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.
More than half of DTAP participants completed the program, and theystayed in treatment six times longer (a medium of 17.8 month versus 3 months) thanthose in nationally comparable long-term residential drug treatment.6 By comparison, research by the Department of Justice on recidivism of offenders foundthat overall, nearly 60% of those released from prison will be re-arrested within 2 years. 37 Within three years after their release, 67.5% of all offenders are expected to be re-arrested.