Complex Systems Summer School 2011-Challenge Questions
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|Complex Systems Summer School 2011|
2011 Complex Systems Summer School Challenge Questions:
Nonlinear Dynamics and Modeling
Given that the brain is a deterministic physical system, is there such a thing as free will?
This challenge is to design a network to be robust against the failure of its nodes. You get 1000 nodes and 2000 edges, which you can join together into a network in any fashion you like. You can think of it as a communication network, for instance. The nodes in the largest component of the network can all communicate with one another, while the rest of the network is cut off. Once you have designed your network, a quarter of the nodes fail at random and are removed from the network. The challenge is to design your network so that, on average, as many nodes as possible still remain in the largest component of the network. You don't know in advance which quarter of the nodes will fail, so you need a design that works well in general. If you can find a good solution to this problem, here are two further variations you could think about:
1. Instead of randomly removing a quarter of the nodes, suppose the quarter with the highest degrees are removed. Now how should you design your network?
2. Now suppose, with equal probability, EITHER a quarter of the nodes fail at random OR the highest-degree quarter fail. Can you design a network that is resilient to both, without knowing in advance which will happen?
In the 19th century, we thought of everything as a steam engine. In the late 20th century, we thought of everything as a computer, and around the turn of the century, as an ecology or an economy. How do each of these metaphors help us understand the world around us, including natural, social, and artificial systems? What aspects of these systems do each of these analogies help make clearer, and which aspects do they obscure?
Write a script/screen play for an episode of Star Trek (TNG or the original series) in which robustness is the central issue. The episode should be no more than ten minutes long and you should be prepared to perform it on the final day of the CSSS. We leave it up to you to decide whether there will be multiple team entries or just one whole CSSS team entry!
1.) Has Biological Evolution come to an end?
2.) Is belief an emergent property?
3.) Will advanced computers use H. Sapiens as batteries?
Short-term survival and an exuberant plunge into building our future are generating a new kind of unintended consequence—hidden fragility. This is a direct effect of the sophistication and structural complexity of the socio-technical systems humans create. It is inevitable. And so the challenge is, How much can we understand and predict about these systems and about the social dynamics that lead to their construction?
What are the emergent phenomena associated with democratic rule? Answer by contrasting reference to the results of the 2000 and 2008 U.S. Presidential elections. Support your hypothesis with either contrasting mathematical models, or analysis of relevant data.