Quantum reparametrizations in the two-dimensional gravity: a look from 2+ϵ\epsilon dimensions

We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations. Some of them are shown to be equivalent to the introduction of $2+\epsilon$-dimensional terms into the initially 2-dimensional theory. We also argue that the $\beta$-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.Comment: 16 page

A Systematic Review of Three-Dimensional Printing in Liver Disease

The purpose of this review is to analyse current literature related to the clinical applications of 3D printed models in liver disease. A search of the literature was conducted to source studies from databases with the aim of determining the applications and feasibility of 3D printed models in liver disease. 3D printed model accuracy and costs associated with 3D printing, the ability to replicate anatomical structures and delineate important characteristics of hepatic tumours, and the potential for 3D printed liver models to guide surgical planning are analysed. Nineteen studies met the selection criteria for inclusion in the analysis. Seventeen of them were case reports and two were original studies. Quantitative assessment measuring the accuracy of 3D printed liver models was analysed in five studies with mean difference between 3D printed models and original source images ranging from 0.2 to 20%. Fifteen studies provided qualitative assessment with results showing the usefulness of 3D printed models when used as clinical tools in preoperative planning, simulation of surgical or interventional procedures, medical education, and training. The cost and time associated with 3D printed liver model production was reported in 11 studies, with costs ranging from US$13 to US$2000, duration of production up to 100 h. This systematic review shows that 3D printed liver models demonstrate hepatic anatomy and tumours with high accuracy. The models can assist with preoperative planning and may be used in the simulation of surgical procedures for the treatment of malignant hepatic tumours