Show us your articles! Or what's your Erdos number?

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Show us your articles! Or what's your Erdos number?

Postby EstLladon » Thu May 03, 2007 11:55 am UTC

http://www.phil.uu.nl/preprints/ckipreprints/PREPRINTS/preprint056.pdf

Here it is.

Post your works too (if available)!

I hope this can lead to some productive collaborations. Well, maybe...

Stickied! - Spitvalve
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Postby CDarklock » Thu May 03, 2007 12:42 pm UTC

Wow!

I don't understand a word of it!

Great job!
And there was much rejoicing.
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Postby EstLladon » Fri May 04, 2007 7:45 pm UTC

Thank you. It is not that difficult to understand.

So am I the only one who has something to show? I thought that there are more mathematicians here...
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Postby 3.14159265... » Fri May 04, 2007 8:54 pm UTC

I will start posting here once I get higher than first year :D
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Postby bbctol » Fri May 04, 2007 10:16 pm UTC

Ah, if only I was... smart. Well, looks very impressive.
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Postby cmacis » Fri May 04, 2007 10:55 pm UTC

We have mathmos here, just not a lot past the first year of BSc.

Saw the title and knew it would make no sense to me.
li te'o te'a vei pai pi'i ka'o ve'o su'i pa du li no
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Postby HenryS » Sat May 05, 2007 12:25 am UTC

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Postby SpitValve » Sat May 05, 2007 1:56 am UTC

I'm writing something for Phys Rev B at the moment... not really maths though
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Postby ptveite » Sat May 05, 2007 5:27 am UTC

I have a couple of papers to my name, but alas, nowhere to post them.....
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Postby kira » Sat May 05, 2007 1:46 pm UTC

cmacis wrote:We have mathmos here, just not a lot past the first year of BSc.

Saw the title and knew it would make no sense to me.


Yeah, I've already got my math degree and I still didn't have to write anything but summaries of other people's papers.
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Postby FiddleMath » Sun May 06, 2007 12:32 am UTC

http://www.tehposse.org/matt/stuff/path_bundles.pdf

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.
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Postby EradicateIV » Sun May 06, 2007 5:46 am UTC

Just something to check, the last example on concatenation b^3a should be 00011 not 0001, right?
1010011010

Our truth is only as good as our assumptions.
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Postby FiddleMath » Sun May 06, 2007 4:11 pm UTC

er, yes. Thanks. :)
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Postby iw » Mon May 07, 2007 6:39 am UTC

Link to my webspace 'cuz you have to buy the original:
http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.
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Postby Mad Giraffe » Mon May 07, 2007 10:01 am UTC

Ahw, these all look mighty interesting, but as usual I'm having a hard(er) time to understand because it is in english.

Drat.

And I'm not going to bother to upload my paper about the mathematics behind depth perception and how to calculate dimensions of a 3d object from a perspective view from 1 plane (My specialisation in maths was (tri)geometry) or 2 planes.
Because it is in dutch.

Not that interesting anyway.
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Postby adlaiff6 » Tue May 08, 2007 6:21 am UTC

iw wrote:Link to my webspace 'cuz you have to buy the original:
http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.


I'll be Erdos 4 in (hopefully) another couple months.
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Postby iw » Tue May 08, 2007 11:40 am UTC

adlaiff6 wrote:
iw wrote:Link to my webspace 'cuz you have to buy the original:
http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.


I'll be Erdos 4 in (hopefully) another couple months.

Yeah, the only Erdos numbers that really count are 1 and 0. Otherwise, it basically just means you got a joint paper with someone reputable published (usually your adviser ;) ).
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Postby cmacis » Tue May 08, 2007 1:50 pm UTC

But there can be only one 0, also no more 1s are possible. If you hunt out the 1s you might get a 2.
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Postby Woxor » Tue May 08, 2007 6:47 pm UTC

FiddleMath wrote:http://www.tehposse.org/matt/stuff/path_bundles.pdf

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.

Interesting stuff!

This might be the wrong thread to mention it, but your paper made me start thinking about words with more possible digits, so I played around with some ternary "path bundles" (obviously the definition had to be modified). It seems that analogues Lemma 1 and Lemma 2 hold for all p-ary path bundles (p a natural number), but I haven't tried it for higher p yet, and I certainly haven't proved the existence theorems!

Let a "path" be as before, but require that adjacent words differ only in one digit AND only by 1, with no wrap-around. So in base p=5, you have 0142~0132, but NOT 0142~0102.

Now specify that B(n,a,p) has p^a paths, and for each w in Qa whose digits include only 0 and p-1 (i.e. the true "vertices" of Qa), the bundle contains Pw such that
1. |Pw|=p^{n-a} (***<----EDIT: This line has been changed.***)
2. Pw(0)=0^{n-a}w
3. Pw(.)=(p-1)^{n-a}(w*) (***<----EDIT: This line has been changed.***)
4. Every word in Qn is in exactly one path
where w* is essentially treating the "p-1" digits as "1"s and taking the complement. So again in base 5, if you have w=4044, then w*=0400.

I THINK that this implies the following Lemmas (with proofs similar to those in your paper):

Lemma 1: B(n,a,p) exists only if n=1(mod p).
Lemma 2: If B(n,a,p) exists, then a <= n-log_p((p-1)n+1)

I could have made a mistake, though. And who knows whether these things ever exist; I haven't bothered to check even the simplest cases.
Last edited by Woxor on Wed May 09, 2007 2:19 am UTC, edited 4 times in total.
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Postby notzeb » Tue May 08, 2007 8:56 pm UTC

You wrote that whole post, and didn't make a Pw(n) joke?

Shame on you!
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Postby Woxor » Tue May 08, 2007 8:58 pm UTC

notzeb wrote:You wrote that whole post, and didn't make a Pw(n) joke?

{n-a}w, I forgot to.
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Postby FiddleMath » Wed May 09, 2007 12:01 am UTC

Woxor wrote:Lemma 1: B(n,a,p) exists only if n=1(mod p).
Lemma 2: If B(n,a,p) exists, then a <= n-log_p((p-1)n+1)

I could have made a mistake, though. And who knows whether these things ever exist; I haven't bothered to check even the simplest cases.


I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 0, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

[edit] It's been a while since I worked with this. :)[/edit]
Last edited by FiddleMath on Wed May 09, 2007 4:20 am UTC, edited 1 time in total.
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Postby Woxor » Wed May 09, 2007 2:13 am UTC

FiddleMath wrote:I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 1, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

I probably misread something, but wouldn't B(3,1,3) need to include p^a=3^1=3 distinct paths, rather than just the one? I'll try to post my "proof" later on if I have time (otherwise it'll have to wait until Thursday or so).

EDIT: Also, my Rule 1 was totally wrong; I wrote 3^n, it should have been p^{n-a}. And Rule 3 had a "2" instead of a "p-1."

EDIT 2: Upon further reflection, I hadn't even considered the obvious fact that there are still only 2^n "true" vertices, so clearly that will influence the structure of the bundle. I'll have to think about whether my generalization even makes sense.
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Postby FiddleMath » Wed May 09, 2007 4:39 am UTC

You're right. Let me fiddle with that, and make me look less foolish on first glance. ;) The idea still holds, though.
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Postby ptveite » Thu May 10, 2007 5:21 am UTC

I have papers pending publication that will give me an erdos number 4, and hence an Erdos-Bacon number 6.
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Postby iw » Thu May 10, 2007 6:32 am UTC

ptveite wrote:I have papers pending publication that will give me an erdos number 4, and hence an Erdos-Bacon number 6.
Wait a second, you were in a motion picture? IIRC, skeptical scientist is on a quest for one of those numbers as well.
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Postby ptveite » Fri May 11, 2007 2:14 pm UTC

I was an extra in the movie Little Big League when I was like 7, you can see me in the background for about 5 seconds during one scene. Yup. I'ma claim that counts, since that's about as far-fetched as some of the erdos-bacon number entries on the wikipedia site.
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Postby HenryS » Fri May 11, 2007 9:50 pm UTC

This paper, on the "100 prisoners and a lightbulb" problem, gets me an Erdős number of 4 :)
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Postby SpitValve » Tue May 15, 2007 2:21 am UTC

I'm going to publish a condensed matter paper soon. Any idea how to link Erdös to condensed matter physics?

I'm very tempted to call it "Madness? Blasphemy? This IS EPITAXY ON A (111) FCC PERIODIC SLAB OF LENNARD-JONESIUM" but it doesn't have a very good ring to it.
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Postby iw » Wed May 16, 2007 1:07 am UTC

SpitValve wrote:I'm going to publish a condensed matter paper soon. Any idea how to link Erdös to condensed matter physics?

I'm very tempted to call it "Madness? Blasphemy? This IS EPITAXY ON A (111) FCC PERIODIC SLAB OF LENNARD-JONESIUM" but it doesn't have a very good ring to it.

How about "This is Epitaxy. This is Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium. Any Questions?"
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Postby Torn Apart By Dingos » Wed May 16, 2007 7:36 am UTC

"This is my article on Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium. There are many like it, but this one is mine."
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Postby FiddleMath » Wed May 16, 2007 7:43 am UTC

Torn Apart By Dingos wrote:"This is my article on Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium. There are many like it, but this one is mine."


We can make this colon-compliant pretty easily...

"This is my article on Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium:
There are many like it, but this one is mine."
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Postby SpitValve » Wed May 16, 2007 7:45 am UTC

Maybe I'm just tired, but I don't think I got the jokes in the last 3 posts.
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Postby iw » Thu May 17, 2007 8:15 am UTC

SpitValve wrote:Maybe I'm just tired, but I don't think I got the jokes in the last 3 posts.
Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.
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Postby SpitValve » Thu May 17, 2007 9:44 am UTC

iw wrote:Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.


ic. Well, I was only in the US during the 80s for one day, and didn't watch any ads about drugs, as far as I recall. I haven't watched Full Metal Jacket (don't hurt me), but I kinda get the colon thing. w00t!
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Postby 3.14159265... » Thu May 17, 2007 5:45 pm UTC

Anyone here working on the 3x+1 problem? I love it, and want to know some good articles written on it already.
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Postby adlaiff6 » Thu May 17, 2007 9:50 pm UTC

3.14159265... wrote:What about quantization? we DO live in a integer world?

crp wrote:oh, i thought you meant the entire funtion was f(n) = (-1)^n
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Postby Woxor » Thu May 17, 2007 11:55 pm UTC

I just realized that one of my profs last year had an Erdos number of 2. I had the opportunity to proofread a book he was writing (and be credited in the published version for as much), but I didn't do it! Curses! I don't know how close I'll get to a 3 again.
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Postby skeptical scientist » Fri May 18, 2007 12:01 am UTC

Does proofreading a book really count for Erdos number? I would think not.
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Postby Woxor » Fri May 18, 2007 12:06 am UTC

skeptical scientist wrote:Does proofreading a book really count for Erdos number? I would think not.

Well I'm sure it doesn't, but I would definitely have grounds to pretend I had a 3. It's slightly better than outright fabrication.
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