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The first mail  this morning (from Nihar Jindal)  brought this very sad news that Tom Cover has passed away. A giant in this field who contributed immensely to many flavours of Information theory will be missed. Everything he touched had class written all over, gracefulness, simplicity, elegance and all the more depth.

A tremendous loss! His legacy will continue.

I was playing a few tricks on a few centrality measures on a few graphs. SO, thought of penning down a quick piece of notes on the notion of centrality (A quick introduction can be found here along with Wikipiedia page on centrality)

The P versus NP has popped up again in to the mainstream. The HP scientist Vinay Deolaikar has recently prepared a manuscript which claims, it is after all P ≠ NP. Greg’s blog seems to be the one which first broadcasted this to general public. I have not had much time to digest the proof claims or counter arguments in detail. Here is a fascinating series of arguments discussing the proof claims. I am going to do some digesting on this in days to come! We will wait for the experts to have their say. I am going to relish this discussion.

On a lighter note, here is a very interesting blog piece, bringing some sort of similarity to the giant component behaviour on a pile of staple pins. This is sort of a layman view of the Erdos Renyi explanation.

In one version of the Erdős-Rényi process, one start with a set of $n$ isolated vertices and then keep adding random edges one at a time;  More specifically, at each stage one choose two vertices at random from among all pairs that are not already connected, then draw an edge between them. It turns out there’s a dramatic change in the nature of the graph when the number of edges reaches $n/2$ . Below this threshold, the graph consists of many small, isolated components; above $n/2$, the fragments coalesce into one giant component that includes almost all the vertices. “The Birth of the Giant Component” was later described in greater detail in an even bigger paper–it filled an entire issue of Random Structures and Algorithms (1993, 4:233–358)–by Svante Janson, Donald E. Knuth, Tomasz Luczak and Boris Pittel.

Ofcourse Joel Spencer has written a beautiful article on AMS commemurating the golden anniversity of the giant component.

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