Slow entropy type invariants and smooth realization of commuting measure-preserving transformations

No abstract

The role of inflammation and oxidative stress in the development of obesity and associated metabolic disorders is under debate. We investigated the redox metabolism in a non-diabetic obesity model, i.e. 11-week-old obese Zucker rats. Antioxidant enzyme activities, lipophilic antioxidant (␣-tocopherol, coenzymes Q) and hydrophilic antioxidant (glutathione, vitamin C) contents and their redox state (% oxidized form), were studied in inguinal white fat and compared with blood and liver. The adipose tissues of obese animals showed a specific higher content of hydrophilic molecules in a lower redox state than those of lean animals, which were associated with lower lipophilic molecule content and lipid peroxidation. Conversely and as expected, glutathione content decreased and its redox state increased in adipose tissues of rats subjected to lipopolysaccharide-induced systemic oxidative stress. In these in vivo models, oxidative stress and obesity thus had opposite effects on adipose tissue redox state. Moreover, the increase in glutathione content and the decrease of its redox state by antioxidant treatment promoted in vitro the accumulation of triglycerides in preadipocytes. Taken together and contrary to the emergent view, our results suggest that obesity is associated with an intracellular reduced redox state that promotes on its own the development of a deleterious proadipogenic process.Redox metabolism corresponds to a complex interacting network involving the generation of reactive oxygen species and enzymatic and non-enzymatic cellular antioxidant defenses. Any small and transient disturbance of this balance induces redox signaling, which can act on several transduction pathways or enzyme and transcription factor activities. In contrast, when antioxidant defenses are chronically overwhelmed, the result is an oxidative stress in which free radicals may exert their deleterious effects (1). Oxidative stress has been implicated in the pathogenesis of several metabolic diseases as well as in the comorbidity of diabetes mellitus and atherosclerosis. In such studies, redox metabolism was evaluated by the pattern of various parameters such as manganese-dependent superoxide dismutase, glutathione peroxidase or catalase activities, and glutathione or ␣-tocopherol content in blood and liver (2-5). A similar pattern was observed in obesity and seemed to indicate that such pathology was related to pro-oxidative context. Indeed, obesity prevalence is correlated with decreased

This paper treats the Pinsker algebra of a dynamical system in a way which avoids the use of an ordering on the acting group. This enables us to prove some of the classical results about entropy and the Pinsker algebra in the general setup of measure preserving dynamical systems, where the acting group is a discrete countable amenable group. We prove a basic disjointness theorem which asserts the relative disjointness in the sense of Furstenberg, of 0-entropy extensions from completely positive entropy (c.p.e.) extensions. This theorem is used to prove several classical results in the general setup. E.g. we show that the Pinsker factor of a product system is equal to the product of the Pinsker factors of the component systems. Another application is to obtain a generalization (as well as a simpler proof) of the quasifactor theorem for 0-entropy systems of [GW].