Influence of Genetic Background and Tissue Types on Global DNA Methylation Patterns

Recent studies have shown a genetic influence on gene expression variation, chromatin, and DNA methylation. However, the effects of genetic background and tissue types on DNA methylation at the genome-wide level have not been characterized extensively. To study the effect of genetic background and tissue types on global DNA methylation, we performed DNA methylation analysis using the Affymetrix 500K SNP array on tumor, adjacent normal tissue, and blood DNA from 30 patients with esophageal squamous cell carcinoma (ESCC). The use of multiple tissues from 30 individuals allowed us to evaluate variation of DNA methylation states across tissues and individuals. Our results demonstrate that blood and esophageal tissues shared similar DNA methylation patterns within the same individual, suggesting an influence of genetic background on DNA methylation. Furthermore, we showed that tissue types are important contributors of DNA methylation states

On weakly compact sets in C(X)

[EN] A subset A of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence {x(n)}(n=1)(infinity) in E contained in A converges to a point x is an element of A (a point x is an element of E). Asanov and Velichko proved that if X is countably compact, every functionally bounded set in C-p (X) is relatively compact, and Baturov showed that if X is a Lindelof Sigma-space, each countably compact (so functionally bounded) set in C-p (X) is a monolithic compact. We show that if X is a Lindelof Sigma-space, every functionally bounded (relatively) sequentially complete set in C-p (X) or in C-w (X), i. e., in C-k (X) equipped with the weak topology, is (relatively) Gul'ko compact. We get some consequences.This work was supported for the first named author by the Grant PGC2018-094431-B-I00 of Ministry of Science, Innovation and Universities of Spain.Ferrando, JC.; López Alfonso, S. (2021). On weakly compact sets in C(X). Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 115(2):1-8. https://doi.org/10.1007/s13398-020-00987-0S181152Arkhangel’skiĭ, A. V.: Topological function spaces. In: Math. Appl. vol. 78, Kluwer Academic Publishers, Dordrecht, Boston, London (1992)Banakh, T., Ka̧kol, J., Śliwa, W.: Josefson-Nissenzweig property for $$C_{p}$$-spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 113, 3015–3030 (2019)Baturov, D.P.: Subspaces of function spaces. Vestnik Moskov. Univ. Ser. I Mat. Mech. 4, 66–69 (1987)Bogachev, V.I., Smolyanov, O.G.: Topological Vector Spaces and Their Applications. Springer, Heidelberg (2017)Buzyakova, R.Z.: In search of Lindelöf $$C_{p}$$ ’s. Comment. Math. Univ. Carolinae 45, 145–151 (2004)Cascales, B., Muñoz, M., Orihuela, J.: The number of $$K$$-determination of topological spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 106, 341–357 (2012)Cembranos, P., Mendoza, J.: Banach Spaces of Vector-Valued Functions. Lecture Notes in Math, vol. 1676. Springer, Berlin, Heidelberg (1997)Ferrando, J.C.: On a Theorem of D.P. Baturov. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 111, 499–505 (2017)Ferrando, J. C.: Descriptive topology for analysts. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 114, Paper No. 107, 34 pp. (2020)Ferrando, J.C., Gabriyelyan, S., Ka̧kol, J., : Metrizable-like locally convex topologies on $$C(X)$$. Topol. Appl. 230, 105–113 (2017)Ferrando, J.C., Ka̧kol, J., Saxon, S. A, : Characterizing $$P$$-spaces in terms of $$C\left( X\right)$$. J. Convex Anal. 22, 905–915 (2015)Ferrando, J.C., López-Pellicer, M.: Covering properties of $$C_{p}\left( X\right)$$ and $$C_{k}\left( X\right)$$ (Filomat, to appear)Floret, K.: Weakly Compact Sets. Lecture Notes in Math, vol. 801. Springer, Berlin, Heidelberg (1980)Gabriyelyan, S.: Ascoli’s theorem for pseudocompact spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 114, Paper No. 174, 10 pp. (2020)Gillman, L., Jerison, M.: Rings of Continuous Functions. Van Nostrand, Princeton (1960)Ka̧kol, J., Kubis, W., López-Pellicer, M., : Descriptive Topology in Selected Topics of Functional Analysis. Springer, Heidelberg (2011)King, D.M., Morris, S.A.: The Stone-Čech compactification and weakly Fréchet spaces. Bull. Austral. Math. Soc. 42, 340–352 (1990)Muñoz, M.: A note on the theorem of Baturov. Bull. Austral. Math. Soc. 76, 219–225 (2007)Orihuela, J.: Pointwise compactness in spaces of continuous functions. J. Lond. Math. Soc. 36, 143–152 (1987)Pełczyński, A., Semadeni, Z.: Spaces of continuous functions (III) (Spaces $$C\left( \Omega \right)$$ for $$\Omega$$ without perfect sets). Studia Math. 18, 211–222 (1959)Robertson, A.P., Robertson, W.: Topological Vector Spaces. Cambridge University Press, Cambridge (1973)Talagrand, M.: Espaces de Banach faiblement $$K$$ -analytiques. Ann. Math. 110, 407–438 (1979)Tkachuk, V.V.: The space $$C_{p}(X)$$: decomposition into a countable union of bounded subspaces and completeness properties. Topol. Appl. 22, 241–253 (1986)Tkachuk, V.V.: A $$C_{p}$$-Theory Problem Book. Topological and Function Spaces. Springer, Heidelberg (2011)Todorcevic, S.: Topics in Topology. Springer, Berlin (1997)Valdivia, M.: Some new results on weak compactness. J. Funct. Anal. 24, 1–10 (1977