Mr. Bloomberg’s gift is the latest by a wealthy American business figure that is focused on health research. Other recent gifts include $250 million from internet entrepreneur Sean Parker to establish the Parker Institute for Cancer Immunotherapy at six major research centers; $185 million from banker and philanthropist Sanford Weill to the University of California, San Francisco for a new institute for neurosciences; and $500 million from Nike Inc. co-founder Phil Knight to Oregon Health & Science University for cancer research.