You do not usually need to notify a function that there has been an update.
If the function runs once and stops, then you would update the variables that the function uses to do its computation.
http://matlab.wikia.com/wiki/FAQ#How_can_I_share_data_between_callback_functions_in_my_GUI.28s.29.3F
If the function is running in a loop, then it would need to have a pause() or drawnow() to permit itself to be interrupted by a callback . If it is using shared variables then it might need to update any deliberately remembered version of a shared variable, but more often it would just use the shared variable and immediately get the updated version. If the looping function is using values associated with a GUI, such as the choice of selection from a popup list, then after it calls pause() or drawnow() it should fetch the current value of the GUI element it is relying on.
If you have a function that looks at the current values of variables and updates something on the screen, then you can have the callback that updates the variables call the function directly.
[...]
handles.EditBox1.String = num2str(NewLatitude);
update_subway_map(hObject, [], handles) %call the update function directly
