Discovering Phase Transitions with Unsupervised Learning

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low dimensional representations the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds out physical concepts such as order parameter and structure factor to be indicators of the phase transition. We discuss future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.Comment: corrected typos, fixed links in reference

Competition Law Enforcement in China: Between Technocracy and Industrial Policy

The article provides a rare reconstruction of a number of early cases decided under the Chinese Anti-Monopoly Law. In particular, the article seeks to go behind the published decisions of the responsible authorities, to reconstruct their decision-making process in particular by identifying the sources of consultation and the arguments that various stakeholders presented to the authorities about what course of action to follow