Unemployment rates are down in the Hudson Valley, the state Labor Department announced Tues., Oct. 23. The jobless rate fell from 9.1 percent to 8.9 percent in Greene County, and from 7.8 percent to 7.4 percent in Columbia, from Aug. 2011 to Sept. 2012, the department said. Rates fell in Delaware, Dutchess and Ulster, as well. The lowest unemployment rates statewide were reported in Tompkins and Hamilton counties; the highest, in Bronx and Fulton counties. The state's overall unemployment rate fell in September, and the number of initial claims for unemployment insurance decreased during that time period.