thanks for your help Robert.

I had in mind  that P(i,j) was the probability that the i-car overtakes the j-car during any one lap of the race, where the index i and j were referring to each car's starting position, i.e. to the cars themselves. That's because I was interested in the case where some cars are faster than others on average but can still be overtaken by a slower car and lose the race.

I'm interested in question like, how likely is it that the first car on the grid ends up last while the last car on the grid ends up first, etc.. I'd imagine that gamblers must have used models like that for horses?

So just to check that I understand correctly. You're saying that if the overtaking probabilities are the same for any two cars we have a reversible continuous-time Markov chain, i.e. an equilibrium probability distribution of the cars' positions. So that means that provided the race has lasted long enough the cars will stabilize in their equilibrium positions? And those would be their starting positions if the cars are all identical?

thanks for your help Robert.

I had in mind  that P(i,j) was the probability that the i-car overtakes the j-car during any one lap of the race, where the index i and j were referring to each car's starting position, i.e. to the cars themselves. That's because I was interested in the case where some cars are faster than others on average but can still be overtaken by a slower car and lose the race.

I'm interested in question like, how likely is it that the first car on the grid ends up last while the last car on the grid ends up first, etc.. I'd imagine that gamblers must have used models like that for horses?

So just to check that I understand correctly. You're saying that if the overtaking probabilities are the same for any two cars we have a reversible continuous-time Markov chain, i.e. an equilibrium probability distribution of the cars' positions. So that means that provided the race has lasted long enough the cars will stabilize in their equilibrium positions? And those would be their starting positions if the cars are all identical?

If I'm not mistaken a previous incarnation of your question received the following comments, outdated now but anyhow just so you know here's a reference:

http://www.mapleprimes.com/posts/101209-Answer-To-The-Recent-Question-About-Fern

The changes you describe all sound like potential improvements, so thumbs up. No-one has down-voted your post, so that's nice. And yes it is not necessary to have that option.

One problem I've had with the current setup is that some messages do not have the up-voting option, because they are classified as comments, I think, and yet in many cases the comments are worthy of being singled out, and I don't just mean to reward the poster, which is a concept I'm sympathetic to even though it is a little childish, but of more general relevance, surely, in order to single out useful information for others to read (or for your future self, sometimes). Sadly many times recently I've wanted to click on a message without being able to because the message was not formally an "answer." Wouldn't it be easier to have every post clickable by default?

and this is a reference to the question formerly known as:

101197-Question-About-Plotting-Fern-In-Maple-Need-Help-ASAP-

@acer 

Unfortunately there was some connection problem, perhaps unavailable from my country, but I must say I'm intrigued by the summary:

Leonard's idea for a smartphone app derails his friendship with Sheldon.

I do hope no Maple friendship will be derailed by this app idea.

I second your suggestion, generally speaking more powerful plot tools would be useful for many maple users, the ability to do all sorts of rotations and to control all aspects of axes and tickmarks, in both 2D and 3D, would be very useful (for publication and presentations): I often find myself doing stuff on Maple and then having to manually draw a graph with, say, LaTeX and PStricks because I lack control over the Maple plot.

I second your suggestion, generally speaking more powerful plot tools would be useful for many maple users, the ability to do all sorts of rotations and to control all aspects of axes and tickmarks, in both 2D and 3D, would be very useful (for publication and presentations): I often find myself doing stuff on Maple and then having to manually draw a graph with, say, LaTeX and PStricks because I lack control over the Maple plot.

@Robert Israel 

that's useful to know, thanks Robert,

in the meantime I noticed the question had been answered in another post.

http://www.mapleprimes.com/questions/100994-Procedure-To-Compute-Function-And-Curvature

@Robert Israel 

that's useful to know, thanks Robert,

in the meantime I noticed the question had been answered in another post.

http://www.mapleprimes.com/questions/100994-Procedure-To-Compute-Function-And-Curvature

P.S. to the above: I let you set the range and color options of your plots, they could be passed to the procedure as well, if you google Maple procedures and programming there's some very helpful stuff out there on how to begin writing procedures, I'm just learning myself.

P.S. to the above: I let you set the range and color options of your plots, they could be passed to the procedure as well, if you google Maple procedures and programming there's some very helpful stuff out there on how to begin writing procedures, I'm just learning myself.

@Robert Israel 

I hope the time will come before this whole internet fad has passed!

to be honest for the likes of me I'll still need to have a running copy of Maple at hand to think properly, but I know many mapleprime users, including you Robert, can run a Maple program in their head without the interface.

A mapleprimes phone app would be a good way to check for updates, I currently receive between 1 and 6 emails per update, in a rather random fashion, and I had just as well disable this email service if I can check my posts and new questions in real time.

@alex_01 

Hi Alex, I'm afraid my note is very primitive and not ready to be made into a Maple document like yours yet! But I plan to pursue my interest in the Secretary problem over the next few months, and hopefully will post back later about it.

@alex_01 

Hi Alex, I'm afraid my note is very primitive and not ready to be made into a Maple document like yours yet! But I plan to pursue my interest in the Secretary problem over the next few months, and hopefully will post back later about it.