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.
85.9 million: Dollars spent treating recent veterans with post-traumatic stress disorder during first year of diagnosis. 67: Percentage of Iraq and Afghanistan vets with PTSD who served in the Army. 39: Percentage of Iraq and Afghanistan veterans with alcohol abuse issues. PTSD in the general population