Of  Center for Advanced Studies in Engineering and University of Idaho which, if either, is a public university?
University of Idaho The University of Idaho (officially abbreviated UI, locally referred to as "the U of I") is the U.S. state of Idaho's oldest public university, located in the city of Moscow in Latah County in the northern portion of the state. It is the state's flagship, land-grant and primary research university. The University of Idaho was the state's sole university for 71 years, until 1963, and its College of Law, established in 1909, was first accredited by the American Bar Association in 1925.
University of Alabama at Birmingham The University of Alabama at Birmingham (UAB) is a public research university in Birmingham in the U.S. state of Alabama. Developed from an academic extension center established in 1936, the institution became an autonomous institution in 1969 and is today one of three institutions in the University of Alabama System and the only R1 research institution in the state. In the fall of 2015, 19,656 students from more than 110 countries were enrolled at UAB pursuing studies in 140 programs of study in 12 academic divisions leading to bachelor's, master's, doctoral, and professional degrees in the social and behavioral sciences, the liberal arts, business, education, engineering, and health-related fields such as medicine, dentistry, optometry, nursing, and public health.