Optimal Concentration of Information Content For Log-Concave Densities

An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).Comment: 15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with more general sufficient conditions for equality in Theorem 2.3. Also some minor corrections and added reference

Transcriptome Analyses of Tumor-Adjacent Somatic Tissues Reveal Genes Co-Expressed with Transposable Elements

Background: Despite the long-held assumption that transposons are normally only expressed in the germ-line, recent evidence shows that transcripts of transposable element (TE) sequences are frequently found in the somatic cells. However, the extent of variation in TE transcript levels across different tissues and different individuals are unknown, and the co-expression between TEs and host gene mRNAs have not been examined. Results: Here we report the variation in TE derived transcript levels across tissues and between individuals observed in the non-tumorous tissues collected for The Cancer Genome Atlas. We found core TE co-expression modules consisting mainly of transposons, showing correlated expression across broad classes of TEs. Despite this co-expression within tissues, there are individual TE loci that exhibit tissue-specific expression patterns, when compared across tissues. The core TE modules were negatively correlated with other gene modules that consisted of immune response genes in interferon signaling. KRAB Zinc Finger Proteins (KZFPs) were over-represented gene members of the TE modules, showing positive correlation across multiple tissues. But we did not find overlap between TE-KZFP pairs that are co-expressed and TE-KZFP pairs that are bound in published ChIP-seq studies. Conclusions: We find unexpected variation in TE derived transcripts, within and across non-tumorous tissues. We describe a broad view of the RNA state for non-tumorous tissues exhibiting higher level of TE transcripts. Tissues with higher level of TE transcripts have a broad range of TEs co-expressed, with high expression of a large number of KZFPs, and lower RNA levels of immune genes