Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation

Formation of H2 and CH4 by weathering of olivine at temperatures between 30 and 70°C

Hydrocarbons such as CH4 are known to be formed through the Fischer-Tropsch or Sabatier type reactions in hydrothermal systems usually at temperatures above 100°C. Weathering of olivine is sometimes suggested to account for abiotic formation of CH4 through its redox lowering and water splitting properties. Knowledge about the CH4 and H2 formation processes at low temperatures is important for the research about the origin and cause of early Earth and Martian CH4 and for CO2 sequestration. We have conducted a series of low temperature, long-term weathering experiments in which we have tested the CH4 and H2 formation potential of forsteritic olivine