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Dairy, September 2013



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Sunday, September 8, 2013

GOGBOT festival

Yesterday and today, I attended the GOGBOT festival. This afternoon, I first went to the Tetem art space. The things I looked at and found worth mentioning are: Next I went to 21Rozendaal, not part of Gogbot, and watched at the various exhibitions there. I found Urban Spa by Harm Rensink interesting. I also looked around the festival at the city center. I took a picture and a short movie of Sound Panzer by Nik Nowak.


Saturday, September 14, 2013

Math books

Last week, when I visited bookshop Polare, I heard that they received many books about philosophy. I discovered that the books also included many about mathematics and cosmology. Today, I bought the following two math books:


Saturday, September 21, 2013

Amsterdam

I went to Amsterdam and visited many bookshops (route in Google Maps). I visited the following bookshops: I also visited Lomography Gallery Store Amsterdam.


Wednesday, September 25, 2013

Four colour theorem

The past days, I have been thinking about the Four colour theorem, which states that each map can be coloured with at most four colours. It is sufficient to prove the theorem for maps where at each cross point exactly three edges meet. Each map having cross points with more than three edges can be transformed into a map with only cross points with three colours by placing small patches on these cross-points. When the map with extra patches can be colour, so can the map where the patches are removed again.

I read that colour a map with only cross points with three colours is equivalent with colouring the edges with three colours. This sounds a little surprising, but is related to the fact that the same colour cannot occur on both sides of an edge. Because of this, each colour can only meet with the three other colours. Suppose that the four colours are A, B, C, and D, then we can assign the edge colour a with A-B and C-D, the edge colour b with A-C and B-D, and the edge colour c with A-D and C-B. For each colouring of a map, every cross point exactly has the three colours on the edges.

I noticed that there are only two directions in which the three colour can occur: clock-wise of counter-clock-wise. We could represent these with the numbers +1 and -1. Which means that a colouring of a map with four colours is equavalent to assigning one of the values +1 and -1 to each cross point. Further more for each area on the map, the sum of the numbers on the cross points is a multiple of three (where zero and negative multiples) are included.

If got the idea to see what would happen if you would lay a cord around one cross point and then extend it every time with another point. You could keep track of the sum of the points of each area inside the cord that the cord is passing through, and see what are the rules when you extend the cord. Whenever you include a cross point inside the cord, either the number of areas the cord crosses is increased by one or reduce by one. I thought that this could lead to some simple proof, after I discovered that the patterns for adding and removing points are symmetric, but today I realized that it comes back to the same constrains that we started with. Nevertheless, I think that the equivalence between assiging the values +1 and -1 to the cross point is equivalent with colouring a map with four colours.

Large nonogram

In the past week, I was contacted by Jan Wolter with the question whether he could publish and distribute the large nonogram I have been working on in the past as part of his collection of hard nonograms. He mentioned that lately there has been a lot of progress with respect to nonogram solvers based on constraint programming, like for example Corpis, and that he wanted to distribute a collection of hard nonograms to challenge these solvers. The large nonogram was created by Kerrin Mansfield and I contacted him through his twitter account to ask him if it is okay with him. He was happy to hear from me and he decided to make the original page about the large nonogram available again on his website. Today, he tweeted the link. So far, nobody has been able to solve the large nonogram. Jan Wolter will inform me when it is solved.


Thursday, September 26, 2013

Four colour theorem

Today, I created the following form with some JavaScript to calculate some things with respect to the Four colour theorem. The starting string should consist of a sequence of 1's and 2's. The second field a sequence of positive and negative numbers can be given to expand or compact the string. Some example input has been given. When executed with example input this results in a sequence of five rows, proving that an odd number of rows can occur when expanding and compacting.

Start strings:

Result:


Saturday, September 28, 2013

Eleventh Dutch Kabuki day

Andy and I went to the Eleventh Dutch Kabuki day held at Ronald McDonald Kindervallei in Valkenburg aan de Geul. The highlight of the day, was the presentation of a 19 year old girl with Kabuki Syndrome. She is definitely one the least affected with respect to mental disability, but is not without limitations. Even if she would have been without disabilities at all, her parents could have been proud of her with respect how she deals with her limitations. She was given a big applaud.

But there was also some news on the scientific front. We are happy to have some of the leading experts with respect to Kabuki Syndrome attending in the morning. In the past two years there have been about 80 new scientific publications, most of them dealing with single cases of Kabuki Syndrome with some percular symptom, of which it is doubtfull whether it is related to Kabuki Syndrome at all. One noteworthy finding was that the top crease (distal interphalangeal crease) of the third and fourth finger is often very weak or missing. Of course, the second gene related to Kabuki Syndrome was mentioned. (See KDM6A point mutations cause Kabuki syndrome..) Also some research group had found that some children who at first scored negative with respect to a defect in the MLL2 gene, when searched further in more cell types, where found to have a defect in the MLL2 gene in only some cells, thus having a mosaic form. (See MLL2 mosaic mutations and intragenic deletion-duplications in patients with Kabuki syndrome.) Another interesting find was, since whole exome sequencing has become a increasingly used as a diagnostic tool, that there are also cases of MLL2 defects without the traditional clinical features of Kabuki Syndrome.

A clinical trial has started to investigate whether the use of growth hormone can be of any benefit to children with Kabuki Syndrome. This trial is needed to make children with Kabuki Syndrome eligible for growth hormone therapy here in the Netherlands. For this the growth curves of children with Kabuki Syndrome has been investigated. These growth curves seems to match those of Turner Syndrome and Prader-Willi Syndrome (if I remember correctly). Both boys and girls are born with a normal length, but the length will deviate more and more when they get older, and for girls the typical growth spurt in puberty seems to be missing, resulting in a much lower adult length. Also it seems that girls have a higher incidence of obesity starting during puberty. The use of growth hormone seems to have a positive effect on muscle tone, concentration, and intellectual abilities. In some cases it also seems to stabilize blood sugar levels.


Monday, September 30, 2013

Catalan numbers

With respect to the Four colour theorem, I believe it is sufficient to prove that every 'round-trip' there exists a colouring such that 'round-trip' is coloured with at most three colours, where each area is visited at most once. But because that followes from the Four-colour theorem, it must be as difficult to prove as the original theorem. I also came across Catalan numbers as the number of ways a sequence can be compacted, which I found through The On-Line Encyclopedia of Integer Sequences sequence A000108.


This months interesting links


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