The document discusses a randomized controlled trial that found 40 minutes of walking 2-3 times per week led to increased brain volume in adults aged 65-67 years old. It also summarizes several studies that found aerobic fitness is positively associated with academic performance and brain activity, while BMI is negatively associated. Aerobic exercise interventions in children led to increased fitness, cognitive test performance, attention, cognitive flexibility, and brain activity related to executive control. The mechanisms by which exercise impacts the brain include increased neurogenesis, BDNF expression, and cell proliferation. BDNF levels increase acutely with exercise in a dose-response manner related to intensity and duration. Exercise training can lead to long-term brain changes and improvements in learning and memory