximate solutions of a partial differential equation become inaccurate if they arecomputed on a fixed grid that is not sufficiently fine in regions of the domain where the variables change rapidly. For time dependent problems, special features of a partial differential equation and their location could change in time as well. Thus, adaptive grid methods are necessary.In this paper, we develop an adaptive deformation method based on the least-squares finite-element method (LSFEM). A main advantage of this method as compared to the existing deformation method is its ability to generate adaptive grids on domains with moving boundary. It computes the node velocity from a div-curl system according to an error indicator (monitor function), and then moves the nodes to new locations so that the size of the new grid cells can be directly controlled. In this method, the connectivity of the nodes is unchanged if the grid quality is acceptable. Otherwise, various optimization procedures can be applied after node movements to improve grid quality. The grid formed becomes refined in regions where the solution error is large

Construction of differentiable transformations

AbstractConstruction of invertible transformations using differential equations is an interesting and challenging mathematical problem with important applications. We briefly review the existing method by means of harmonic maps in 2D and propose a method of constructing differentiable, invertible transformations between domains in two and three dimensions. Preliminary numerical results demonstrate the effectiveness of the method

Identification of Renal Long Non-coding RNA RP11-2B6.2 as a Positive Regulator of Type I Interferon Signaling Pathway in Lupus Nephritis

Objective: Lupus nephritis (LN) is one of the most serious complications of systemic lupus erythematosus (SLE). Type I interferon (IFN-I) is associated with the pathogenesis of LN. Long non-coding RNAs (lncRNAs) have been implicated in the pathogenesis of SLE, however, the roles of lncRNAs in LN are still poorly understood. Here, we identified and investigated the function of LN-associated lncRNA RP11-2B6.2 in regulating IFN-I signaling pathway.Methods: RNA sequencing was used to analyze the expression of lncRNAs in kidney biopsies from LN patients and controls. Antisense oligonucleotides and CRISPRi system or overexpression plasmids and CRISPRa system were used to perform loss or gain of function experiments. In situ hybridization, imaging flow cytometry, dual-luciferase reporter assay, and ATAC sequencing were used to study the functions of lncRNA RP11-2B6.2. RT-qPCR, ELISA, and western blotting were done to detect RNA and protein levels of specific genes.Results: Elevated lncRNA RP11-2B6.2 was observed in kidney biopsies from LN patients and positively correlated with disease activity and IFN scores. Knockdown of lncRNA RP11-2B6.2 in renal cells inhibited the expression of IFN stimulated genes (ISGs), while overexpression of lncRNA RP11-2B6.2 enhanced ISG expression. Knockdown of LncRNA RP11-2B6.2 inhibited the phosphorylation of JAK1, TYK2, and STAT1 in IFN-I pathway, while promoted the chromatin accessibility and the transcription of SOCS1.Conclusion: The expression of lncRNAs is abnormal in the kidney of LN. LncRNA RP11-2B6.2 is a novel positive regulator of IFN-I pathway through epigenetic inhibition of SOCS1, which provides a new therapeutic target to alleviate over-activated IFN-I signaling in LN

Broadband Linear-Dichroic Photodetector in a Black Phosphorus Vertical p-n Junction

The ability to detect light over a broad spectral range is central for practical optoelectronic applications, and has been successfully demonstrated with photodetectors of two-dimensional layered crystals such as graphene and MoS2. However, polarization sensitivity within such a photodetector remains elusive. Here we demonstrate a linear-dichroic broadband photodetector with layered black phosphorus transistors, using the strong intrinsic linear dichroism arising from the in-plane optical anisotropy with respect to the atom-buckled direction, which is polarization sensitive over a broad bandwidth from 400 nm to 3750 nm. Especially, a perpendicular build-in electric field induced by gating in black phosphorus transistors can spatially separate the photo-generated electrons and holes in the channel, effectively reducing their recombination rate, and thus enhancing the efficiency and performance for linear dichroism photodetection. This provides new functionality using anisotropic layered black phosphorus, thereby enabling novel optical and optoelectronic device applications.Comment: 18 pages, 5 figures in Nature Nanotechnology 201