Ranks count the 195 countries (193 UN members and two observer states) with a figure for that measure, so each ranking has its own denominator. Territories keep their figures and are not ranked. Missing figures are unranked, never zero. Ties are ordered alphabetically.
The GDP change column is computed by Rank.ai from the World Bank's nominal GDP series: each country's rank in 2014 against its rank in 2024. Nominal GDP is in current US dollars, so exchange rates move it as well as output. The map shades countries in five groups by where they fall in the chosen ranking: fifths for even measures, and for skewed ones (GDP, population, AI research, GDP per person, R&D) the top 5% and 15% get the darkest steps so the largest stand out.