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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:
- Pictures (slides) by Rob Mellink.
- Room with art works by Florian Rosier.
- Harmony of the
Spheres by Momoko Noguchi.
- Video by Merel Theloesen of six year old girl being photographed.
- Table with controversial black and white pictures by Jochem van Laarhoven.
- Jacoba by
Margriet van Breevoort, which (who) I first walked past thinking it was
a person visiting the exhibition. It looks frightning real except for
the eyes which are kind of spooky.
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.
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:
- The Last Recreations: Hydras, Eggs, and Other Mathematical
Mystifications by Martin Gardner, ISBN:9780387949291, for
€ 14.95.
- Mathematical Vistas: From a Room With Many
Windows by Peter Hilton, Derek Holton, and Jean Pedersen,
ISBN:978-0387950648, for € 19.50.
Amsterdam
I went to Amsterdam and visited many bookshops (route in Google Maps). I visited the following bookshops:
- Antiquariaat A. Kok & Zn.
- The Book Exchange, where I bought:
- Citizen of the Galaxy by Robert Heinlein for € 4.00.
- Understanding Women: The Definitive Guide to Meeting, Dating and
Dumping, if Necessary by Romy Miller, ISBN:9781932420203, for
€ 5.00.
- Polare (Selexyz Scheltema), where I bought:
- Dagboek van een nymfomane by
Valérie
Tasso, ISBN:9789045200484, for € 7.99
- Athenaeum Boekhandel, where I was impressed by the book
This is Mars by Alfred McEwen, Francis Rocard, Nicolas Mangold,
and Xavier Barral (Editor), but found it too expensive.
- Polare (De Slegte), where I bought:
- X: De ultieme pornogids voor de vrouw by Erika Lust,
ISBN:9789490822019, for € 4.00
- JOOT books: Just Out Of Time
- Boekie Woekie
- Mendo
I also visited Lomography Gallery Store Amsterdam.
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.
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.
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.
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.
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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