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.
Heroin Relapse. Relapse rates for heroin and opiate addiction hover around 90%, according to some research. One study found that of 109 subjects who had achieved sobriety in heroin rehab, 99 relapsed. Of the 99 people who relapsed, 64 did so within one week.