Bowen entropy for actions of amenable groups

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered condition, the Bowen entropy of the whole compact space for a given F{\o}lner sequence equals to the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin-Katok's local entropy formula for dynamical systems with amenable group actions.Comment: 13 page

Thyroid function in chronic hepatitis C patients treated with interferon

Purpose: To investigate the effect of interferon (IFN) treatment for chronic hepatitis C (CHC) patients on thyroid function.Methods: 65 patients (27 males and 38 females, aged 28 - 61 years) with mild or moderate CHC and early fibrosis admitted to Second Hospital of Lanzhou University from January 2017 to January 2018 were enrolled in this study, while 65 healthy subjects served as the control group. The study group received 135μg peginterferon alfa-2a injection (Peloxin)  subcutaneously, once a week for 48 weeks. Ribavirin was administered orally once a day at doses ranging from 10 - 15 mg/kg body weight. Chemiluminescence immunoassay was used to measure thyroid hormone and antibody levels in both groups.Results: After interferon therapy, the positive expressions of TGAb and TPOAb in the study group were lower than the corresponding values observed before treatment (χ2 = 8.188, p = 0.004; χ2 = 11.527, p < 0.001). Thyroid hormone levels in the study group were normal before treatment, but free triiodothyronine (FT3) and free thyroxine (FT4) were significantly lower in the study group (t1 = -9.58, t2 = -14.61, p < 0.001). However, FT3 and FT4 significantly increased after treatment in the study group, relative to the control group (p < 0.05). The level of TSH in the study group was significantly higher than the level before treatment (p < 0.05), but gradually returned to normal.Conclusion: Chronic hepatitis C patients may have thyroid dysfunction, and IFN therapy may result in transient disorder in thyroid hormone  metabolism. Thus, TSH, TGAb and TPOAb can be used as predictors of thyroid disease development during IFN therapy for CHC.Keywords: Chronic hepatitis C, Thyroid hormone, Anti-thyroid autoantibody, Interfero