[POLITICO] Former Rep. Anthony Weiner, whose career in public life came to an abrupt end when he sent lewd pictures to a college student on Twitter, jumped back into politics on Wednesday by announcing a bid for mayor of New York City."Look, I've made some big mistakes and I know I've let a lot of people down," the Democrat said in a two-minute video announcing his bid. "But I've also learned some tough lessons. I'm running for mayor because I've been fighting for the middle class and those struggling to make it for my entire life. And I hope I get a second chance to work for you."