Comments on: The birth of the giant component http://bit-player.org/2009/the-birth-of-the-giant-component An amateur's outlook on computation and mathematics. Thu, 17 May 2012 10:01:06 +0000 http://wordpress.org/?v=2.6.3 By: deepa http://bit-player.org/2009/the-birth-of-the-giant-component#comment-3074 deepa Fri, 23 Jul 2010 07:55:45 +0000 http://bit-player.org/?p=519#comment-3074 concept is very interesting. I got the idea of giant component very easily. concept is very interesting. I got the idea of giant component very easily.

]]> By: Jasper Crowne http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2546 Jasper Crowne Mon, 11 Jan 2010 22:21:39 +0000 http://bit-player.org/?p=519#comment-2546 I asked a friend of mine about whether people had studied this sort of phenomenon before and he pointed me to a recent American Physical Society March Meeting talk by Christopher LaSota (then at Kenyon College, now at Gonzaga). http://meetings.aps.org/Meeting/MAR08/Event/78234 As far as I can tell he hasn't published yet, but apparently he's speaking about this again at this year's March Meeting: http://meetings.aps.org/Meeting/MAR10/Event/120147 I asked a friend of mine about whether people had studied this sort of phenomenon before and he pointed me to a recent American Physical Society March Meeting talk by Christopher LaSota (then at Kenyon College, now at Gonzaga).

http://meetings.aps.org/Meeting/MAR08/Event/78234

As far as I can tell he hasn’t published yet, but apparently he’s speaking about this again at this year’s March Meeting:

http://meetings.aps.org/Meeting/MAR10/Event/120147

]]> By: Carnival of Mathematics #60 « ?idiot's Blog http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2353 Carnival of Mathematics #60 « ?idiot's Blog Fri, 04 Dec 2009 05:03:31 +0000 http://bit-player.org/?p=519#comment-2353 [...] 6) Brian, at bit-player, finds some interesting math in a collection of staples, as described in The birth of the giant component. [...] [...] 6) Brian, at bit-player, finds some interesting math in a collection of staples, as described in The birth of the giant component. [...]

]]> By: Stephan Mertens http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2346 Stephan Mertens Fri, 27 Nov 2009 21:20:09 +0000 http://bit-player.org/?p=519#comment-2346 I guess that a sort of entropic ratchet mechanism is (at least partly) responsible for the formation of the giant component: there are many ways how two staples can hook up, but it requires a coordinated move to separate a pair of linked staples. And I think that the same argument applies to the power cords in your drawer that always form a giant knot. I guess that a sort of entropic ratchet mechanism is (at least partly) responsible for the formation of the giant component:
there are many ways how two staples can hook up, but it requires a coordinated move to separate a pair of linked staples.

And I think that the same argument applies to the power cords in your drawer that always form a giant knot.

]]> By: Thanksgiving weekend miscellany — The Endeavour http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2342 Thanksgiving weekend miscellany — The Endeavour Wed, 25 Nov 2009 13:04:45 +0000 http://bit-player.org/?p=519#comment-2342 [...] Hayes has a blog post entitled The birth of the giant component. Random networks explain why staples stick together into a giant [...] [...] Hayes has a blog post entitled The birth of the giant component. Random networks explain why staples stick together into a giant [...]

]]> By: Jess http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2339 Jess Wed, 25 Nov 2009 04:09:23 +0000 http://bit-player.org/?p=519#comment-2339 My thought is that the staple as a whole is a vertex and an edge is formed when two staples get hooked on each other. That seems simpler than the proposed "merging" process. Wouldn't we expect the concept of edge to be more about the relation between two objects than some crude physical analogue? My thought is that the staple as a whole is a vertex and an edge is formed when two staples get hooked on each other. That seems simpler than the proposed “merging” process. Wouldn’t we expect the concept of edge to be more about the relation between two objects than some crude physical analogue?

]]> By: Ben http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2335 Ben Mon, 23 Nov 2009 21:18:18 +0000 http://bit-player.org/?p=519#comment-2335 The first thing I thought of when you started talking about random graphs was that the *flat* part of the staple should be a vertex, and the *ends* should be the edges - after all, the edges form the "bonds" you describe when discussing water molecules. The links between edges form randomly as the staples are deposited into the bowl, or as they're stirred around in the bowl or something. Then, the change from two to three dimensions, from the surface to the bowl, changes the probability that a random bond forms between any two vertices. How exactly would require some thought, but presumably on a surface, the expected number of bonds is less than n/2, while in a bowl, it is greater. The first thing I thought of when you started talking about random graphs was that the *flat* part of the staple should be a vertex, and the *ends* should be the edges - after all, the edges form the “bonds” you describe when discussing water molecules. The links between edges form randomly as the staples are deposited into the bowl, or as they’re stirred around in the bowl or something. Then, the change from two to three dimensions, from the surface to the bowl, changes the probability that a random bond forms between any two vertices. How exactly would require some thought, but presumably on a surface, the expected number of bonds is less than n/2, while in a bowl, it is greater.

]]> By: Kevembuangga http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2334 Kevembuangga Mon, 23 Nov 2009 12:41:24 +0000 http://bit-player.org/?p=519#comment-2334 I think this kind of "research" is deeply cretinous, however I am <b>truly grateful</b> that some people engage in it, the same way I am grateful to video games addicts for boosting the development of high performance CPU chips. I think this kind of “research” is deeply cretinous, however I am truly grateful that some people engage in it, the same way I am grateful to video games addicts for boosting the development of high performance CPU chips.

]]> By: brian http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2328 brian Sat, 21 Nov 2009 15:46:38 +0000 http://bit-player.org/?p=519#comment-2328 Thanks to Barry, to Yonkou, and to unekdoud for raising several interesting questions and suggesting further avenues to explore. Before saying anything further, I would like to note that this is one of those rare instances in experimental science where anyone can play. The materials are readily available. You don't need an NSF grant to finance the research (although I suppose we might seek funding from Staples, the office-supplies store). By all means: Grab the stapler and join in. In the spirit of scientific collaboration and zealous pursuit of the truth, I'm willing to share my stock of used staples. Barry asks about the emergence of clustering in small populations of staples. I don't know how that goes. With Erdos-Renyi graphs, the known results are strictly valid only in the limit of infinite <em>n</em>, but in practice infinity seems to be a pretty small number in graph theory. unekdoud asks about the largest attainable clusters. Again I don't know, but of course there must be a physical limit. At some point the weight of the cluster exceeds the strength of the single staple from which it's suspended. As for open questions about the shape of the bowl, the manner of stirring, the size of the staples, etc.: To the extent that these factors are important, we don't really have a system that lends itself to clean analysis. I'd prefer to get out of this messy world of real metal staples and retreat into the tidier realm of a model we can simulate computationally or solve mathematically. But of course I don't have such a model. Finally, about paper clips. Those are the province of my <em>American Scientist</em> colleague Henry Petroski. He wrote the book on them, and I'm going to stay off his turf. Thanks to Barry, to Yonkou, and to unekdoud for raising several interesting questions and suggesting further avenues to explore.

Before saying anything further, I would like to note that this is one of those rare instances in experimental science where anyone can play. The materials are readily available. You don’t need an NSF grant to finance the research (although I suppose we might seek funding from Staples, the office-supplies store). By all means: Grab the stapler and join in. In the spirit of scientific collaboration and zealous pursuit of the truth, I’m willing to share my stock of used staples.

Barry asks about the emergence of clustering in small populations of staples. I don’t know how that goes. With Erdos-Renyi graphs, the known results are strictly valid only in the limit of infinite n, but in practice infinity seems to be a pretty small number in graph theory.

unekdoud asks about the largest attainable clusters. Again I don’t know, but of course there must be a physical limit. At some point the weight of the cluster exceeds the strength of the single staple from which it’s suspended.

As for open questions about the shape of the bowl, the manner of stirring, the size of the staples, etc.: To the extent that these factors are important, we don’t really have a system that lends itself to clean analysis. I’d prefer to get out of this messy world of real metal staples and retreat into the tidier realm of a model we can simulate computationally or solve mathematically. But of course I don’t have such a model.

Finally, about paper clips. Those are the province of my American Scientist colleague Henry Petroski. He wrote the book on them, and I’m going to stay off his turf.

]]> By: unekdoud http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2326 unekdoud Sat, 21 Nov 2009 13:50:46 +0000 http://bit-player.org/?p=519#comment-2326 I guess you should look at the possibility of doing this with different office equipment, say paper clips. Also, does the staple size matter? Mix and match different types to form "alloys". If you consider them as impurities in the ice, there might be a certain noticeable effect on the structure (is there an analog of the freezing point in ice? What are the changes in density?) Necessarily, the size of the bowl has a role to play. It might even be possible to make the giant component in a nonconvex shape. As for the structure itself, you might want to consider actually mapping it out as a graph, to study properties like subgraphs and cycles, as well as things like vertex density. Some glue might be added to preserve the structure, to make it easier to observe. Do the graph properties change if some other method is used to create the giant component, like using a magnet or magnetised scissors to stir up the mixture? How would this change if the staples are submerged in oil? What if they are heated or cooled in the middle of the process? What about vibration at different frequencies? In terms of the size of the component, you might want to keep adding staples to see how far it can grow. Is it possible for two components to merge? And what applications might that have toward chemistry, or physics? It may also be possible to recreate this experiment in the context of a social network. Similar effects will then be observable on different scales, or perhaps it will be totally different. I guess you should look at the possibility of doing this with different office equipment, say paper clips. Also, does the staple size matter? Mix and match different types to form “alloys”. If you consider them as impurities in the ice, there might be a certain noticeable effect on the structure (is there an analog of the freezing point in ice? What are the changes in density?)

Necessarily, the size of the bowl has a role to play. It might even be possible to make the giant component in a nonconvex shape.

As for the structure itself, you might want to consider actually mapping it out as a graph, to study properties like subgraphs and cycles, as well as things like vertex density. Some glue might be added to preserve the structure, to make it easier to observe. Do the graph properties change if some other method is used to create the giant component, like using a magnet or magnetised scissors to stir up the mixture? How would this change if the staples are submerged in oil? What if they are heated or cooled in the middle of the process? What about vibration at different frequencies?

In terms of the size of the component, you might want to keep adding staples to see how far it can grow. Is it possible for two components to merge? And what applications might that have toward chemistry, or physics?

It may also be possible to recreate this experiment in the context of a social network. Similar effects will then be observable on different scales, or perhaps it will be totally different.

]]> By: Yonkou http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2324 Yonkou Sat, 21 Nov 2009 00:23:17 +0000 http://bit-player.org/?p=519#comment-2324 Very beautiful work. I wonder if the shape of the bowl plays a role. I do understand flat plate experiment... but did you add the staples on top of each other (which gets kind of enforced when you add them in a bowl)? Also I wonder what would happen if we add them in a more constrained container, say a test tube. Very beautiful work.

I wonder if the shape of the bowl plays a role.
I do understand flat plate experiment… but did you add the staples on top of each other (which gets kind of enforced when you add them in a bowl)?
Also I wonder what would happen if we add them in a more constrained container, say a test tube.

]]> By: Barry Cipra http://bit-player.org/2009/the-birth-of-the-giant-component#comment-2323 Barry Cipra Sat, 21 Nov 2009 00:00:13 +0000 http://bit-player.org/?p=519#comment-2323 It might be worth repeating the shiny-new-staple experiment, pausing periodically as you add staples (say every 10 or 20 staples), giving a shake to what you've got in the bowl, and then seeing how large an aggegration comes with it when you pick up one of the staples. (It might be well to repeat the shake and aggegate step several times and look at the statistics of what you get.) My guess is that the (average) percentage of staples that lift with the tangle will be pretty small until the total number of staples in the bowl gets to a hundred or so, and then will start increasing toward something pretty close to 100%. Will it follow some sort of logistic curve? And if so, how steep? In any event, it's a wonderful observation! It might be worth repeating the shiny-new-staple experiment, pausing periodically as you add staples (say every 10 or 20 staples), giving a shake to what you’ve got in the bowl, and then seeing how large an aggegration comes with it when you pick up one of the staples. (It might be well to repeat the shake and aggegate step several times and look at the statistics of what you get.) My guess is that the (average) percentage of staples that lift with the tangle will be pretty small until the total number of staples in the bowl gets to a hundred or so, and then will start increasing toward something pretty close to 100%. Will it follow some sort of logistic curve? And if so, how steep?

In any event, it’s a wonderful observation!

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