SHANGHAI — U.S. Secretary of State Hillary Clinton this week has embarked on her first overseas trip to Asia as America's chief diplomat. While the leadership in all four capitals she visits are eager to gauge the pulse of the new U.S. government, Beijing is probably more anxious to figure out the Obama administration's thinking on China and its vision of U.S.-China relations, a subject that was substantively absent from the runup to last year's presidential election.