Aberrant microRNA (miRNA) expression has been investigated in gastric cancer, which is one of the most common malignancies. However, the roles of miRNAs in gastric cancer remain largely unknown. In the present study, we found that microRNA-372 (miR-372) directly targets tumor necrosis factor, α-induced protein 1 (TNFAIP1), and is involved in the regulation of the NFκB signaling pathway. Furthermore, overexpression of TNFAIP1 induced changes in AGS cells similar to those in AGS cells treated with miR-372-ASO. Collectively, these findings demonstrate an oncogenic role for miR-372 in controlling cell growth and apoptosis through downregulation of TNFAIP1. This novel molecular basis provides new insights into the etiology of gastric cancer.
For a nondegenerate $r$-graph $F$, large $n$, and $t$ in the regime $[0, c_{F} n]$, where $c_F>0$ is a constant depending only on $F$, we present a general approach for determining the maximum number of edges in an $n$-vertex $r$-graph that does not contain $t+1$ vertex-disjoint copies of $F$. In fact, our method results in a rainbow version of the above result and includes a characterization of the extremal constructions. Our approach applies to many well-studied hypergraphs (including graphs) such as the edge-critical graphs, the Fano plane, the generalized triangles, hypergraph expansions, the expanded triangles, and hypergraph books. Our results extend old results of Simonovits~\cite{SI68} and Moon~\cite{Moon68} on complete graphs and can be viewed as a step towards a general density version of the classical Corr\'{a}di--Hajnal Theorem~\cite{CH63}.
The triangle covering number of a graph is the minimum number of vertices that hit all triangles. Given positive integers $s,t$ and an $n$-vertex graph $G$ with $\lfloor n^2/4 \rfloor +t$ edges and triangle covering number $s$, we determine (for large $n$) sharp bounds on the minimum number of triangles in $G$ and also describe the extremal constructions. Similar results are proved for cliques of larger size and color critical graphs. This extends classical work of Rademacher, Erd\H os, and Lov\'asz-Simonovits whose results apply only to $s \le t$. Our results also address two conjectures of Xiao and Katona. We prove one of them and give a counterexample and prove a modified version of the other conjecture.
The celebrated Andr\'{a}sfai--Erd\H{o}s--S\'{o}s Theorem from 1974 shows that every $n$-vertex triangle-free graph with minimum degree greater than $2n/5$ must be bipartite. Its extensions to $3$-uniform hypergraphs without the generalized triangle $F_5 = \{abc, abd, cde\}$ have been explored in several previous works such as~\cite{LMR23unif,HLZ24}, demonstrating the existence of $\varepsilon > 0$ such that for large $n$, every $n$-vertex $F_5$-free $3$-graph with minimum degree greater than $(1/9-\varepsilon) n^2$ must be $3$-partite. We determine the optimal value for $\varepsilon$ by showing that for $n \ge 5000$, every $n$-vertex $F_5$-free $3$-graph with minimum degree greater than $4n^2/45$ must be $3$-partite, thus establishing the first tight Andr\'{a}sfai--Erd\H{o}s--S\'{o}s type theorem for hypergraphs. As a corollary, for all positive $n$, every $n$-vertex cancellative $3$-graph with minimum degree greater than $4n^2/45$ must be $3$-partite. This result is also optimal and considerably strengthens prior work, such as that by Bollob\'{a}s~\cite{Bol74} and Keevash--Mubayi~\cite{KM04Cancel}.
The classical Kruskal-Katona theorem gives a tight upper bound for the size of an $r$-uniform hypergraph $\mathcal{H}$ as a function of the size of its shadow. Its stability version was obtained by Keevash who proved that if the size of $\mathcal{H}$ is close to the maximum, then $\mathcal{H}$ is structurally close to a complete $r$-uniform hypergraph. We prove similar stability results for two classes of hypergraphs whose extremal properties have been investigated by many researchers: the cancellative hypergraphs and hypergraphs without expansion of cliques.
BACKGROUND:The aim of this study was to establish a predictive model for prognostic factors and overall survival (OS) in nasopharyngeal lymphoepithelial carcinoma (NLEC) patients. MATERIAL AND METHODS:The data of 538 NLEC patients diagnosed between 1988 and 2015 were extracted from the Surveillance, Epidemiology, and End Results database. Patients who were diagnosed from 1988 to 1999 were included in the validation cohort, and those diagnosed from 2000 to 2015 in the primary cohort. Least absolute shrinkage and selection operator and multivariate Cox regression analyses were performed. The discrimination and calibration capabilities of the predictive models were evaluated using the receiver operating characteristic (ROC) curve and calibration plot, respectively. RESULTS:Radiotherapy (P<0.0001), early-stage cancer based on the American Joint Committee on Cancer (AJCC) staging system (P<0.0001), younger age (P=0.0005) were associated with better OS rates. In the primary cohort, the areas under the ROC curves (AUC) of the nomogram for predicting 1-, 10-, and 15-year OS were 0.749, 0.754, and 0.81, respectively. Meanwhile, in the validation cohort, the AUC of the nomogram for predicting 1-, 10-, and 15-year OS were 0.692, 0.692, and 0.682, respectively. Furthermore, the calibration plot exhibited optimal agreements between the nomogram-predicted and actual 1-, 10-, and 15-year OS in both cohorts. The 1-, 10-, and 15-year OS rates were 93.6%, 62.7%, and 49.9%, respectively. CONCLUSIONS:Age, early-stage cancer based on the AJCC staging system, radiotherapy, and gender can be used to predict OS in nasopharyngeal lymphoepithelial carcinoma patients.
Let $\ell \ge r\ge 3$. The $r$-graph $H_{\ell+1}^{r}$ is the hypergraph obtained from $K_{\ell+1}$ by adding a set of $r-2$ new vertices to each edge. Using a stability result for $H_{\ell+1}^{r}$, Pikhurko determined ${\rm ex}(n,H_{\ell+1}^{r})$ for sufficiently large $n$. We prove a new type of stability theorem for $H_{\ell+1}^{r}$ that goes beyond this result, and determine the structure of $H_{\ell+1}^{r}$-free hypergraphs $\mathcal{H}$ that satisfy a certain inequality involving the sizes of $\mathcal{H}$ and its shadow $\partial\mathcal{H}$. Our result can be viewed as an extension of a stability theorem of Keevash about the Kruskal-Katona theorem to $H_{\ell+1}^{r}$-free hypergraphs.
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