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.
Average Stay in Rehabilitation Treatment Centers. The average length of stay for short-term residential treatment was 26 days, while the average length of stay for long-term residential treatment was 70 days, according to 2003 data from the Treatment Episode Data Set.