Comments for Big Red Bits

Comment on MHR, Regular Distributions and Myerson’s Lemma by Reshef

Reshef — Tue, 01 Jan 2013 11:25:10 +0000

Hi Renato, nice summary!
here are some question:
suppose we have some variables x ~ D1, y ~ D2 where D1 and D2 are m.h.r. distributions.
Seems that any linear transformation of x is still m.h.r.
- How about x+y when x,y are independent?
- What if x,y, are correlated?
- What about the same questions when D1,D2 are regular (not necessarily m.h.r.)?

Comment on Reasoning about Knowledge by Paper Trail » Blog Archive » Links

Paper Trail » Blog Archive » Links — Mon, 06 Aug 2012 21:05:53 +0000

[...] Reasoning about Knowledge [...]

Comment on Reasoning about Knowledge by Guilherme De Napoli

Guilherme De Napoli — Sat, 23 Apr 2011 06:32:20 +0000

The puzzle is REALLY non-trivial. I’ve spent far too much time trying to decide how the mere fact of someone DECLARING that someone has blue eyes (something everyone already knows) starts a logical “domino effect” that ends up killing every blue-eyed person (I’m convinced that the second answer is the right one, although I’m far from knowing how to prove it).

You, sir, have just destroyed my day.

…Just kidding, I loved the puzzle! I just hope I can forget about it soon =)

Comment on Submodular Allocation Problem by Ashwin

Ashwin — Thu, 07 Apr 2011 18:00:43 +0000

Actually 1-1/e is known even for value queries(http://www.math.princeton.edu/~jvondrak/data/submod-value.pdf). For demand queries even better than 1-1/e is known(http://www.math.princeton.edu/~jvondrak/data/submod-improve-ToC.pdf).

Comment on Happy Perihelion by SOS LED 1.0 released for iPhone 4 – More than a Handy Flashlight | Apple News, Rumors and Reviews, iPhone Reviews, iPad Rumors, iMac Applications

Sat, 07 Aug 2010 09:21:27 +0000

[...] Big Red Bits » Happy Perihelion [...]

Comment on Duality Theorem for Semidefinite Programming by renatoppl

renatoppl — Thu, 10 Jun 2010 02:35:08 +0000

Thanks, Ives. I am trying to make the changes, but all the time I make them, I loose all the formatting in the post. Let me try to figure out how to do that without loosing formatting.

Comment on Duality Theorem for Semidefinite Programming by Ives Macedo

Ives Macedo — Tue, 18 May 2010 04:46:09 +0000

Renato, I found some very simple mistakes and typos.
Typos first: “inomogeneous” both in Theorem 5 and the Strong Duality proof of Theorem 7 should read “inhomogeneous”.
Now, the simple mistakes: in the convex separation Theorem 3, v should be nonzero, for that reason, in both versions of Farkas’ Lemma, Y is also supposed to be nonzero. The slightly trickier mistake is that you haven’t proved that the problems in Farkas’ Lemma can’t both be solved at the same time (actually, without the nonzero hypothesis, Y=0 is a solution for both versions of problem 2). Assuming Y nonzero in problem 2, you can prove the alternative by taking two solutions x and Y for 1 and 2, taking the dot product between Y and 1, using the equalities in 2, and arriving at a contradiction by noticing that the dot product between a nonzero psd matrix and a pd matrix is strictly greater than zero (this can be deduced by inspecting the proof of Theorem 6).

Congrats for the nice post, my friend!

Comment on Cayley-Hamilton Theorem and Jordan Canonical Form by renatoppl

renatoppl — Fri, 19 Feb 2010 19:06:39 +0000

Thanks for the comment. I think it is actually the same proof, but you are hiding the Jordan Canonical Form in the concept of generalized eigenvectors.

Comment on Cayley-Hamilton Theorem and Jordan Canonical Form by Jorge Miranda

Jorge Miranda — Fri, 19 Feb 2010 18:56:44 +0000

I think it’s even easier than that using the Jordan Canonical Form.

The idea is that $p_A(A)=(A-\lambda_1I)…(A-\lambda_nI)$. If we compute $p_A(A)v$ for any $v$ that is a generalized eigenvector $p_A(A)v=0$ because we have enough factors in $p_A(A)$ to use that $(A-\lambda_iI)^kv=0$.

Since the generalized eigenvectors are a basis, we conclude that $p_A(A)v=0$ for any $v$, and that means that $p_A(A)=0$ as we wanted to prove.

Still, neat proof

Comment on Bounded Degree Spanning Tree and an Uncrossing Lemma by Ashwin

Ashwin — Wed, 18 Nov 2009 05:38:19 +0000

I was thinking about minimizing the number of violated degree constraints(with the restriction that we have that each degree bound is violated by atmost one). It looks to me that any bound of o(n) will imply a \omega(log(n)) approximation algorithm for the longest path problem when the graph has hamiltonian path. Any thoughts about this?

Comment on Competitive Auctions by Big Red Bits » More about hats and auctions

Big Red Bits » More about hats and auctions — Thu, 29 Oct 2009 05:43:01 +0000

[...] this blog post, I discussed the concept of truthful auction. If an auction is randomized, an universal truthful [...]

Comment on Hats, codes and puzzles by Big Red Bits » More about hats and auctions

Big Red Bits » More about hats and auctions — Thu, 29 Oct 2009 05:41:57 +0000

[...] my last post about hats, I told I’ll soon post another version with some more problems, which I ended up not doing [...]

Comment on Duality Theorem for Semidefinite Programming by tarun

tarun — Mon, 26 Oct 2009 13:31:48 +0000

i dont know its usefull or nt 4 u

Comment on Duality Theorem for Semidefinite Programming by renatoppl

renatoppl — Wed, 12 Aug 2009 04:58:33 +0000

Nice you liked. Thanks for pointing me the typos, Igor. I already corrected them.

Comment on Duality Theorem for Semidefinite Programming by Igor

Igor — Tue, 11 Aug 2009 18:51:03 +0000

Great stuff, Renato – I can see you’re doing your homework on SDP. Small typo in Thm 3: one of the inequalities should be reversed.

Comment on Eigenvectors and communities by Big Red Bits » More on eigenvalues and social networks

Big Red Bits » More on eigenvalues and social networks — Thu, 30 Jul 2009 02:32:55 +0000

[...] to , it must also represent a good partition of the graph. Therefore I ploted the same graph as in my last post but associating each node with the coordinates where $x_i$ is the eigenvector corresponding to [...]

Comment on Prisioners and boxes by renatoppl

renatoppl — Thu, 23 Jul 2009 03:04:39 +0000

Cool! Nice you liked the book. It was the last good mystery novel I read. I am waiting for the sequence, but it wasn’t released here yet, what is strange because I think the second was already released in Brazil.

Those proofs by the probabilistic method are awesome. I remember of seeing a couple of them by Erdös — he was one of the main persons responsible for making it popular. One interesting problem is to try to give deterministic constructive proofs for them. The STOC best paper award this year was for a beautiful deterministic construction of the Lovasz Local Lemma: http://arxiv.org/abs/0810.4812

Comment on Prisioners and boxes by Ítalo

Ítalo — Wed, 22 Jul 2009 20:15:21 +0000

Hello Renato!
Very nice blog! Parabéns!
I remember the day I first saw a proof using the probabilistic method. Although I can’t remember the problem/proof, I do remember that was one solved by Erdös himself. I got completely astonished by the elegance of the proof. It’s a really simple idea, yet a really, really powerful tool.

I’ve started reading “The girl with the dragon tattoo” following your recommendation on your other blog. I’m enjoying it.
Best,
Ítalo.

Comment on The Obligatory Hello World! by renato

renato — Fri, 05 Jun 2009 02:52:44 +0000

Now I can also post on comments, as for example, the Jensen’s inequality: for convex .

Comment on The Obligatory Hello World! by renato

renato — Thu, 04 Jun 2009 04:22:04 +0000

I am glad C came first.