1. Achille’s Heel

2. An Achilles's heel is a term for a person's weak spot and is based upon the hero who was dipped in the river that granted immortality; however, he was left vulnerable in the area he was held in: his heel.

3. Introduction It is easy to forget how dependent we are on modern technology. To appreciate it, we must witness its occational failure. Summer 1996 failure of power. Repeat of Great Northeast Blackout left for 13 hrs.( 30 million people ) The Electric animal

4. 1996 blackout has highlighted the Underlying vulnerability of this formidable system. When some thing goes wrong, it can cascade through the system. Often ignored property of complex networks :: –Vulnerabilty due to interconnectivity

5. Errors and failures corrupt all human designs. Eg: Car’s Engine But natural systems are Different Species disappeared at a rate of one per million each year.( 3 mil – 100 mil species) No harm, Insensitivity to errors and failures, yucatan Meteorite-Dinosaurs. Eco-system displays tolerance, rarely seen in human made systems. Introduce Robustness-oak(strength and longevity) Achieving robustness is the ultimate goal in interdependent comm systems. Maintain a highdegree of readiness despite errs.

6. Nature strives to acheive robustness through interconnectivity. DARPA-Defense Advanced Research Projects Agency- Study Fault-tolerant N/ws Node Failures can easily break a n/w into isolated non communicating fragments. How long will it take to break when we start removing the nodes randomly? How many routers must we remove from the internet to break it? 80% node removal didnot affect the network connectivity. The Unsuspected robustness against failures is that SFN’s display a property not shared by Random Networks Their wellknown resilence to errors is an inherent property of their topology.

7. What is the source of this amazing topological robustness? Existence of hubs, (the few highly connected nodes). Failures affect small nodes and large hubs with the same probability. 10 red of 10000 white balls Small nodes contribute little to networks integrity Accidental removal of a single hub is not fatal,other hubs manage the integrity. Failures disproportionately affect small nodes. Do all the SFN’s display the same degree of tolerance? For the SFN’s the critical threshold disappears in cases and the degree exponent is smaller or equal to three. Therefore the networks break apart only after all nodes have been removed.

8. The removal of a few hubs broke the internet into tiny, hopelessly isolated pieces. Therefore, the response of SFN’s to attacks is similar to the behavior of random networks under failure. Hidden with their structures, SFN’s harbor an unsuspected Achilles heel, coupling a robustness against failures with vulnerability to attack. Otter-1911, urchins and kelps example. Although SFN’c are vulnerable to attack, several of the largest hubs must be simultaneiously removed to crash them.(5-15%) To disable the several hubs the crackers should disable the several hundred routers first and is very time consuming. Despite its Achilles heel, the internet’s topology harbors strong defense against both random breakdowns and malicious assaults.

9. Cascading Failures Routers do not break down under too mush traffic. They Queue, process and drop the rest. 1996 blackout example. Topological Robustness is a structural feature of networks. Cascading Failures are a dynamic property of complex systems. Ends with ’ there are still undiscovered laws that govern cascading failures.

10. Conclusion The Topology, Robustness, and Vulnerability cannot be fully separated from one another. All complex systems have their Achille’s Heel.