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Michi’s blog » archive for August, 2008

R and topological data analysis

  • August 23rd, 2008
  • 4:38 pm

This is extremely early playing around. It touches on things I’m going to be working with in Stanford, but at this point, I’m not even up on toy level.

We’ll start by generating a dataset. Essentially, I’ll take the trefolium, sample points on the curve, and then perturb each point ever so slightly.

idx <- 1:2000
theta <- idx*2*pi/2000
a <- cos(3*theta)
x <- a*cos(theta)
y <- a*sin(theta)
xper <- rnorm(2000)
yper <- rnorm
xd <- x + xper/100
yd <- y + yper/100
cd <- cbind(xd,yd)
 

As a result, we get a dataset that looks like this:
Trifolium data

So, let’s pick a sample from the dataset. What I’d really want to do now would be to do the witness complex construction, but I haven’t figured enough out about how R ticks to do quite that. So we’ll pick a sample and then build the 1-skeleton of the Rips-Vietoris complex using Euclidean distance between points. This means, we’ll draw a graph on the dataset with an edge between two sample points whenever they are within ε from each other.

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RIP Henri Cartan

  • August 22nd, 2008
  • 6:29 pm

As John Armstrong said, I didn’t know he was still alive!

On the algebraic topology mailing list, the announcement came today that Henri Cartan, once co-founder of Nicholas Bourbaki, died August 13, 2008:

La Société Mathématique de France (SMF) a la tristesse d’annoncer le décès d’Henri Cartan survenu le 13 août 2008 à Paris à l’age de 104 ans. Auteur d’une oeuvre scientifique considérable, membre fondateur du groupe Bourbaki, Henri Cartan a initié des générations de mathématiciens à la pensée mathématique, à son exposition et à son écriture. Président de la SMF en 1950, il a joué dès cette période un rôle de premier plan dans la vie mathématique mondiale. Européen de la première heure, il a fondé en 1957 l’Association européenne des enseignants et proposé dès lors la création d’un Livret Européen de l’Étudiant.
Militant des droits de l’homme, il a participé à la création du Comité des mathématiciens et oeuvré pour la libération de mathématiciens injustement emprisonnés à travers le monde.

This is a preview of RIP Henri Cartan. Read the full post (220 words)

The end of the line

  • August 4th, 2008
  • 6:15 pm

And a new beginning.

We seem to be a whole crowd finishing our PhDs all at the same time: pozorvlak, Gooseania and I. While my blog started as inspired by Gooseania, I won’t close it just because I’m done. I’ll continue blogging my Postdoc years, and hopefully all the way through my academic career.

(55 words)