In every country except China, COVID-19 first infection cases were imported by travelers, which are either people coming back to their own country or visiting foreigners (international or external tourists). In a global and regional phenomenological analysis of COVID-19 spread, we assume that tourism inflow is a trigger mechanism of worldwide dissemination at the pandemic onset days. Taking into account all countries, a convenient common-time origin timeline was employed as if the beginning of the epidemic would have occurred simultaneously in every country. We obtained very good statistical Pearson and Spearman correlations between accumulated infected cases by country and a positive power of the product [Formula: see text], where [Formula: see text] is the tourism inflow before the pandemic and [Formula: see text] is the country population.

In the USA, COVID-19 first infection cases were imported by external travelers. At the epidemic onset days, we assume that the disease partially spreads due to domestic passengers air transportation in its densely connected airport network. Taking into account all USA states, we arranged COVID-19 infected cases data in a convenient common time origin timeline as if the beginning of the epidemic would have occurred simultaneously in every state. Looking for a trend between cases and air passengers, we obtained with this timeline very good statistical Pearson and Spearman correlations between accumulated infected cases by state and a positive power of the product [Formula: see text], where [Formula: see text] is the domestic flight passengers (travelers) inflow by state before the epidemic and [Formula: see text] is its population. We also found a good correlation between percentages of urban area by state and their COVID-19 daily new cases growth rates at onset days.

In any legal chess position, we define an attacked-square entropy [Formula: see text] for either Black or White pieces in terms of the square occupation probability [Formula: see text], where [Formula: see text] is the number of all possible movements to square [Formula: see text] (free or occupied by an opponent’s piece) and [Formula: see text] is the total mobility defined as the sum of all possible movements. Thus, each attacked square contributes to the entropy according to its received “firepower” concentration. A simpler nonsquare-dependant equiprobable entropy [Formula: see text] in terms of equal probabilities [Formula: see text] always yields [Formula: see text]. On average, the difference [Formula: see text] is very large in the Opening phase and [Formula: see text] decreases faster for lower ranked players after move 25. A major cause of the reduction of [Formula: see text] during a game is material loss, which is an irreversible process. By game outcome, gaps in average [Formula: see text] among winners, draws and losers are larger for Amateur players than for Elite players, both in the Middlegame and Endgame. Statistically, Elite players exhibit narrower dispersions in [Formula: see text]. Also, the entropy rates of the Elite level fluctuate much less than the entropies of other levels. Density of attacks in the four-square central zone is very high in the Opening, specially for Elite players.