On extropy of past lifetime distribution

Recently Qiu et al. (2017) have introduced residual extropy as measure of uncertainty in residual lifetime distributions analogues to residual entropy (1996). Also, they obtained some properties and applications of that. In this paper, we study the extropy to measure the uncertainty in a past lifetime distribution. This measure of uncertainty is called past extropy. Also it is showed a characterization result about the past extropy of largest order statistics

On Dynamic Cumulative Residual Entropy of Order Statistics

The entropy functions are useful tools to measure the uncertainty in a random variable. Dynamic Cumulative Residual Entropy (DCRE) introduced by Asadi and Zohrevand [1] as a useful dynamic measure of Cumulative Residual Entropy. They studied some properties and applications of these measures. In this paper, Dynamic Cumulative Residual Entropy is proposed based on order statistics and under conditions is showed a characterization result that Dynamic Cumulative Residual Entropy of order statistics can determine the distribution function uniquely. Then some properties for DCRE of order statistics is presented

Interval extropy and weighted interval extropy

Recently, Extropy was introduced by Lad, Sanfilippo and Agrò as a complement dual of Shannon Entropy. In this paper, we propose dynamic versions of Extropy for doubly truncated random variables as measures of uncertainty called Interval Extropy and Weighted Interval Extropy. Some characterizations of random variables related to these new measures are given. Several examples are shown. These measures are evaluated under the effect of linear transformations and, finally, some bounds for them are presented

Toll-like receptors in liver disease

Activation of inflammatory signaling pathways is of central importance in the pathogenesis of alcoholic liver disease (ALD) and nonalcoholic steatohepatitis (NASH). Recent studies demonstrated that Toll-like receptors, the sensors of microbial and endogenous danger signals, are expressed and activated in innate immune cells as well as in parenchymal cells in the liver and thereby contribute to ALD and NASH. In this review, we emphasize the importance of gut-derived endotoxin and its recognition by TLR4 in the liver. The significance of TLR-induced intracellular signaling pathways and cytokine production as well as the contribution of individual cell types to the inflammation is evaluated. The contribution of TLR signaling to the induction of liver fibrosis and to the progression of liver pathology mediated by viral pathogens is reviewed in the context of ALD and NASH