A New Generalized Varentropy and its Properties

The variance of Shannon information related to the random variable X, which is called varentropy, is a measurement that indicates, how the information content of X is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions that improved the quality of the paper

Mast cell lineage diversion of T lineage precursors by the essential T cell transcription factor GATA-3

GATA-3 is essential for T cell development from the earliest stages. However, abundant GATA-3 can drive T lineage precursors to a non–T cell fate, depending on Notch signaling and developmental stage. Here, overexpression of GATA-3 blocked the survival of pro–T cells when Notch-Delta signals were present but enhanced viability in their absence. In fetal thymocytes at the double-negative 1 (DN1) stage and DN2 stage but not those at the DN3 stage, overexpression of GATA-3 rapidly induced respecification to the mast cell lineage with high frequency by direct transcriptional 'reprogramming'. Normal DN2 thymocytes also showed mast cell potential when interleukin 3 and stem cell factor were added in the absence of Notch signaling. Our results suggest a close relationship between the pro–T cell and mast cell programs and a previously unknown function for Notch in T lineage fidelity