So what exactly does Scuderi's concept involve? I think it's best shown via an animation or a walk though the company's full theory of operation, but if forced to put it into a few words, I'd describe this as a Miller-cycle engine that uses half of the engine's cylinders to provide mechanical supercharging. So, what are the advantages of this combustion cycle? Well essentially, it aims to do what any refinement of the Otto cycle wishes to achieve - higher peak pressure, and lower post-combustion pressures. If we look at this graph of the cycle to the left, it's advantageous to increase the height of points 3 and 4 while decreasing the height of point 5 and 6 (and the closer we can gets points 5 and 6 to each other, the more energy we extract from the fuel).
Specifically, Scuderi's cycle is much like the Miller cycle in that it attempts to delay the opening of the exhaust valve as much as possible to take full advantage of the expanding combustion gases. Traditionally, the Miller cycle -completely unrelated to Miller Time, by the way - uses a mechanical supercharger to prevent reversion of the exhaust gases into the intake tract. Scuderi uses the compression cylinder and a poppet valve and check valve arrangement in the crossover passage to the same effect.
Additionally, Scuderi claims that the mixture has a much faster burn rate, and can be ignited at or just after top dead center (TDC). Typical Otto cycle engines touch off the mixture 30-40 degrees before TDC, and thus there is some counterproductive use of the mixture as it starts to expand while the piston is still attempting to compress it. Because of this, there's also said to be a decrease in the oxides of nitrogen (NOx) emissions. Since preignition is less of a concern, the compression ratio can be increased as well.
Scuderi claims that, despite the use of half the cylinders for compression, the engine is more efficient and powerful than a traditional Otto cycle engine of the same displacement and cylinder count. I have no way of personally verifying these claims, so we'll just have to wait and see what the outcome is of the company's DoD contract win.