Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical Mechanics and its Application

Design of hydraulic output Stirling engine

A hydraulic output system for the RE-1000 free piston stirling engine (FPSE) was designed. The hydraulic output system can be readily integrated with the existing hot section of RE-1000 FPSE. The system has two simply supported diaphragms which separate the engine gas from the hydraulic fluid, a dynamic balance mechanism, and a novel, null center band hydraulic pump. The diaphragms are designed to endure more than 10 billion cycles, and to withstand the differential pressure load as high as 14 MPa. The projected thermodynamic performance of the hydraulic output version of RE-1000 FPSE is 1.87 kW at 29/7 percent brake efficiency