Achilles in Biology

(from http://www.podiatrychannel.com/anatomy/)

Achilles in Mythology
Achilles, son of the mortal Peleus, king of the Myrmidons, and the Nereid, or sea nymph, Thetis. He was the bravest, handsomest, and greatest warrior of the army of Agamemnon in the Trojan War.

Picture: Achilles and Hector during the trojan war.

(from http://www.britannica.com/eb/article?eu=3568 and http://www.cin.butte.cc.ca.us/~tben/greece/achilles.gif )

Achilles' Heel of the Internet

Cover story on 27 July 2000 issue of Nature

(from http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v406/n6794/abs/406378a0_fs.html)

The robustness of a complex system against errors and failures can be tested by investigating the effect of removing nodes. (a) Removing the circled nodes causes the network to break into several smaller clusters. (b) The largest cluster decreases in size from 22 nodes to seven when we disconnect three, i.e. 14%, of the nodes. (c) Percolation theory predicts that a random network will break into tiny clusters when a critical fraction, f_c, of nodes is removed. This prediction does not hold for scale-free networks as can be shown by plotting the of size of the largest cluster versus the fraction of nodes removed. Calculations show that the cluster size only falls to zero when all the nodes have been disconnected (green). However, if the most-connected nodes are removed then the scale-free network will break at a small f_c. (d) By randomly removing domains from the Internet, we found that more than 80% of the nodes have to fail before the network fragments (green). However, if hackers targeted the most connected nodes (red), then they could achieve the same effect by removing a small fraction of the nodes.
(from http://www.physicsweb.org/box/world/14/7/9/pw1407094)

Prof. Shlomo Havlin, , who, together with Reuven Cohen, Keren Erez and Daniel ben-Avraham have shown that for scale-free networks the percolation threshold is zero. See REF. Similar results were obtained independently by Callaway et al [REF].

(from http://ory.ph.biu.ac.il/~havlin/)

Prof. Ricard V. Sole,
at University Politecnica de Catalunya in Barcelona, who have shown, together with Jose Montoya, the ecosystems can easily survive species deletions [Ref].

(from http://complex.upc.es/~ricard/)