I really liked "The Housekeeper and the Professor" by Yoko Ogawa. Maybe its not exactly what you were looking for since the math is pretty simple and is not the sole focus of the story, but the story itself is excellent and its hard not to read the book without being inspired by how beautiful mathematics is.
The headline was a bit misleading. You still can't measure a quantum state without having its superposition collapse to what was measured. If I understand what the article is saying properly, these scientists are not able to peak into the box to measure "Schrodinger's Cat's" state of aliveness, but they can still peak to see if the cat is a tabby or a calico. If fur pattern isn't a good quantum number, then that will cause the "cat" to change its spots, but later probes can be used to nudge it back to its original state. Meanwhile, you haven't disturbed the "cat's" aliveness or deadness. The important part seems to be being able to "nudge" certain states with probes to get some information out of the system without really changing it.
There are a lot of intermediate isotopes from the main uranium fission reaction in the spent fuel rods and although the main reaction can not take place because the storage geometry they still produce heat from those secondary reactions. That heat is a small fraction of that from the main reaction that runs a nuclear power plant, but it still must be carried away somehow or the spent fuel rods can get extremely hot. They are put into a large amount of water in a system which has a heat exchanger for several years until these secondary reactions have become so weak that there is no risk of damaging them anymore. They are then sent to dry storage. The problem with transporting them off-site at the beginning is that you *must* have a large amount of water covering them both to dissipate heat and to block radiation. Its very difficult to transport them when they need to be in so much water during the entire transportation process. As a result they are usually stored on site. I think the reason why they are on the roof of the Fukushima Daiichi reactors is because they can then lift the spent fuel rods with a crane on the roof and move them directly to storage very quickly without the risks involved in transporting them to a location somewhere else across the plant.
It is kind of a interesting paper, but how in the world did it get into Physical Review? Just because you do some statistics doesn't mean you are doing research in physics. Shouldn't this have been sent to a sociology journal?