An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their data structure as a progress measure, allowing for a backward implementation instead of a complete unravelling of the game. To achieve this, a number of changes have to be made to their techniques, where the main one is to add power to the antagonistic player that allows for determining her rational move without changing the outcome of the game. We provide a first implementation for a quasi-polynomial algorithm, test it on small examples, and provide a number of side results, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al

Mathematical modeling of the West Africa Ebola epidemic

As of November 2015, the Ebola virus disease (EVD) epidemic that began in West Africa in late 2013 is waning. The human toll includes more than 28,000 EVD cases and 11,000 deaths in Guinea, Liberia, and Sierra Leone, the most heavily-affected countries. We reviewed 66 mathematical modeling studies of the EVD epidemic published in the peer-reviewed literature to assess the key uncertainties models addressed, data used for modeling, public sharing of data and results, and model performance. Based on the review, we suggest steps to improve the use of modeling in future public health emergencies. DOI: http://dx.doi.org/10.7554/eLife.09186.00