Overdetermined boundary value problems with strongly nonlinear elliptic PDE

We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition F(∇u) = c on the boundary. Here F is convex and positively homogeneous of degree 1, and its polar F ∗ represents the anisotropic norm on R n. We prove that, if this overdetermined boundary value problem admits a solution in a suitable weak sense, then Ω must be of Wulff shape

On a nonlocal problem for a confined plasma in a Tokamak

summary:The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms $u'_{\ast }(|u>u(x)|)$ and $|u>u(x)|$, which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem

Aloperine: A Potent Modulator of Crucial Biological Mechanisms in Multiple Diseases

Aloperine is an alkaloid found in the seeds and leaves of the medicinal plant Sophora alopecuroides L. It has been used as herbal medicine in China for centuries due to its potent anti-inflammatory, antioxidant, antibacterial, and antiviral properties. Recently, aloperine has been widely investigated for its therapeutic activities. Aloperine is proven to be an effective therapeutic agent against many human pathological conditions, including cancer, viral diseases, and cardiovascular and inflammatory disorders. Aloperine is reported to exert therapeutic effects through triggering various biological processes, including cell cycle arrest, apoptosis, autophagy, suppressing cell migration, and invasion. It has also been found to be associated with the modulation of various signaling pathways in different diseases. In this review, we summarize the most recent knowledge on the modulatory effects of aloperine on various critical biological processes and signaling mechanisms, including the PI3K, Akt, NF-κB, Ras, and Nrf2 pathways. These data demonstrate that aloperine is a promising therapeutic candidate. Being a potent modulator of signaling mechanisms, aloperine can be employed in clinical settings to treat various human disorders in the future

Image1_Experimental verification and comprehensive analysis of m7G methylation regulators in the subcluster classification of ischemic stroke.TIF

Background: Ischemic stroke (IS) is a fatal cerebrovascular disease involving several pathological mechanisms. Modification of 7-methylguanosine (m7G) has multiple regulatory functions. However, the expression pattern and mechanism of m7G in IS remain unknown. Herein, we aimed to explore the effect of m7G modification on IS.Methods: We screened significantly different m7G-regulated genes in Gene Expression Omnibus datasets, GSE58294 and GSE22255. The random forest (RF) algorithm was selected to identify key m7G-regulated genes that were subsequently validated using the middle cerebral artery occlusion (MCAO) model and quantitative polymerase chain reaction (qPCR). A risk model was subsequently generated using key m7G-regulated genes. Then, “ConsensusClusterPlus” package was used to distinguish different m7G clusters of patients with IS. Simultaneously, between two m7G clusters, differentially expressed genes (DEGs) and immune infiltration differences were also explored. Finally, we investigated functional enrichment and the mRNA–miRNA–transcription factor network of DEGs.Results: RF and qPCR confirmed that EIF3D, CYFIP2, NCBP2, DCPS, and NUDT1 were key m7G-related genes in IS that could accurately predict clinical risk (area under the curve = 0.967). NCBP2 was the most significantly associated gene with immune infiltration. Based on the expression profiles of these key m7G-related genes, the IS group could be divided into two clusters. According to the single-sample gene set enrichment analysis algorithm, four types of immune cells (immature dendritic cells, macrophages, natural killer T cells, and TH1 cells) were significantly different in the two m7G clusters. The functional enrichment of 282 DEGs between the two clusters was mainly concentrated in the “regulation of apoptotic signaling pathway,” “cellular response to DNA damage stimulus,” “adaptive immune system,” and “pyroptosis.” The miR-214–LTF–FOXJ1 axis may be a key regulatory pathway for IS.Conclusion: Our findings suggest that EIF3D, CYFIP2, NCBP2, DCPS, and NUDT1 may serve as potential diagnostic biomarkers for IS and that the m7G clusters developed by these genes provide more evidence for the regulation of m7G in IS.</p

Table1_Experimental verification and comprehensive analysis of m7G methylation regulators in the subcluster classification of ischemic stroke.XLSX

Background: Ischemic stroke (IS) is a fatal cerebrovascular disease involving several pathological mechanisms. Modification of 7-methylguanosine (m7G) has multiple regulatory functions. However, the expression pattern and mechanism of m7G in IS remain unknown. Herein, we aimed to explore the effect of m7G modification on IS.Methods: We screened significantly different m7G-regulated genes in Gene Expression Omnibus datasets, GSE58294 and GSE22255. The random forest (RF) algorithm was selected to identify key m7G-regulated genes that were subsequently validated using the middle cerebral artery occlusion (MCAO) model and quantitative polymerase chain reaction (qPCR). A risk model was subsequently generated using key m7G-regulated genes. Then, “ConsensusClusterPlus” package was used to distinguish different m7G clusters of patients with IS. Simultaneously, between two m7G clusters, differentially expressed genes (DEGs) and immune infiltration differences were also explored. Finally, we investigated functional enrichment and the mRNA–miRNA–transcription factor network of DEGs.Results: RF and qPCR confirmed that EIF3D, CYFIP2, NCBP2, DCPS, and NUDT1 were key m7G-related genes in IS that could accurately predict clinical risk (area under the curve = 0.967). NCBP2 was the most significantly associated gene with immune infiltration. Based on the expression profiles of these key m7G-related genes, the IS group could be divided into two clusters. According to the single-sample gene set enrichment analysis algorithm, four types of immune cells (immature dendritic cells, macrophages, natural killer T cells, and TH1 cells) were significantly different in the two m7G clusters. The functional enrichment of 282 DEGs between the two clusters was mainly concentrated in the “regulation of apoptotic signaling pathway,” “cellular response to DNA damage stimulus,” “adaptive immune system,” and “pyroptosis.” The miR-214–LTF–FOXJ1 axis may be a key regulatory pathway for IS.Conclusion: Our findings suggest that EIF3D, CYFIP2, NCBP2, DCPS, and NUDT1 may serve as potential diagnostic biomarkers for IS and that the m7G clusters developed by these genes provide more evidence for the regulation of m7G in IS.</p

Long-Term Satellite Observations of Microcystin Concentrations in Lake Taihu during Cyanobacterial Bloom Periods

Microcystins (MCs) produced by cyanobacteria pose a serious threat to public health. Intelligence on MCs distributions in freshwater is therefore critical for environmental agencies, water authorities, and public health organizations. We developed and validated an empirical model to quantify MCs in Lake Taihu during cyanobacterial bloom periods using the atmospherically Rayleigh-corrected moderate resolution imaging spectroradiometer (MODIS-Aqua) (<i>R</i>_rc) products and in situ data by means of chlorophyll a concentrations (Chl<i>a</i>). First, robust relationships were constructed between MCs and Chl<i>a</i> (<i>r</i> = 0.91; <i>p</i> < 0.001; <i>t</i>-test) and between Chl<i>a</i> and a spectral index derived from <i>R</i>_rc (<i>r</i> = −0.86; <i>p</i> < 0.05; <i>t</i>-test). Then, a regional algorithm to analyze MCs in Lake Taihu was constructed by combining the two relationships. The model was validated and then applied to an 11-year series of MODIS-Aqua data to investigate the spatial and temporal distributions of MCs. MCs in the lake were markedly variable both spatially and temporally. Cyanobacterial bloom scums, temperature, wind, and light conditions probably affected the temporal and spatial distribution of MCs in Lake Taihu. The findings demonstrate that remote sensing reconnaissance in conjunction with in situ monitoring can greatly aid MCs assessment in freshwater