Social inequalities are ubiquitous and here we show that the values of the Gini (g) and Kolkata (k) indices, two generic inequality indices, approach each other (starting from g = 0 and k = 0.5 for equality) as the competitions grow in various social institutions like markets, universities, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at g = k ≃ 0.87) under unrestricted competitions. We propose to view this coincidence of inequality indices as generalized version of the (more than a) century old 80-20 law of Pareto. Further, this proposition is validated by analyzing data from different social sectors and with analytical considerations of different Lorenz functions.

The estimate of the remaining time of an ongoing wave of epidemic spreading is a critical issue. Due to the variations of a wide range of parameters in an epidemic, for simple models such as Susceptible-Infected-Removed (SIR) model, it is difficult to estimate such a time scale. On the other hand, multidimensional data with a large set attributes are precisely what one can use in statistical learning algorithms to make predictions. Here we show, how the predictability of the SIR model changes with various parameters using a supervised learning algorithm. We then estimate the condition in which the model gives the least error in predicting the duration of the first wave of the COVID-19 pandemic in different states in India. Finally, we use the SIR model with the above mentioned optimal conditions to generate a training data set and use it in the supervised learning algorithm to estimate the end-time of the ongoing second wave of the pandemic in different states in India.