At the Johns Hopkins School of Medicine, Alfredo Quiñones-Hinojosa has four positions. He is a neurosurgeon who teaches oncology and neurosurgery, directs a neurosurgery clinic and heads a laboratory studying brain tumors. He also performs nearly 250 brain operations a year. Twenty years ago, Dr. Quiñones-Hinojosa, now 40, was an illegal immigrant working in the vegetable fields of the Central Valley in California. He became a citizen in 1997 while at Harvard.