Multiple Cold Cathodes with Diming

hello.

This is my first time to use a cold cathodes lightings. The cold cathodes I have is 2 lightings + 1 inverter = 1 set and, I want to control the dimming and powering 4 sets (total 8 cold cathodes and 4 inverters) all together. Since 1 set supposed to connect 1 AC/DV 12V adapter, I wonder if I can connect 4sets with one power adapter. Also, one arduino and dimming circuit between dc adapter and a connector from all inverters. The company suggests use 5amps adapter for 4 sets connection. (2amps for 1 set)

I have not tried dimming cold cathodes, only incandescent with PWM dimmer. I am going to connect a 'ultrasonic distant sensor' to brightens and dims the lights.

without the sensor : http://vimeo.com/6560599

Will I not require external dimmer, but with the breadboard circuit? what schematic should I look into? with the sensor? Will this work?

thank you.