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A Cascadic...Algorithm...Computing the Fiedler Vector of Graph Laplacians (Urschel NFL Ravens)
arXiv ^ | 3-17-15 | John Urschel

Posted on 03/17/2015 6:47:36 PM PDT by FlJoePa

In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.


TOPICS: Education; Miscellaneous; Sports
KEYWORDS: nfl
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Raven fans are really going to love John Urschel. He spends a lot of time with kids and math. Great guy.
1 posted on 03/17/2015 6:47:36 PM PDT by FlJoePa
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To: FlJoePa
Even if you are not a mathematician, you can always have a look at some nice drawings here. And remember about this class of problems whenever you ask your GPS to calculate a route :-) The road network is one of most obvious examples of a graph.
2 posted on 03/17/2015 6:53:49 PM PDT by Greysard
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To: FlJoePa

Well, of course it’s easy if you use a cascadic multigrid algorithm. :=)

A what?


3 posted on 03/17/2015 6:55:22 PM PDT by Bob (Violence in islam? That's not a bug; it's a feature.)
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To: FlJoePa
cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue

Gesundheit

4 posted on 03/17/2015 6:58:55 PM PDT by doc1019 (Blue lives matter)
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To: All

BTW, the reason I posted this is because he just tweeted that it had been published today. He played in his first chess tournament a couple of weekends ago in Pittsburgh.


5 posted on 03/17/2015 6:59:43 PM PDT by FlJoePa
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To: FlJoePa

I’m lost. Did I stumble into the wrong forum? How does this algorithm help us defeat Dems and elect Ted Cruz as President? Is it some sort of special sauce that increases GOPe backbone?


6 posted on 03/17/2015 6:59:44 PM PDT by InterceptPoint (>http://rss.cnn.com/rss/cnn_topstories.rss)
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To: FlJoePa

Can you say “Fiedler vector” on a family forum?


7 posted on 03/17/2015 7:04:08 PM PDT by sphinx
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To: Bob

Exactly my comment. Felt like Penny, on The Big Bang Theory, when reading this!


8 posted on 03/17/2015 7:04:29 PM PDT by Red_Devil 232 ((VietVet - USMC All Ready On The Right? All Ready On The Left? All Ready On The Firing Line!))
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To: FlJoePa

Interesting. I was just thinking about this the other day while trimming my toenails.


9 posted on 03/17/2015 7:04:42 PM PDT by smokingfrog ( sleep with one eye open (<o> ---)
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To: Greysard

By all means, read (or scan) the paper. It’ll help you see how information technology is and will be used for social engineering.


10 posted on 03/17/2015 7:06:00 PM PDT by 9thLife ("Life is a military endeavor..." -- Pope Francis)
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To: InterceptPoint

Not sure. It was posted in general chat. Do the poetry readings and music contests posted in chat help in that regard?

John Urschel is a very smart guy and spends a lot of time going to schools teaching math to kids. This isn’t normal activity for an NFL starter unfortunately.

Guys like Urschel should be celebrated. Sorry if you see otherwise.


11 posted on 03/17/2015 7:07:47 PM PDT by FlJoePa
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To: FlJoePa

Guys like Urschel should be celebrated. Sorry if you see otherwise.
++++
Not so.

I was just pulling your leg. It was such an unusual post and I must confess that I’ve never heard of Urschel. I’ll look him up.

And I’m a big math fan. So posts like yours always pull me in.


12 posted on 03/17/2015 7:13:57 PM PDT by InterceptPoint (>http://rss.cnn.com/rss/cnn_topstories.rss)
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To: FlJoePa
Urschel would make an awesome guest star on Big Bang Theory.
13 posted on 03/17/2015 7:17:46 PM PDT by Sherman Logan
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To: Sherman Logan

Big Bang Theory. Have no idea where the letters went.


14 posted on 03/17/2015 7:18:38 PM PDT by Sherman Logan
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To: FlJoePa

I will second your motion! I am not a Ravens fan, but Mr. Urshel showed up on a Saturday morning at Penn State a couple of weekends ago to talk to a small group of high school kids who are finalists for relatively new engineering/sciences scholarship program (I am blessed that my son was one of those finalists...). He was on a small stage with a group of the current participants in the scholarship program (he looked like a literal giant compared to the other kids!). You could tell he was as passionate about math, sciences and research as he must be about football. He looked like he was “beaming” on the stage talking about a life of pursuing research. Seemed like a great guy who was accommodating to everyone there. I suspect that he is the kind of guy who will definitely go back to get his Ph.D when his football career is over. Heck, I may even root for the Ravens (on occasion) this season!


15 posted on 03/17/2015 7:29:16 PM PDT by juan_galt (De oppresso liber - Quien es Juan Galt?)
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To: FlJoePa

The Trafalmadorians had to slowly explain this me.

Montana Wildhack seemed to already understand it however.


16 posted on 03/17/2015 7:31:28 PM PDT by bakeneko
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To: juan_galt

Lots of these football guys do good things - especially with the kids it seems.

Never heard of one with this depth of knowledge of math though! Cool stuff.


17 posted on 03/17/2015 7:35:58 PM PDT by 21twelve (http://www.freerepublic.com/focus/f-news/2185147/posts It is happening again.)
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To: Bob; doc1019; InterceptPoint; sphinx; Red_Devil 232; smokingfrog; 9thLife
Aw, come on, guys! It's so simple, maybe you need a refresher course!

It's all ball bearings now-a-days!

18 posted on 03/17/2015 7:48:52 PM PDT by Rodamala
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To: Rodamala

Trust me, I would need more that a refresher course. LOL!


19 posted on 03/17/2015 7:52:08 PM PDT by doc1019 (Blue lives matter)
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To: Rodamala

I’m sure it will come in handy when I design my robotic cab driver.


20 posted on 03/17/2015 8:11:12 PM PDT by smokingfrog ( sleep with one eye open (<o> ---)
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