Technological advancements won’t do anything to stop pilots from suddenly falling ill, collapsing and even dying while flying. This does happen and so it would never really be safe for widespread commercial flights to be flown with one member of flight crew, regardless of the technology on board.

Certainly it does.

How frequent, in the fields where single pilots now fly (private planes and small commercial planes) are crashes due to solo pilot illness, as opposed to crashes due to solo pilot being overwhelmed and distracted by flying duties, or making stupid errors that a copilot would have corrected?

Cseries about to freeze!

Due to freeze in July:
http://www.flightglobal.com/articles/2010/06/11/343204/bombardier-to-freeze-cseries-design-next-month.html

Vmcg is estimated base on weight and selected takeoff thrust. The definition of Vmcg is the minimum speed an aircraft can maintain directional control on the runway using rudder only at takeoff thrust. On a derated takeoff all v-speeds are calculated based on that selected takeoff thrust, the current weight of the aircraft and pressure altitude, that includes Vmcg if an aircraft has one. For a given weight the value of all v-speeds will vary depending on the selected takeoff thrust setting and temp/altitude.

The use of the remaining available thrust after an engine loss has no impact on Vmcg. Vmcg can’t exceed V1 and any emergency situation prior to V1 requires aborting the takeoff and not flying. In other words, once the takeoff is aborted that excessive thrust will never be applied no matter what takeoff thrust setting that was selected.

So, suppose that a takeoff thrust is selected, lower than the available emergency thrust, Vmcg is lowered based on the selected takeoff thrust and V1 is lowered accordingly, so that it is bigger than Vmcg for selected takeoff thrust, but lower than what Vmcg had been for available emergency thrust.

And right after V1 – still below what Vmcg had been for available emergency thrust – one engine fails.

What thrust will then be applied by the remaining engine – the selected takeoff thrust, or the available emergency thrust?

You’ve answered your own question and probably don’t realize it. Derated takeoffs extend the life of the engine but don’t change the amount of available thrust in an emergency situation.

What exactly do paper derates do to the Vmcg?

Shouldn’t this be in Commercial, for what it’s worth.

What does this have to do with Commercial? It is a dedicated VIP plane of no commercial use. Whether Catherine Ashton ends up with Socata TBM850 or an Airbus 380, it is general aviation.

Hopefully it will see additional orders soon.

It has. Republic airways. 40 firm orders, 40 options for CS300. Single class interior, 138 seats.