Proof: Wikipedia

“A mathematician is a machine for turning coffee [and wikipedia articles] into theorems” [A. Rényi]

In the last couple of weeks (or months, I lost track of space and time!) I tried to prove something. 



This “something” turned out not to be as trivial as I thought it would be and I had to invoke the power of a lot of mathematical concepts. Although I studied math, a lot of things were new to me (or I just forgot them) and I had to (re)learn quite a bit. Of course taking courses or reading books would be too time consuming, so I used Wikipedia as a reference (Disclaimer: Do not admit doing that in real life). Continue reading

Soccer Analytics Part 3: Transitivity of Soccer

“If Bayern Munich won 3:1 against FC  Barcelona and Borussia Dortmund won 3:0 against Barcelona, then Dortmund will win 6:1 against Munich.” We all did this calculations when we were younger! What we didn’t know back then is that we implicitly assumed a strong transitivity in soccer and therefore a high predictability of results. Because when we know that A beat B and B beat C, than we can be quite sure that A will beat C. But of course we all know that soccer does not work like that. But how transitive is soccer actually. That is, how often can we observe a triplet A beats B, B beats C and A beats C?
This entry will deal with this question and also compare the transitivity of soccer with other sports around the world.

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The Walk of Pi: In 736036 Days Digits Around the World

Happy $pi$ day everyone! But it is not just an ordinary $pi$ day, no, it is the ultimate $pi$ day!

3/14/15 9:26:53
To celebrate this awesome day, i decided to write an entry devoted to the beauty of $pi$. Specifically, about the random walk of $pi$.

 

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Soccer Analytics Part 2: Why Al Kuwait SC was (probably not) the Best Team in 2013

In the first part of my Soccer Analytics series, I talked about general statistics of my dataset of the season 2013. As a reminder, i scraped all results from 177 domestic leagues and intra continental cups world wide. This entry will deal with the question “Who was the best team in 2013?” according to network analysis and why the result is (most likely) wrong.

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Not Interesting Networks: The Human Body

“Networks are everywhere” is THE catch phrase of social network analysis. As I said in a previous post, if you are a network scientist everything looks like a network to you.  That’s why I decided to start a series about “everywhere” networks. But not just any. No! In particular those that are just not interesting at all. Although networks might be ubiquitous, that does not always make them worthwhile studying.

With this special kind of networks, I will just do some fancy visualizations and maybe some boring statistical analysis. To emphasize the non-scientific relevance, the visualizations and statistics will be presented with the dearly beloved comic sans.


Body Part Relationships Network

I got the data from here. The description of the data is as follows:

“[…] contributors classified if certain body parts were part of other parts. Questions were phrased like so: “[Part 1] is a part of [part 2],” or, by way of example, “Nose is a part of spine” or “Ear is a part of head.”

Well if that’s not exciting…

Here is a visualization of the network

A cluster analysis revealed, to which class of body parts (upper in light blue, lower in light red) certain body parts belong. The algorithm was not so sure about the belly though.

The following table shows the most important body parts according to some centrality measures and what these measures could stand for.

So the head is the most important body part and the face is full of other things. Good to know.

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