PAR

Hello. I think your reformatting in probability-generating function put lines so close together that it looked cluttered. I've redone it somewhat. Michael Hardy 02:00, 21 Nov 2004 (UTC)

Some tips inspired by your editing of Skellam distribution:

• Don't use gratuitous capitalization either in article titles or in the text of an article.

• There's no need to write (e.g.) [[hyphen|hyphenated]]; one may write [[hyphen]]ated, and it has the same effect (the whole word, not just the part between the brackets, appears as a clickable link).

• There's no need to capitalize the first letter of a link, nor to include underscores. Thus: [[negative binomial distribution]].

Michael Hardy 04:05, 21 Nov 2004 (UTC)

Hello - Thanks for the suggestions on the page. I'm obviously new to Wikipedia, and I'm trying to figure a lot of things out, such as is this the right way to respond to your message on my talk page? Also, I wanted to start a Voigt profile page, which is a convolution of a Doppler profile and a Lorentzian profile, or, viewed as probability distributions, a normal distribution and a Cauchy distribution. I guess a Voigt profile would translate to a Voigt distribution. There are no such profile pages, but there is a Lorentzian function page which contains just what a Lorentzian profile page should contain. I'm not sure of what to do here, or the etiquette of going about doing it. Any suggestions?

Perhaps moving the Lorentzian function page to Lorentzian profile would be the best thing to do, but I don't know this topic. Just click on "move this page". The edit history and discussion page get moved along with it, and the Lorentzian function page will then become a redirect page with an edit history showing that it was created by you at the time of the move. Michael Hardy 21:46, 22 Nov 2004 (UTC)

PS: Also, notice that if you type ~~~~ in a page you edit, your user name gets signed along with the date and time of the edit, and your user name will appear as a clickable link to your user page. Michael Hardy 21:46, 22 Nov 2004 (UTC)

PPS: The above is appropriate for discussion pages, but not for articles. Michael Hardy 21:47, 22 Nov 2004 (UTC)

Price equation edit

Hi, I've seen your major edit on the Price equation page, and have commented on it in the Talk:Price_equation page. Please review my comments. --Anthony Liekens 11:04, 30 Nov 2004 (UTC)

Lambert's cosine law

I replied on my talk page. Oleg Alexandrov 01:24, 1 Jan 2005 (UTC)

Oh, and the last sentence on that page, For a Lambertian reflector, the light reflected from this source will be the same in all directions, so the radiance seen by any observer will then be proportional that incident flux which will be proportional to the cosine of the incident (not the observing) angle. does not sound right. Oleg Alexandrov 01:29, 1 Jan 2005 (UTC)

I had some comments here earlier, but removed them. I need to think more about this law. Oleg Alexandrov 21:32, 1 Jan 2005 (UTC)

Hi Paul, Welcome to Wikipedia! I asked a question on Talk:Lambert's cosine law that I suspect you could answer. Just mentioning it here in case you don't have that page on your watchlist. Dbenbenn 02:10, 6 Jan 2005 (UTC)

Lévy flight

In the Lévy flight article you recently changed "the direction of each step follows a uniform distribution" to "the direction of each step follows a Lévy distribution". Although the length of each step may follow a Lévy distribution, doesn't the direction of the step have to be uniformly distributed - otherwise the random walk would not be isotropic ? I've checked The Fractal Geometry of Nature, which definitely says that Lévy flight random walks are isotropic. Gandalf61 10:27, Jan 21, 2005 (UTC)

Thank you for your response. I guess the definition of "direction" depends on the dimension of the process. For a 1-dimensional Lévy flight then I agree the direction of each step is either "up" or "down", with equal probability. For a 2-dimensional Lévy flight (which is the type that Mandelbrot describes in FGoN) then the direction of each step can take any value between 0 and 360 degrees, so in this context I think the distribution of the direction would be uniform on the interval [0,360]. But the important characteristic of Lévy flights is, as you say, the distribution of the step length. I have split up the opening paragraph of the article to make it more readable, but I have not changed your new explanation, which is very clear. Gandalf61 12:00, Jan 22, 2005 (UTC)

GSL link

As far as I could see, the GSL link you want to include does not contain anything about the gamma function except its definition. It is only potentially useful for someone who wants to compute it, but then they have to have GSL installed already and that gives them the docs readily accessible on their machine. Futhermore there are lots of bits of code out there that can compute the gamma function, including some large libraries like IMSL and NAG, and packages like Maple, Mathematica, probably Matlab. Do a google search for <"gamma function" procedure> and you'll get pages of them. There is no special reason to give just GSL. We should provide links that give information about the function, not just programming manuals. That's my opinion. --Zero 11:55, 23 Jan 2005 (UTC)

Sinc

I notice you edited Sinc function, though I think there may be a problem with the definition overall. Could you take a look at Talk:Sinc function? Thanks Dysprosia 08:59, 1 Feb 2005 (UTC)

German "Sun" article

Thanks for the Babelfish translation, there's still a lot of work to be done, especially with the terminology. I have no idea what "hauptreihenstern" means for example :) so it might be a good idea for some of the german folk to help with that :). After a brief look at the article I think I can recover about 2/3 of the information for incorporation in the enlish version article. And I just want to briefly introduce myself, I go by the nickname of Smartech and I'm heading a major Solar System effort in bg: and I was looking for article about the Sun. Anyway, thanks for your efforts. Regards. --Smartech 01:16, 14 Mar 2005 (UTC)

Email

Hi Oleg - do you have an email set in preferences? I sent an email, but got no reply PAR 13:14, 18 Mar 2005 (UTC)

I just replied. Sorry for the delay. Oleg Alexandrov 16:56, 18 Mar 2005 (UTC)

Fourier Series

Hi Michael - I was about to revert edits by 142.150.160.187 on the Fourier series article (please see its

discussion page for reasons) but I noticed you had edited it for style. I want to make sure this doesn't constitute an endorsement of the article as it stands (please, I hope not!) PAR 17:22, 18 Mar 2005 (UTC)

I didn't look at it closely; I was just doing some stylistic adjustments. I have noticed that that person has written some dubious things in some math articles, so go ahead and delete his stuff if necessary. Michael Hardy 23:57, 18 Mar 2005 (UTC)

Brownian Motion

I liked your BM-Picture. How did you make it?
I tried to do the same in the German wikipedia: de:Brownsche_Molekularbewegung any help for me? :)
Thomas

Yours looks good. I just used a Gaussian random number generator in the x and y directions and plotted it. You could just use the image on the English page for the German page if you wanted to, after all, all images are in the public ___domain. I have grabbed an image off the German de:Sonne article for the English Sun article. PAR 16:29, 22 Mar 2005 (UTC)

I know that I could grab it, but I wanted to make my own one as nice as yours and I wanted to be sure that it's really Brownian Motion (I published the R source code as well, just two gaussian random walks). What software did you use? Any ideas for improving it?

This and many related articles in the german wikipedia are quite poor: a lot of work to do...

Thomas, --128.130.51.96 08:08, 23 Mar 2005 (UTC)

I wrote the program in IDL. It looks something like this:

n=1000
seed=0
x=randomn(seed,n)
y=randomn(seed,n)
plot,x,y

where randomn() is a random number generator, which generates an n-element, 1-dimensional array of normally distributed random numbers. Seed is the random number seed, and its returned value is different from its input value. PAR 13:21, 23 Mar 2005 (UTC)

I believe you did not this: In your example x and y are normally distributed, but for Brownian Motion incements should be normally distributed. I guess (quick first look) this is the case in your picture.

Just in the case you are curious: I added another picture in the German wikipedia, where you can see (well, execute the R-code and you really see it ;) ) the convergenace of a discrete process towards BM.

Thomas, --128.130.51.96 09:48, 24 Mar 2005 (UTC)

Yes, you are right, sorry about that. I deleted the old code and was trying to rewrite from memory. This is

more like what I did:

n=1000
seed=0
x=randomn(seed,n)
y=randomn(seed,n)
for i=1,n-1 do x[i]=x[i-1]+x[i]
for i=1,n-1 do y[i]=y[i-1]+y[i]
plot,x,y

I don't understand the phrase "convergence of a discrete process towards BM". BM is a discrete process, right?

I think you're doing some good work on that page. I will check with it occasionally to make sure the English page is competitive. Also, you might want to check out a related topic Levy flight. Its sort of a generalized Brownian motion for other stable distributions.

Brownian motion is definitely not discrete, but continous (and, btw nowhere differentiable). But it is constructed the way I tried to draw the second picture: Take an interval [t-1, t] and two normally distributed numbers B_t and B_{t-1}. Then devide the interval by two and add in the center another random number B_{t-1/2}. This process is discrete. Now you let the mesh go to zero and the discrete process tends to something that really exists (Wiener proved it first), it is continous and we call it BM. Correct me if I'm wrong.

I'd really like to improve especially the german wikipedia on this (and related) topic and there is really a lot of work to do, but I am not very expereinced yet...

Thomas, --128.131.219.28 22:54, 24 Mar 2005 (UTC)

I just assumed that Brownian motion referred to e.g. the motion of a particle in a liquid as it is hit by the molecules of the liquid. This is a discrete process, (assuming the duration of the impact is short compared to the free travel time between collisions). I have never tracked down the precise definition of Brownian motion, however. Are you saying that the motion of particles under molecular bombardment is only a discrete approximation to Brownian motion? This seems strange to me. PAR 03:14, 25 Mar 2005 (UTC)

I reffered to BM as a mathematical object, that's right.

But never the less I think that BM is continous. I do not want to start a philosophical question, but I can't imagine molecules that move discrete. As far as I know discrete moving does just exist in quantum physics (read this article! or just this paragraph) for electrons and other particles. (But honestly I know nothing about Quantum physics)

So I think that the mathimatical model "BM" is a quite good model for "random" movements of molecular particles - they are both very rough and not discrete, but continous.

Thomas, --128.131.219.28 23:47, 25 Mar 2005 (UTC)

Hello Thomas - The way I picture it is that a particle gets hit by a molecule, which instantaneously changes its direction and speed. Then it travels as a free particle for some distance L1, at which point it gets hit again.

It changes direction and speed again, and moves L2, until it is hit again. This motion, described by [L1,L2,...] is discrete, not continuous. There is no quantum physics involved, just classical free particles, undergoing collisions, like billiard balls. Maybe you are saying that if we go to the limit of infinitely many collisions per second, and infinitely small distances between collisions, that that is sufficiently accurate to describe what is really a discrete situation? PAR 01:01, 26 Mar 2005 (UTC)

You think of billiard balls? Very good! They definitely can't move in a discrete way. Discrete moving means, that the billiard ball is now at one end of the table and an instant later (not one second, not 0.00000001 msec later) at the other end of the table. It did not move very fast, no it jumped. You were talking about immediatement change of the direction (and speed) of the ball. I would say this means that (at some point in space and time) the movement of the ball is not differentiable.

Think of the following: billiard balls and molecules move the same way. In one dimension (on the x-axis you plot the time, on y the position) a crash lookes somehow like abs(x). If we assume Continuous time a discrete movement could be modeled by a discrete function like the Sign function.

But perhaps I missunderstood you (my poor English?) or I am wrong... we just discuss! :) I hope that now be are both happy with the layout of our discussion :) (I changed your postings as well, I hope you don't mind)

Thomas, --128.131.219.28 10:22, 26 Mar 2005 (UTC)

Ok, good - I think we agree on the mechanism of the motion of a particle undergoing BM. It is just the definition of "discrete" that we had trouble with. I agree - the motion of the particle is continuous except perhaps at the points of impact with molecules. I was using "discrete" to mean that the distance travelled between collisions is small, but not zero. PAR 11:13, 26 Mar 2005 (UTC)

Quantum chaos

Any chance you have a reference to the article by what's-his-name on a quantum-mechanical derivation of particles-in-a-box? Its a fascinating article: the wave functions are shown to be fractal, and space-filling the entire box. The energy levels of each eigenfunction are shown to extremely close to each other (spacing as 1/avogadro's N). Thus, for example, if you start with all of the particles on one side of the box at time=0, the wave functions, though technically filling the whole box, are destructively interfering on the empty side of the box. But at time!=0 they rather quickly fill the box. You also get a very strong sense of why irreversibility happens (due to the closeness of the spacing of the energy levels, and the fractal-space-fillingness). The author is from UC santa barbera or UC san diego .. I lost the reference... linas 17:40, 26 Mar 2005 (UTC)

No, sorry, I don't know of that article. Let me know if you find it, I would be interested. PAR 20:40, 26 Mar 2005 (UTC)

discrete is a disambiguation page

... so it's usually better to link to one of the pages listed on it than to it directly. Michael Hardy 23:16, 3 Apr 2005 (UTC)

Entropy

Just noticed you added the "entropy" entry to the chi-square distribution infobox. How did you evaluate that integral? I've tried, but obviously I'm missing something. Presumably the same technique would also work for the gamma distribution. --MarkSweep 20:17, 10 Apr 2005 (UTC)

I used Mathematica. It wouldn't give the integral directly but these three statements gave that result:

f=(1/2)^(k/2)/Gamma[k/2]

logp=Log[f]+(k/2-1)*Log[x]-x/2

Simplify[PowerExpand[Integrate[-p[x]*logp,{x,-Infinity,Infinity}]]]

There is a on-line Mathematica integrator at http://integrals.wolfram.com/ but it only gives indefinite integrals, so I'm not sure if it will help, if you don't have Mathematica. Looking at the page, I realized that the psi or polygamma function is not mentioned, so I will fix that. PAR 20:42, 10 Apr 2005 (UTC)

Strange, I can't get Mathematica 5.0 to symbolically evaluate that integral. Which version did you use? --MarkSweep 21:39, 10 Apr 2005 (UTC)

I'm using an old version, 2.2. The troublesome part of the integral is

Integrate[x^(k/2-1)Exp[-x/2]*Log[x],{x,-Infinity,Infinity}]

which returns an expression involving the PolyGamma(0,k/2) term. I tried it on the Mathematica web page and it too solved the integral, but gave an expression involving HypergeometricPFQ. Whether the two are equivalent, I don't know. Looking at Abramowitz & Stegun, I don't see any integrals involving a Log() defining the Digamma function. PAR 22:20, 10 Apr 2005 (UTC)

I see. Can you try to evaluate the corresponding definite integral for the standard Gamma distribution (i.e. with scale parameter equal to one)? The difficult part is again to compute ${\displaystyle \mathrm {E} (\ln(x))}$ . I end up with the following:

${\displaystyle (1-k)\,\Gamma '(k+1)+k+\ln \Gamma (k)}$ 

The indefinite integral corresponding to the expectation of ln(x) is expressed in terms of a hypergeometric 2F2 function that I know nothing about. Only the definite integral seems to have a simple closed form. --MarkSweep 23:20, 10 Apr 2005 (UTC)

I put in these Mathematica lines:

f=1/(s^k*Gamma[k])

logp=Log[f]+(k-1)*Log[x]-x/s

Simplify[PowerExpand[Integrate[-p[x]*logp,{x,xmin,xmax}]]]

and it returned:

k + Log[s] + Log[Gamma[k]] + PolyGamma[0, k] - k PolyGamma[0, k]

For s=1 thats almost the same as yours, since ${\displaystyle \Gamma '(x)/\Gamma (x)=\psi (x)}$  = Polygamma(0,x) PAR 23:59, 10 Apr 2005 (UTC)

Linking, etc.

Looking at several edits you've made (such as Image:PoissonDistribution.png), you don't seem to know how to *link* to images and categories.

To link to an image or category, preceed it with a colon: [[:Image:PoissonDistribution.png]] will create Image:PoissonDistribution.png.

Also, don't put text immediately after {{ifd}} otherwise it will

make text act like fixed-width font and put a block around it

Cburnett 03:18, Apr 11, 2005 (UTC)

I picked up on the linking to categories after you mentioned it on the template talk page. I didn't know about the ifd thing or the

first space causing a box.

Thanks for the help on that. PAR 03:34, 11 Apr 2005 (UTC)

Cburnett's admin nomination

I was nominated for administrator and I'd like to hear your opinion at Wikipedia:Requests for adminship/Cburnett. Cburnett 07:23, Apr 24, 2005 (UTC)

Source of Parthenon image

You recently uploaded ParthenonGoldenRatio.png. I am interested in an image without the white lines. Can you tell me the source of this image? Thank you in advance! --Wolfgangbeyer 07:48, 30 Apr 2005 (UTC)

204.184.37.2

Latest comment: 20 years ago1 comment1 person in discussion

Someone removed the earlier block because it was too long. I've reblocked for one year.--Duk 18:22, 2 May 2005 (UTC)Reply

Image:Autorecessive.png

Thanks for improving the image! --cprompt 14:54, May 4, 2005 (UTC)

Trilobites

Latest comment: 20 years ago2 comments2 people in discussion

Hi, probably best not to make so many trilobite articles with only a taxobox and no text. They are likely to get deleted. I'd love more trilobite articles, but they have to have some text. Also, some of the taxa might need to be combined into single articles because the differences between them are not that great to merit separate articles (e.g. between a superfamily and family). Thanks for the effort though and feel free to ask me any questions. --DanielCD 00:33, 7 May 2005 (UTC)Reply

Ok, no problem. Its just that I looked at Phacops rana, and the next available link upwards was order Phacopida, so I clicked on that and then all of the suborders had no links downward. It seemed to me that (maybe) I was filling in some blanks. PAR 05:49, 7 May 2005 (UTC)Reply

Wikipedia:WikiProject Mathematics

Hi Paul. Just wondering, are you aware of the math project? Its talk page is where a lot of math issues on Wikipedia are discussed, and could be of interest to a mathematician to have on the watchlist (sort of like math news). There is also a list of participants to sign on. All this assuming you don't mind rubbing shoulders with other mathematicians. :) Oleg Alexandrov 03:09, 5 Jun 2005 (UTC)

Thanks, Oleg - Its now on my watch list. It looks interesting. PAR 03:27, 5 Jun 2005 (UTC)

Pareto distribution

Why link likelihood to maximum likelihood rather than to likelihood function? The method of maximum likelihood is not the only use of likelihood functions. Michael Hardy 22:29, 12 Jun 2005 (UTC)

Hi Michael - The technique shown in the Pareto distribution article is directly addressed in the maximum likelihood article (section="philosophy of the MLE"). Thats the only reason. I think it should be one jump to the relevant section. I will revert it soon if you have no objection. PAR 23:17, 12 Jun 2005 (UTC)

A theorem by Boltzmann

I thought I'd ask you, since you've contributed to statistical physics articles here: In the article on maximum entropy probability distributions it says under the heading A theorem by Boltzmann:

All the above examples are consequences of the following theorem by Boltzmann.

(The theorem is about the form of the maxent distribution when the expectation of a family of functions is known.)

The article doesn't provide any explicit source for that statement. I'm not doubting the veracity of the statement or the theorem it refers to (I've seen it proved by Jaynes), just wondering where Boltzmann stated or proved that theorem. Would you happen to know the primary source, or could you point me to the secondary literature? Thanks! --MarkSweep 14:05, 13 Jun 2005 (UTC)

Hi Mark - I've seen the theorem before, but no, I don't know of the primary (or secondary) sources. I'm sure it was in some statistical mechanics course or book. PAR 16:36, 13 Jun 2005 (UTC)

Ok, I'll check some textbooks. --MarkSweep 16:58, 13 Jun 2005 (UTC)

Correlation dimension

Sorry I didn't back to you sooner. I haven't looked at it carefully, but as it progresses on the queue of to do's I'll get to it. It generally looks OK, though. No bogosity alarms went off.--CSTAR 20:24, 22 Jun 2005 (UTC)

Hypergeometric functions

Hmm, I created that category hoping it would cover the theory of hypergeometric functions, rather than listing various special functions that are special cases. Oh well, I'll have to regroup, I guess, and maybe start a category Category:Hypergeometric function theory or something like that. No problem, I just want to keep a distinction between the theory and the list of miscellaneous special functions. linas 05:27, 27 Jun 2005 (UTC)

Well, lets do the right thing. I mean, there's the possibility of two sub-categories of hypergeometric functions instead of just one. PAR 28 June 2005 13:44 (UTC)

Dilogarithm - your opinion

Hi,

I looked through the article on the polylogarithm and noticed that you are one of the main contributors to that topic. Here the dilogarithm is mentioned as a special case. I feel tempted to initiate a stub article on the dilogarithm, because it is a function that relatively often pops up in physics. However, I noticed that you have made a redirection from the dilogarithm to the polylogarithm - and based on this I began wondering whether it is to specialize too much to mention the dilogarithm explicitly???

In the article I plan to start out by defining ${\displaystyle \mathrm {Li} _{2}(z)\equiv -\int _{0}^{z}{\frac {\ln(1-z)}{z}}dz}$  for general complex variables, show the series expansion for ${\displaystyle |z|<1}$ . Then I will focus a little on real, negative arguments, show the asymptotic form, and a useful relation for converting a dilog with an argument smaller than -1 into the ${\displaystyle ]-1;0[}$  range.

Finally, I plan to add a reference to : Lewin, Polylogarithms

Not at all as comprehensive as the polylog article...but a start

Anyway, I would like to hear your opinion on this. I have never written a wikipedia article before, and today is the first time I have seen one. I am just exited to see all the material that is in here, and I began wondering if I could contribute with anything usefull... KimViborg 29 June 2005 22:35 (UTC)

I think that would be an excellent idea. Any material that is specific to the dilogarithm, but not to the polylogarithm could go in a separate article. If there is enough material, then it SHOULD go in a separate article. If you have results that apply to the polylogarithm AND the dilogarithm, please put it in the polylogarithm article as well. Not that I am an expert, but if you have any questions, just ask. PAR 30 June 2005 03:27 (UTC)

Fluctuation theorem

I thought you might be interested in this article based on your user page: Fluctuation theorem :-) --HappyCamper 3 July 2005 20:28 (UTC)

Polylogs

Hi, I replied on Talk:Polylogarithm linas 8 July 2005 19:22 (UTC)

Grassmann

Latest comment: 20 years ago2 comments1 person in discussion

If you look at the biography of Grassmann, you'll see it mentions his color work. The law comes, I believe, from his article "Theory of compound colors", Philosophical Magazine 4 (7), 1854, 254-264. You can cross-check in a few library catalogues under, e.g. Sources of color science, ed. David L. MacAdam, MIT Press [1970]. --Macrakis 23:35, 11 July 2005 (UTC)Reply

Web search finds Grassmann's three color laws covered in http://wwwzenger.informatik.tu-muenchen.de/lehre/vorlesungen/graphik/info/csc/COL_11.htm. See also http://www.colorsystem.com/grundlagen/bibl1.htm for more bibliography. Then there is Grassmann's Law in historical linguistics. --Macrakis 13:47, 12 July 2005 (UTC)Reply

Revived WikiProject on probability and statistics

Latest comment: 20 years ago3 comments2 people in discussion

Hi PAR, got your message. I've started to revive Wikipedia:WikiProject Probability, which had been more or less dormant for well over a year. I think this would be a natural place to discuss guidelines for probability related articles, open tasks, etc. My plan is to expand it and clean it up a bit, and then notify the people who are already signed up on the WikiProject page, as well as the regular contributors on Template talk:probability distribution, and perhaps others who might be interested. What do you think? --MarkSweep 03:00, 18 August 2005 (UTC)Reply

Yes, sounds like a good idea to me. Whats the time frame on this? PAR 06:11, 18 August 2005 (UTC)Reply

Don't know how long it's going to take. I personally don't have a lot of time at the moment, and the project page needs a bit more work. But I've cleaned out Wikipedia talk:WikiProject Probability, which could be used for discussions right away. --MarkSweep 06:54, 18 August 2005 (UTC)Reply

Balcoracania dailyi

Latest comment: 20 years ago1 comment1 person in discussion

If you don't know the authority for a name, you can use {{Taxobox section binomial simple}}. That allows taxoboxes without authorities to be found and fixed. It's not a good idea to guess; Balcoracania dailyi wasn't named by Daily — that would have been the height of vanity! — but by Pocock. Gdr 23:29:43, 2005-08-22 (UTC)

Ok, I understand. Thanks for pointing that out. PAR 01:07, 23 August 2005 (UTC)Reply

Tent map

Latest comment: 19 years ago1 comment1 person in discussion

Really nice bifurcation diagram - thanks ! You are right, I had got the Julia set wrong in my original description of the behaviour for μ between 1 and 2 - it is not the whole of the interval from 0 to μ/2, but just the part from μ-μ^2/2 to μ/2. I have fixed this in the article. I am interested in your views on how the explanation of the map's dynamic behaviour can be improved - which parts are still not very clear, for example ? Gandalf61 15:28, 13 September 2005 (UTC)Reply