1. New York Proton Center, 225 E 126th St., New York, NY 10035, USA
2. United Imaging Microelectronics, Shanghai 201807, China
3. Department of Mathematics and Computer Science, College of Arts and Sciences, Adelphi University, One South Avenue, Garden City, NY 11530, USA
4. Department of Radiation Oncology, Johns Hopkins University, 401 North Broadway, Suite 1440, Baltimore, MD 21231, USA