12.10 - Touchscreen and digitizer not working on Sony Vaio Duo 11

I have a Sony VAIO Duo 11 (SVD112...) which features both multi-touch and stylus input. However, booting up Ubuntu 12.10 gives me

• no stylus reaction


• touch input works very strange: when I touch with 1-3 fingers, usually nothing happens but sometimes there is some reaction


• when I tap the screen with 4 fingers, the dash shows up, consistently

Where can I start to find out the underlying issue and how to fix it?

EDIT: On Ubuntu 12.04.1 the touchscreen isn't recognized at all.

EDIT2: On Fedora 18, the touchscreen works a little bit better. I have found out that the USB ID of the touchscreen is not contained in the hid-ntrig module, so that's probably why some of the quirks needed for it are not appplied.