User talk:XaosBits

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[edit] dynamical system rewrite

Hi XaosBits. Thanks for rewriting dynamical system. I think you did a good job. I appreciate your contribution and I hope you continue to contribute to Wikipedia. All the best & happy editing, Wile E. Heresiarch 18:10, 12 Jun 2005 (UTC)

[edit] KAM theory

Hello. After your impressive rewrite of dynamical system, I wondered if you have time to have a look at Kolmogorov-Arnold-Moser theorem. I think the explanation on that article is wrong (the article claims that the KAM theorem states that all invariant tori persist under perturbation), but I do not know KAM theory well enough to amend the article without consulting some sources. Thanks in advance. Cheers, Jitse Niesen 12:18, 19 Jun 2005 (UTC)

Thanks. Jitse Niesen 09:23, 20 Jun 2005 (UTC)

[edit] Wikipedia:WikiProject Physics

I invite you to participate in, or at least keep an eye on the discussions over at Wikipedia:WikiProject Physics. We've had a successful run at Wikipedia:WikiProject Mathematics but the physics project is just starting up. linas 23:30, 24 Jun 2005 (UTC)

[edit] Exemplar

Your exemplar article was quite nice; quick and to the point. I just wanted to say I appreciated it! Always nice to find people who are interested in writing articles on the history and philosophy of science. --Fastfission 22:22, 16 July 2005 (UTC)

[edit] "Isometries" in Bios theory

You seem to understand something more about "novelty" than I do. When I read the definition in that article, I understand it to be saying the following, paraphrased: "Consider a set of elements. Consider the set of distances between pairs of elements in the first set. Now permute the elements in the first set. If any of the distances changed, then the set has novelty". But to me, this is non-sense: simply permuting something cannot possibly change a relationship defined between pairs of elements. What am I missing, what did I misunderstand here? linas 01:16, 8 February 2006 (UTC)

That is what the article says and also how I understood it. It made no sense. What Lakinekaki failed to explain in the article is that one has to first embed the time series in an m-dimensional space. (I got that from his first post in the novelty discussion, the vectors elements not separated by commas, 12 -> [1, 2], ...). For example, a scalar time series in a 3-embedding becomes a new time series u1 = (x1, x2, x3), u2 = (x2, x3, x4) ... This new time series is then used for approximate isometry counting. The count of approximate isometries is then compared to the count of isometries from a shuffled version of the time series (meaning, shuffle the scalar version, embed in m dimensions, count isometries within ε).
Now imagine a chaotic system and its time series. When the system comes back close to a point already in the series, it remains close to the image of that point for a while. That will produce two subsequences in the time series that are similar to each other. That means that there will be two vectors that are similar to each other. If the close return was within δ, then after m iterations the distance will be about δ λ m. As long as this number is less than the radius ε for approximate isometries, the m terms of each of the two nearby subsequences will form vectors that are isometric within ε. How often a δ occurs is related to the entropy of the system. To see longer sequences that are close to each other one needs exponentially longer time series. The novelty plots all have an initial part where the dynamical system has more isometries than the shuffled one. This region will grow with the log of the length of the time series. Instead of all this confusion about novelty, a simple histogram of close return statistics would have been in line with the literature and just as informative. XaosBits 03:04, 8 February 2006 (UTC)
Ah-ha! Thank you! Now we just have to figure out what to do Lakinekaki and his article. His attitude coupled with his inability to explain anything sure rubs me the wrong way. linas 04:42, 8 February 2006 (UTC)

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[edit] Chaos definitions

Why didn't you like them, and why did you move them?Lakinekaki 03:13, 8 April 2006 (UTC)

See the Chaos Theory talk page.

[edit] Grave concerns about apparently deceptive behavior by Lakinekaki

Hi, I see you have also criticized Bios theory, which has been created almost entirely by Lakinekaki and one ameritech.com anon in Chicago. I have presented some pretty startling evidence in Talk:Bios theory that Lakinekaki is in real life one Lazar Kovacevic (BSEE, University of Belgrade) of Chicago, IL, who has a personal website and who appears to be employed at something called the Chicago Center for Creative Development, which is apparently run by one Linnea Carlson-Sabelli, who appears to be affiliated with Rush University Medical Center. Indeed, it seems that the CCCD is the organization which has been promoting bios theory.

I have also listed specific problems with the very first paragraph of the article in Talk:Bios theory.

It is relevant to state that I have a academic background in dynamical systems theory, specifically symbolic dynamics, with strong interest in information theory. To judge from your interests, you do too! :-)

So, what to do about Bios theory?---CH 05:25, 12 May 2006 (UTC)

[edit] Encyclopedia of Mathematical Systems

IMO, it would be best to cite the entire thing and skip the details, or cite the specific volumes being used (even if it is lengthy). Subpages are deperecated, but it is a possible solution. Another would be to link to your page with an external link, so that the link would not be broken on mirrors. Both of these solutions do not work well with print publications, however. Kotepho 04:28, 6 June 2006 (UTC)

[edit] Butterfly effect

Could you put in a white background in the following image:

Black backgrounds don't print well, i.e. they are un-discernable. Thanks:--Sadi Carnot 12:03, 7 June 2006 (UTC)

I will see if I can re-create them with a white background. XaosBits 21:16, 1 July 2006 (UTC)

[edit] Attractors

Thanks for checking my stuff on the attractor.

My definition of B(A) is correct I believe. The mention of all neighborhoods is just spelling out the definition of the limit, I'm not requiring that for all neighborhoods the points converge to the attractor.

I'm not convinced the invariance of A is deducable from the other two points. What prevents points in the attractor from slipping out of the attractor and then spiraling back in in the limit? Does this require some homogenity of dynamics with time? At the very least it isn't obvious and so we might as well include the invariance in the definition.

When I originally wrote the example function I made I thought I made it clear it was just an example and wasn't fully general. The wording now looks like it implies this so either someone cleaned it up incorrectly or I wasn't clear.

Anyway I just mentioned these because you brought them up and I wanted to explain what I was trying to do. I have no doubt that my wording and statement wasn't the clearest thing in the world and I may very well be incorrect. However, while what was written there already probably would be perfectly correct to someone who already knew the definition it wasn't very illuminating if one didn't (for instance it didn't make it clear what a dynamics was) and so forth. I was hoping to get something a bit closer to a comphrenensive explanation and that someone else would clean it up. I will go fix the function that was supposed to be an example not the general case.

Logicnazi 23:35, 1 October 2006 (UTC)

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