Michael M. Danziger Profile picture
Feb 18 β€’ 21 tweets β€’ 13 min read
Paper alert! I'm going to share the story of my paper with @barabasi , "Recovery Coupling in multilayer networks" out today in @NatureComms rdcu.be/cHcDN #networkscience #resilience #research πŸ‘¨β€πŸ”¬πŸ§‘β€πŸ’»A thread.🧡
People have been solving models for interdependent networks for a while. The math is elegant and the models can easily show a plethora of interesting dynamical phenomena. I even wrote a review on the subject link.springer.com/chapter/10.100… #resilience #infrastructure #physics
The trouble is, most models require that a power asset can fail and cause a communication outage AND that a communication outage can cause a power outage. The first is common. The second? Hard to find. Both at once? No one has ever reported it. Image
Does that mean there's no such thing as interdependence? That seems unlikely. Electricity affects other systems but is not acted upon? Maybe? Or maybe just not in the extreme way that existing models assume. Then how? Image
After talking to @DanielPAldrich about disaster recovery amazon.com/dp/0226012883 and reading Sharkey et al's paper about Sandy ascelibrary.org/doi/10.1061/%2… , I learned that a lot of interdependence is slow--days to years. Image
That led me to the idea of recovery coupling. Resilience means not breaking AND bouncing back quickly. Maybe the interactions between networks play a role in the bounce back, and not in the breaking, a more holistic interdependence via recovery processes... Image
Interact via recovery processes? Holistic? That's all well and good for a seance, but this is science man! I learned something important from the disaster researchers, but if I can't connect it to the modeling and data analysis, what's it good for? Image
Let's start simple. Surely we can model a stochastic process of damage and recovery, like Majdandzic et al nature.com/articles/nphys… and my own work nature.com/articles/s4156… in @NaturePhysics, with sometips from @spcornelius, @baruchbarzel and others, voila: recovery coupling! Image
Cool, we have a kawaii model with damage, recovery and interdependence... and we're more or less right where we started: with a toy model that may or may not describe reality because no one can measure anything to adduce evidence for or against it. Why are we doing this again? Image
Vacating in #ABQ, after a beautiful out-of-the-blue thunderstorm, our power went out. Without thinking, I Googled the power company @PNMtalk and checked their outage map--outage! Later, working with @ryanqiwang on our Harvey paper nature.com/articles/s4159… I realized: OUTAGE MAPS!
There are tons of outage maps recording every outage all the time! The power companies publish them so people won't call so much. If I can record them, I'd have a nearly perfect record of all the outages and restoration times, and I could parameterize damage and recovery! Image
Now I've got a new problem. Millions of outages recorded from around the country. Data overload. What am I going to do with all this? xkcd.com/2582
In #physics, we describe materials using stress-strain curves. Actually the word #resilience was first used in science to describe that. What if we use elasticity to analyze this data? #Elastic would mean that the more outages, the more restorations, with a linear relationship. ImageImage
The good news is that US utilities are mostly elastic in their response to outages. BUT when we put them all together we see that they all tend to lose that elasticity when they get a lot of failures. Actually, that's exactly what recovery coupling predicts. Interesting... Image
It's 2019 hurricane season, and I'm watching my outage maps like a hawk. I realize that there are also State DOT maps with flooded roads. When Dorian hit, I was tracking everything I could find. But Dorian was kind of a dud. Then #Imelda came and I was ready. #houston Image
For #Imelda, I watched all the outages AND all the flooded roads. The damage lasted a week. I could geolocate each outage and flooded road and compare the outages near flooded roads from those that were far. The outages closest to the flooded roads lasted MUCH longer. #outages Image
Now we can use elasticity and recovery coupling to analyze a real case in detail. The hypothesis of recovery coupling was not only validated, but we could even point to specific intersections that showed stronger interdependence!
Let's have fun with the model. Make it simple, make it symmetric, solve the equations, simulate the results. What do we see? Recovery coupling alone is enough to cause a total collapse. That's kind of surprising. Image
Recovery coupling is a new lens for understanding network interdependence. We've shown how it fits Infrastructures and disasters. Taneja et al. journals.aps.org/pre/abstract/1… and @DervisVural et al. journals.aps.org/pre/abstract/1… have shown similar results re frailty and aging. What's next?
In the end we did find coupling, but surprisingly, it was in the slower messier processes of recovery and not in the faster processes with wires and switches.
Check out the paper at rdcu.be/cHcDN and the code and data at github.com/mmdanziger/rec… and let me know what you think.

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