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

Additional file 4: of ANXA2 promotes esophageal cancer progression by activating MYC-HIF1A-VEGF axis

Figure S3. Silencing of HIF1A downregulates VEGF expression. KYSE30 and KYSE150 cells were transiently transfected with ANXA2 siRNA or control non-silencing siRNA for 48 h. a Real-time RT-PCR analysis. b Western blot analysis. GAPDH was use as a loading control. (PDF 324 kb)

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)