Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and RCD(K,∞)RCD(K,\infty) spaces

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings

Clinicopathologic characteristics of patients with esophageal squamous cell carcinoma.

<p>Note. sums of numbers may not be added to total number of patients in cohort because of missing data. Abbreviations: pT, pathologic T stage; pN, lymph node metastases; AJCC7, American Joint Committee on Cancer (Seventh Edition).</p><p>Clinicopathologic characteristics of patients with esophageal squamous cell carcinoma.</p

Overall survival analysis according to the expression of PI3K-p85α, EGFR and p53.

<p>(<b>A</b>) Overall survival analysis in the first cohort of 213 ESCCs. (<b>B</b>) Overall survival analysis in the second cohort of 377 ESCCs. (<b>C</b>) Overall survival analysis in a total of 590 ESCCs. Blue graph: patients with “PI3K-p85α low” or “EGFR low” or “p53 low”. Green graph: patients with “PI3K-p85α high” or “EGFR high” or “p53 high”. PI3K, phosphatidylinositol 3-kinases; EGFR, epidermal growth factor receptor.</p

Overall survival analysis according to numbers of highly expressed proteins in ESCC tumors.

<p>(<b>A–C</b>) ESCCs are divided into four groups in both the two cohorts or together: better prognosis (high expression of 0 marker), good prognosis (high expression of 1 marker), average prognosis (high expression of 2 markers) and poor prognosis (high expression of 3 markers). (<b>D</b>) ESCCs are divided into two groups: good prognosis (high expression of 0–1 marker) and poor prognosis (high expression of 2–3 markers).</p

Multivariate cox regression analysis of factors predicting survival time of patients with esophageal squamous cell carcinoma.

<p>Abbreviations: HR: hazard ratio; CI: confidence interval; PI3K, phosphatidylinositol 3-kinases; EGFR, epidermal growth factor receptor; pT, pathologic T stage; pN, lymph node metastases; AJCC7, American Joint Committee on Cancer (Seventh Edition); IHC, immunohistochemistry.</p><p>Multivariate cox regression analysis of factors predicting survival time of patients with esophageal squamous cell carcinoma.</p

Representative IHC images of PI3K-p85α, EGFR, p53, c-KIT and TIMP1.

<p>IHC results reveal that these proteins are highly expressed in ESCC tumors, whereas a low/no expression in adjacent normal tissues. IHC, immunohistochemistry; ESCC, esophageal squamous cell carcinoma; PI3K, phosphatidylinositol 3-kinases; EGFR, epidermal growth factor receptor; TIMP1, TIMP metallopeptidase inhibitor 1. Original magnification: 200 × and 400 ×.</p

Relationship between high expression of proteins and clinicopathologic parameters.

<p>Abbreviations: pT, pathologic T stage; pN, lymph node metastases; AJCC7, American Joint Committee on Cancer (Seventh Edition); PI3K, phosphatidylinositol 3-kinases;</p><p>EGFR, epidermal growth factor receptor; TIMP1, TIMP metallopeptidase inhibitor 1.</p><p>Relationship between high expression of proteins and clinicopathologic parameters.</p

Overall survival analysis according to the combination of the protein panel and clinicopathologic parameters.

<p>(<b>A</b>) A combination of the protein panel and lymph node metastases could stratify patients more accurately (right Kaplan-Meier curves) than just only lymph node metastases (left Kaplan-Meier curves). (<b>B</b>) A combination of the protein panel and pathologic stage could stratify patients more accurately (right Kaplan-Meier curves) than just only stage (left Kaplan-Meier curves).</p

Additional file 7: of ANXA2 promotes esophageal cancer progression by activating MYC-HIF1A-VEGF axis

Figure S6. The effect of ANXA2 phosphorylation on MYC mRNA expression. Real-time RT-PCR analysis of MYC mRNA expression in KYSE30 and KYSE150 cells transiently transfected with pcDNA3.1-ANXA2-Y23A or pcDNA3.1-ANXA2-Y23D for 48 h. MYC mRNA levels were normalized with the exogenously expressed ANXA2 level. (PDF 150 kb)

Additional file 5: of ANXA2 promotes esophageal cancer progression by activating MYC-HIF1A-VEGF axis

Figure S4. Correlation data between ANXA2, HIF1A and VEGF mRNA expression in ESCC tissues. The Pearson’s correlation analyses were performed to assess the correlation between ANXA2, HIF1A and VEGF mRNA levels in ESCC samples (n = 95) from TCGA database. a-c The mRNA expression levels of ANXA2, HIF1A and VEGF. The X and Y-axis denote the log2 of mRNA expression level. R represents Pearson’s correlation coefficient. d Summary of correlation between ANXA2, HIF1A and VEGF mRNA expression. The circles are filled in blue clockwise for positive values and the intensity of color increases with the correlation value moving away from 0. (PDF 466 kb)