We introduce a simple class of distribution networks that withstand damage by being repairable instead of redundant. Instead of asking how hard it is to disconnect nodes through damage, we ask how easy it is to reconnect nodes after damage. We prove that optimal networks on regular lattices have an expected cost of reconnection proportional to the lattice length, and that such networks have exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks.
This research output has an Altmetric Attention Score of 31. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 08 October 2014.
All research outputs
#1,584,651
of 32,950,213 outputs
Outputs from Physical Review Letters
#4,800
of 50,032 outputs
Outputs of similar age
#14,240
of 284,578 outputs
Outputs of similar age from Physical Review Letters
#57
of 546 outputs
Altmetric has tracked 32,950,213 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 95th percentile: it's in the top 5% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 50,032 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 13.8. This one has done particularly well, scoring higher than 90% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 284,578 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 94% of its contemporaries.
We're also able to compare this research output to 546 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 89% of its contemporaries.
