The mini-ITX motherboard of my new home server lacks an "AC power loss restart" feature in the BIOS and in case of UPS shutdown the server won't turn on again after power is restored. Googling around I found that shorting pins 13 and 14 of the ATX connector would do the job, but unfortunately this solution is not praticable in my case because I have a Pico-PSU plugged directly into the ATX power socket and there isn't an ATX cable to hack.
So I came up with my own solution: a capacitor in parallel to the power button which acts like a temporary short when power is restored and is afterwards charged by the pull-up resistor of the power button circuit. A second resistor in parallel to the capacitor allows it to discharge when the AC power is cut and a diode, probably unnecessary, protects the power-on crcuit of the motherboard.
The assembly is a remarkable exercise in minimality: instead of etching some PCB or modifying the power-on cable I soldered the entire circuit on two brass pins which are inserted in the back of the power-on cable connector. You need brass pins because stainless steel pins are impossible or very difficult to solder.