Cascading failures in interconnected networks

Wired covers a new article in Nature, investigating massive failures in linked networks.


The interesting thing is that feedback between the connected networks destabilizes the whole:

“When networks are interdependent, you might think they’re more stable. It might seem like we’re building in redundancy. But it can do the opposite,” said Eugene Stanley, a Boston University physicist and co-author of the study, published April 14 in Nature.

The interconnections fueled a cascading effect, with the failures coursing back and forth. A damaged node in the first network would pull down nodes in the second, which crashed nodes in the first, which brought down more in the second, and so on. And when they looked at data from a 2003 Italian power blackout, in which the electrical grid was linked to the computer network that controlled it, the patterns matched their models’ math.


Interestingly, the interconnection alters the relationship between network structure (degree distribution) and robustness:

Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves.


Chalk one up for counter-intuitive behavior of complex systems.

What looks like last year’s version of the paper is on arXiv.

US manufacturing … are you high?

The BBC today carries the headline, “US manufacturing output hits 6 year high.” That sounded like an April Fool’s joke. Sure enough, FRED shows manufacturing output 15% below its 2007 peak at the end of last year, a gap that would be almost impossible to make up in a quarter. The problem is that the ISM-PMI index reported by the BBC is a measure of growth, not absolute level. The BBC has confused the stock (output) with the flow (output growth). In reality, things are improving, but there’s still quite a bit of ground to cover to recover the peak.


In the 80s, my mom had an Audi 5000. It’s value was destroyed by allegations of sudden, uncontrollable acceleration. No plausible physical mechanism was ever identified.

Today, Toyota’s suffering from the same fate. A more likely explanation? Operator error. Stepping on the gas instead of the brake transforms the normal negative feedback loop controlling velocity into a runaway positive feedback:

… A driver would step on the wrong pedal, panic when the car did not perform as expected, continue to mistake the accelerator for the brake, and press down on the accelerator even harder.

This had disastrous consequences in a 1992 Washington Square Park incident that killed five and a 2003 Santa Monica Farmers’ Market incident that killed ten …

Given time, the driver can model the situation, figure out what’s wrong, and correct. But, as my sister can attest, when you’re six feet in front of the garage with the 350 V8 Buick at full throttle, there isn’t a lot of time.

Read more at the Washington Examiner

The Health Care Death Spiral

Paul Krugman documents an ongoing health care death spiral in California:

Here’s the story: About 800,000 people in California who buy insurance on the individual market — as opposed to getting it through their employers — are covered by Anthem Blue Cross, a WellPoint subsidiary. These are the people who were recently told to expect dramatic rate increases, in some cases as high as 39 percent.

Why the huge increase? It’s not profiteering, says WellPoint, which claims instead (without using the term) that it’s facing a classic insurance death spiral.

Bear in mind that private health insurance only works if insurers can sell policies to both sick and healthy customers. If too many healthy people decide that they’d rather take their chances and remain uninsured, the risk pool deteriorates, forcing insurers to raise premiums. This, in turn, leads more healthy people to drop coverage, worsening the risk pool even further, and so on.

A death spiral arises when a positive feedback loop runs as a vicious cycle. Another example is Andy Ford’s utility death spiral. The existence of the positive feedback leads to counter-intuitive policy prescriptions: Continue reading “The Health Care Death Spiral”

The Dynamics of Science

First, check out SEED’s recent article, which asks, When it comes to scientific publishing and fame, the rich get richer and the poor get poorer. How can we break this feedback loop?

For to all those who have, more will be given, and they will have an abundance; but from those who have nothing, even what they have will be taken away.
—Matthew 25:29

Author John Wilbanks proposes to use richer metrics to evaluate scientists, going beyond publications to consider data, code, etc. That’s a good idea per se, but it’s a static solution to a dynamic problem. It seems to me that it spreads around the effects of the positive feedback from publications->resources->publications a little more broadly, but doesn’t necessarily change the gain of the loop. A better solution, if meritocracy is the goal, might be greater use of blind evaluation and changes to allocation mechanisms themselves.


The reason we care about this is that we’d like science to progress as quickly as possible. That involves crafting a reward system with some positive feedback, but not so much that it easily locks in to suboptimal paths. That’s partly a matter of the individual researcher, but there’s a larger question: how to ensure that good theories out-compete bad ones?


Now check out the work of John Sterman and Jason Wittenberg on Kuhnian scientific revolutions.

Update: also check out filter bubbles.

Hadley cells for lunch

quinoa convection

At lunch today we were amazed by these near-perfect convection cells that formed in a pot of quinoa. You can DIY at NOAA. I think this is an instance of Benard-Marangoni convection, because the surface is free, though the thinness assumptions are likely violated, and quinoa is not quite an ideal liquid. Anyway, it’s an interesting phenomenon because the dynamics involve a surface tension gradient, not just heat transfer. See this and this.

The side effects of parachuting cats

I ran across a nice factual account of the fantastic “cat drop” story of ecological side effects immortalized in Alan Atkisson’s song.

It reminded me of another great account of the complex side effects of ecosystem disturbance, from the NYT last year, supplemented with a bit of wikipedia:

  • In 1878, rabbits were introduced to Macquarie Island
  • Also in the 19th century, mice were inadvertently introduced
  • Cats were subsequently introduced, to reduce mouse depredation of supplies stored on the island
  • The rabbits multiplied, as they do
  • In 1968, myxoma virus was released to control rabbits, successfully decimating them
  • The now-hungry cats turned to the seabird population for food
  • A successful campaign eradicated the cats in 1985
  • The rabbits, now predator-free, rebounded explosively
  • Rabbit browsing drastically changed vegetation; vegetation changes caused soil instability, wiping out seabird nesting sites
  • Other rodents also rebounded, turning to seabird chicks for food

An expensive pan-rodent eradication plan is now underway.

But this time, administrators are prepared to make course corrections if things do not turn out according to plan.“This study clearly demonstrates that when you’re doing a removal effort, you don’t know exactly what the outcome will be,” said Barry Rice, an invasive species specialist at the Nature Conservancy. “You can’t just go in and make a single surgical strike. Every kind of management you do is going to cause some damage.”

Maya fall to positive feedback

NASA has an interesting article on the fall of the Maya. NASA-sponsored authors used climate models to simulate the effects of deforestation on local conditions. The result: evidence for a positive feedback cycle of lower yields, requiring greater deforestation to increase cultivated area, causing drought and increased temperatures, further lowering yields.

Mayan vicious cycle


“They did it to themselves,” says veteran archeologist Tom Sever.

A major drought occurred about the time the Maya began to disappear. And at the time of their collapse, the Maya had cut down most of the trees across large swaths of the land to clear fields for growing corn to feed their burgeoning population. They also cut trees for firewood and for making building materials.

“They had to burn 20 trees to heat the limestone for making just 1 square meter of the lime plaster they used to build their tremendous temples, reservoirs, and monuments,” explains Sever.

“In some of the Maya city-states, mass graves have been found containing groups of skeletons with jade inlays in their teeth – something they reserved for Maya elites – perhaps in this case murdered aristocracy,” [Griffin] speculates.

No single factor brings a civilization to its knees, but the deforestation that helped bring on drought could easily have exacerbated other problems such as civil unrest, war, starvation and disease.

An SD Conference article by Tom Forest fills in some of the blanks on the other problems:

… this paper illustrates how humans can politically intensify resource shortages into universal disaster.

In the current model, the land sector has two variables. One is productivity, which is exhausted by people but regenerates over a period of time. The other… is Available Land. When population exceeds carrying capacity, warfare frequency and intensity increase enough to depopulate land. In the archaeological record this is reflected by the construction of walls around cities and the abandonment of farmlands outside the walls. Some land becomes unsafe to use because of conflict, which then reduces the carrying capacity and intensifies warfare. This is an archetypal death spiral. Land is eventually reoccupied, but more slowly than the abandonment. A population collapse eventually hastens the recovery of productivity, so after the brief but severe collapse growth resumes from a much lower level.

The key dynamic is that people do not account for the future impact of their numbers on productivity, and therefore production, when they have children. Nor does death by malnutrition and starvation have an immediate effect. This leads to an overshoot, as in the Limits to Growth, but the policy response is warfare proportionate to the shortfall, which takes more land out of production and worsens the shortfall.

Put another way, in the growth phase people are in a positive-sum game. There is more to go around, more wealth to share, and population increase is unhindered by policy or production. But once the limits are reached, people are in a zero-sum game, or even slightly negative-sum. Rather than share the pain, people turn on each other to increase their personal share of a shrinking pie at the expense of others. The unintended consequence-the fatal irony-is that by doing so, the pie shrinks much faster than it would otherwise. Apocalypse is the result.

Making climate endogenous in Forest’s model would add another positive feedback loop, deepening the trap for a civilization that crosses the line from resource abundance to scarcity and degradation.

Dynamic Drinking

Via ScienceDaily,

A large body of social science research has established that students tend to overestimate the amount of alcohol that their peers consume. This overestimation causes many to have misguided views about whether their own behaviour is normal and may contribute to the 1.8 million alcohol related deaths every year. Social norms interventions that provide feedback about own and peer drinking behaviours may help to address these misconceptions.

Erling Moxnes has looked at this problem from a dynamic perspective, in Moxnes, E. and L. C. Jensen (in press). “Drunker than intended; misperceptions and information treatments.” Drug and Alcohol Dependence. From an earlier Athens SD conference paper,

Overshooting alcohol intoxication, an experimental study of one cause and two cures

Juveniles becoming overly intoxicated by alcohol is a widespread problem with consequences ranging from hangovers to deaths. Information campaigns to reduce this problem have not been very successful. Here we use a laboratory experiment with high school students to test the hypothesis that overshooting intoxication can follow from a misperception of the delay in alcohol absorption caused by the stomach. Using simulators with a short and a long delay, we find that the longer delay causes a severe overshoot in the blood alcohol concentration. Behaviour is well explained by a simple feedback strategy. Verbal information about the delay does not lead to a significant reduction of the overshoot, while a pre test mouse-simulator experience removes the overshoot. The latter policy helps juveniles lessen undesired consequences of drinking while preserving the perceived positive effects. The next step should be an investigation of simulator experience on real drinking behaviour.