The Department of Transportation will give $40 million to the winning city; Vulcan Inc., a private entity run by Seattle billionaire Paul Allen, has pledged $10 million. Nearly 80 cities applied for the grant. The other finalists are Denver, San Francisco, Portland, Ore., Kansas City, Mo., Columbus, Ohio, and Austin, Texas. Stan Caldwell, a professor of transportation and public policy at Carnegie Mellon University who helped with Pittsburgh’s application, was optimistic about the city’s chances. Cooperation among city and county officials as they finalized Pittsburgh’s proposal gives it an advantage, Caldwell said. “It’s been a very collaborative process,” he said.