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.
According to Ã¢ Relapse & Recovery: Behavioral Strategies for Change, a research report by the Caron Foundation, rates of relapse vary from 50 percent returning to heavy use, to 90 percent experiencing brief relapse. Heroin. A highly addictive opiate drug, heroin is recognized as having a relapse rate of 87 percent after drug treatment. Particularly for chronic users who have become chemically dependent on the drug, heroin cravings have been known to exist for years after treatment.