Negations of Probability Distributions: A Survey

In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager\u27s negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager\u27s negator and uniform negator. Involutivity of negations is important in logic, and such involutive negator is considered in the paper. We propose a new simple definition of the class of linear negators generalizing Yager\u27s negator. Different examples illustrate properties of negations of PD. Finally, we consider some open problems in the analysis of negations of probability distributions

Relationship of Serum Levels of IL-17, IL-18, TNF-α, and Lung Function Parameters in Patients with COPD, Asthma-COPD Overlap, and Bronchial Asthma

Determination of markers of systemic inflammation is one of the important directions in the study of pathogenesis and improvement of diagnosis of chronic obstructive pulmonary disease (COPD), asthma-COPD overlap (ACO), and bronchial asthma (BA). The aim of our work was a comparative study of the features of changes in serum levels of IL-17, IL-18, and TNF-α in patients with COPD, ACO, and BA with various severity of the disease, as well as evaluation of the relationship between the level of these cytokines and lung ventilation function. A total of 147 patients with COPD (n=58), ACO (n=57), and BA (n=32) during a stable period have been examined in this study. The control group included 21 healthy nonsmokers with similar sex-age indicators. Serum levels of IL-17, IL-18, and TNF-α were determined by ELISA. The concentrations of these cytokines in the circulation in the studied patients with COPD, ACO, and BA were higher than those in healthy nonsmokers (p≤0.001). IL-17 and IL-18 levels in the blood serum were comparable in all examined patients. The mean TNF-α concentrations in the circulation in COPD and ACO were significantly higher than those in BA (p<0.001). In patients with COPD, the levels of IL-17 and TNF-α increased progressively against the background of a decrease in numerous spirometric indicators, which allows us to consider these cytokines as systemic biomarkers of disease severity. In BA, the inverse correlations between the level of IL-17 and FEV1/FVC (%) and FEV1 have been found. In patients with ACO, the increase in IL-18 levels was associated with a decrease in FEV1 and TNF-α with FEV1/FVC (%). These findings indicate that IL-17, IL-18, and TNF-α can participate in the mechanisms of systemic inflammation and the genesis of disorders of airway obstruction in COPD, AСO, and BA. An increase in the levels of IL-17 and TNF-α may be associated with impaired bronchial patency in COPD and BA. The established associations of the IL-18 concentration in the blood serum and FEV1 only in patients with ACO allow using the level of IL-18 as a potential marker of the degree of impaired airway obstruction in this disease