We give sharp upper bounds for the ordinary spectral radius and signless Laplacian spectral radius of a uniform hypergraph in terms of the average 2-degrees or degrees of vertices, respectively, and we also give a lower bound for the ordinary spectral radius. We also compare these bounds with known ones.then ρ is called an eigenvalue of T , and x an eigenvector of T corresponding to ρ, see [7,8]. Let ρ(T ) be the largest modulus of the eigenvalues of T .Let G be a hypergraph with vertex set V (G) = [n] and edge set E(G), see [1]. If every edge of G has cardinality k, then we say that G is a k-uniform hypergraph. Throughout this paper, we consider k-uniform hypergraphs on n vertices with 2 ≤ k ≤ n. A uniform hypergraph is a hypergraph that is k-uniform for some k. For i ∈ [n], E i denotes the set of edges of G containing i. The degree of a vertex i in G is defined asthen G is called a regular hypergraph (of degree d). For i, j ∈ V (G), if there is a sequence of edges e 1 , . . . , e r such that i ∈ e 1 , j ∈ e r and e s ∩ e s+1 = ∅ for all s ∈ [r − 1], then we say that i and j are connected. A hypergraph is connected if every pair of different vertices of G is connected.The adjacency tensor of a k-uniform hypergraph G on n vertices is defined as the tensor A(G) of order k and dimension n whose (i 1 . . . i k )-entry iswhere e 1 = {1, 2, 5}, e 2 = {1, 2, 6}, e 3 = {1, 2, 7}, e 4 = {1, 2, 8}, e 5 = {1, 2, 9}, e 6 = {1, 2, 10}, e 7 = {1, 2, 11}, e 8 = {1, 2, 12}, e 9 = {1, 2, 13}, e 10 = {3, 4, 5}, e 11 = {3, 4, 6}, e 12 = {3, 4, 7}, e 13 = {3, 4, 8}, e 14 = {3, 4, 9}, e
Background: Despite advances in colon cancer screening, diagnosis, chemotherapy, and targeted therapy, the prognosis remains poor once colon cancer develops distant metastasis or local recurrence. To further improve the prognosis of colon cancer patients, researchers or clinicians may need to identify new indicators for predicting the prognosis and treatment of colon cancer. Methods:In order to discover the new mechanism of epithelial-mesenchymal transition (EMT) promoting tumor progression and to find new indicators of colon cancer diagnosis, targeted therapy and prognosis, this study conducted The Cancer Genome Atlas (TCGA) analysis, differential gene analysis, prognostic analysis, protein-protein interaction (PPI), enrichment analysis, molecular typing, and a machine algorithm were combined with data from TCGA and Gene Expression Omnibus (GEO) databases and EMT-related genes.Results: Our study identified 22 EMT-related genes with clinical prognostic value in colon cancer. On the basis of 22 EMT-related genes, we divided colon cancer into 2 different molecular subtypes by non-negative matrix factorization (NMF) model using 14 differentially expressed genes (DEGs), and the DEGs were enriched in multiple signaling pathways related to tumor metastasis process. Further analysis of EMT DEGs revealed that the PCOLCE2 and CXCL1 genes were characteristic genes for clinical prognosis of colon cancer.Conclusions: In this study, 22 prognostic genes were screened out from 200 EMT-related genes, and then the PCOLCE2 and CXCL1 molecules were finally focused on through the combination of the NMF molecular typing model and machine learning screening feature genes, suggesting that PCOLCE2 and CXCL1 may have good application potential. The findings provide a theoretical basis for the next clinical transformation in the treatment of colon cancer.
Colorectal cancer (CRC) is a common malignancy of the gastrointestinal tract. CircRNAs have been reported to play regulatory roles in many cancers, including CRC. This study focuses on the role of circ_0007331 in CRC. Differentially expressed circRNAs in CRC were screened using the GEO database. RT-qPCR was used to analyze mRNA expression. StarBase and TargetScan were used to predict targeting relationships and then verified by the dual luciferase reporter assay along with the RNA pull-down assay. CCK-8 as well and transwell assays were used to measure cell viability, migration, and invasion. Protein levels were determined using western blotting. circ_0007331 is expressed more frequently in patients with CRC. The inhibition of circ_0007331 expression reduced the viability, colony formation, migration, and invasion of CRC cells. However, inhibition of miR-205-5p or elevation of high-mobility group A2 (HMGA2) can reverse the function of inhibited circ_0007331 in tumor cells. This study demonstrated that the circ_0007331/miR-205-5p/HMGA2 axis promotes CRC development. Thus, circ_0007331 may be a potential biomarker for CRC.
A novel nonenzymatic glucose sensor based on CuO@Carbon nanostructures capped with gold nanoparticles (AuNPs) arrayed on three‐dimensional porous carbon derived from kenaf stem (3D‐KSC) was proposed. Here, the massive 3D‐KSC with honeycomb‐like structure was used as supporting matrix to load CuO@Carbon nanostructures. A small amount of AuNPs were coated on CuO@Carbon nanostructures, which were arrayed on 3D‐KSC uniformly. The AuNPs improved the electrical conductivity and catalytic activity of CuO@Carbon nanostructures greatly. Thus, the 3D‐KSC/CuO@Carbon/AuNPs integrated electrode based nonenzymatic glucose sensor showed good performance with the linear range of 3.71 μM–8.5 mM, the detection limit of 1.22 μM and the sensitivity of 935 μA cm−2 mM−1. The satisfied performance made sure it can be used to detect glucose in real blood samples.
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