Can a brain live for a minute after decapitation?

Since I was a kid, I've been fascinated by 19th century guillotine anecdotes about severed heads winking, attempting to speak, or smiling. The "Guillotine" entry in Wikipedia has a section on "Living heads" and The Straight Dope has investigated the topic as well. And now, two new scientific studies also push on the question of whether the brain is still "alive" after decapitation. From Science News (painting by Francisco de Goya):
 Wikipedia Commons 9 9A Francisco De Goya - The French Penalty Almost a minute after a rat’s head is severed from its body, an eerie shudder of activity ripples through the animal’s brain. (Research published in January by Radboud University Nijmegen neuroscientists suggest that this) post-decapitation wave marks the border between life and death. But the phenomenon can be explained by electrical changes that, in some cases, are reversible, researchers (from the University of Twente in Enschede, the Netherlands) report online July 13 in PLoS ONE.

Whether a similar kind of brain wave happens in humans, and if so, whether it is inextricably tied to death could have important implications. An unambiguous marker could help doctors better decide when to diagnose brain death, knowledge that could give clarity to loved ones and boost earlier organ donation.

"'Wave of death' may not be a last gasp"