The second day.

The first talk was by Nitin. Some basic knowledge about wireless networks - however, it is completely new to me.

Then, Dina Katabi gave a talk about network coding, actually mainly about her recent sigcomm papers. Her talk was very light and easy to follow. Some gossip:). There was post a while ago on mitbbs computer science board. The post raised the following "interesting" question "who is the prettiest cs phd female student you've even seen." Many candidates were proposed and numerous argument ensued , google photo search was extensively used, personal stories one after another, ppl's aesthetics tastes were questioned.......it was a mess all in all. Nevertheless, Dina was consensusly aknowledged as one of the prettiest! I have to say i sat pretty far from her and wouldn't be able to personally justify this claim..:P

I slept over the second network coding talk.

In the afternoon, P.R.Kumar gave a very good talk on the QoS scheduling(this paper). The model proposed is fairly clean and a surprisingly neat neccessary and sufficient condition was proven. The analysis is a ECE type analysis rather the worst case analysis which TCS community usually adopted. In the proof, a very interesting theorem, called blackwell approachability theorem, was used. It was the first time I saw this theorem and it seems to be a pretty useful theorem. The theorem basically describes as follows:

We have a game that goes in iterations. in each iteration t, we can take some action a(t) and will
get a reward v(t).

v(t) is a n-dim random vector s.t.
(1) its distrbution depends only on a(t)
(2) Mean = R(a) (R(a) is a vector)

Let A be a close set in R^n.
We say A is approachable if there is some policy (strategy of taking actions) s.t.
the time average of rewards (\sum_{t\in T}v(t)*(1/T)) will come arbitrarily close to A (or in A) for enough number of iterations with arbitrary high prob.

The Blackwell thm says that
for any x\notin A, if there is an action a with R(a) lies on the other side of the hyperplane H
that passing through the point of A closest of x and perpendicular to line xy
then A is approachable.