When we write vectors as matrices, we tend to write an $n$-dimensional vector vector as $n \times 1$ column matrix. We emphasize that the gradient vector is defined only for scalar-valued functions. For vector valued functions, we will stick with viewing the derivative as a matrix.
Gloomy Addiction Relapse Statistics. Drug and alcohol rehab statistics show that the percentage of people who will relapse after a period recovery ranges from 50% to 90%. This is a frightening statistic and it is often used as justification for those who wish to carry on with their addiction.
The AA-based approach seemed to work and compared favorably with the other therapies. In all three groups, participants were abstinent on roughly 20 percent of days, on average, before treatment began, and the fraction of alcohol-free days rose to about 80 percent a year after treatment ended.