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Dairy, October 2010



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Saturday, October 9, 2010

Going into the city

This afternoon, Li-Xia and I went into the city. We first went to Rijksmuseum Twenthe, a museum of fine arts and modern art. Admission was free because the museum celebrated their 80 years existance. We first looked at the Abstract USA 1958-1968 exhibition and then continued walking around the museum. I saw the following paintings/works: Next we went to bookshop De Slegte, where at 16:46 I bought the following three books for one euro each:


Sunday, October 10, 2010

10-10-10

Today is a special date again.

Nederland leest Oeroeg

Around 19:06, I bought a copy of the poster displayed here on the right. The poster contains the full text of the novel Oeroeg by Hella S. Haasse and was used in the campain to encourage the Dutch people to read the novel between October 23 and November 20, 2009. A free copy of the novel was made available for all members of public libraries in the Netherlands. I got a copy from my mother. The official web site of this campain is Nederland leest Oeroeg, where one can listen to the novel being read by eight Dutch persons. As far as I know, this is the first Dutch literary novel printed on a poster. The poster does not have an ISBN number, thus it cannot be considered as an official book publication, yet, I am happy to add this 'book' to my collection. I found the poster throught marktplaats.nl, a Dutch trading web site. For English poster with books see Postertext.


Tuesday, October 12, 2010

Symple

Today, Christian Freeling announced his abstract game Symple at his web site. It is a game in the category of connection games, such as Hex and Havannah. However, there is no explicit connection goal. The goal of the game is to get as much stones on the board, but there is a penalty of two points for each separate group of connected stones. During the game however, the number of groups determines how much stones you can add. That means in the first phase of the game the goal is on creating additional groups, while in the later phase of the game the goal is to connect as many groups as possible and/or prevent the opponent from connecting groups. At each turn a player can either create a new group, or grow some (or all) group with the restriction that at most one of neighbouring cells of a group may be filled with a stone. Symple is played on a hexagonal board, but I think it will also work on other types of boards, preferable with an odd number of cells to avoid a draw.


Thursday, October 14, 2010

Symple Number

The Symple number of a graph is minimum number of steps by which the graph can be covered with one colour according to the rules of the abstract game Symple. I got the idea for this definition while thinking about the optimal number of groups one should make when playing a game of Symple. And then I realized that even filling a board with a single colour in the least number of moves isn't trivial.


Wednesday, October 20, 2010

Double date

Today is a double date according to the DD-MM-YYYY format, because in that format it is 20-10-2010. This is the 238th of such dates. There are a total of 365 (because 2902 is not a leap year).


Sunday, October 24, 2010

Symple Numbers

In the past weeks I have been working on a program for calculating Symple Numbers for graphs of the form Pn (path graphs) and PnxPm (square grid graphs). The latter are equivalent with square board measuring n by m fields. The program calculated for path graphs the exact solution and for square grid graphs an upper limit.

For the path graphs the program tries all possibilities for finding a solution by combining smaller solutions. A solution can be extended by adding one at the end. This means that Symple Number for Pn is at most one more than the number for Pn-1. It is also possible to combine two solutions with one or two positions in the middle, meaning that the Symple Number of Pn can be calculated with the Symple Number of Pn1 and Pn2 where n1+n2+1==n or n1+n2+2==n. But in this case, the number of groups in each solution should be taken into account, because these need to be added. The remaining number of steps can be made simultaneously. The maximum of these should be added, and finally one to connect the two solutions. A colleague came up with the formulea 2*sqrt(n) - 2 + 4log(n) as an approximation. The results (as printed by the program) by number of groups, preceded by 2*sqrt(n) - 2 + 4log(n), are:

 2:  1.328427   2
 3:  2.256583   3   3
 4:  3.000000   4   3
 5:  3.633100   5   4   5
 6:  4.191461   6   4   5
 7:  4.695180   7   5   5   6
 8:  5.156854   8   5   5   6
 9:  5.584963   9   6   6   6   8
10:  5.985519  10   6   6   6   8
11:  6.362965  11   7   6   7   8   9
12:  6.720684  12   7   7   7   8   9
13:  7.061322  13   8   7   7   8   9  10
14:  7.386992  14   8   7   7   8   9  10
15:  7.699412  15   9   8   8   8   9  10  11
16:  8.000000  16   9   8   8   8   9  10  11
17:  8.289943  17  10   8   8   9   9  10  11  13
18:  8.570244  18  10   9   8   9   9  10  11  13
19:  8.841762  19  11   9   9   9  10  10  11  13  14

Calculating the Symple Number for square grid graphs is far more complicated, because there are far more possibilities to split a square grid graph in two parts. To calculate an upper limit, the program only calculates splits along a line cutting the graph in two smaller square grid graphs. Again the number of groups need to be taken into account. Joining two square grid graphs with a Pm graph, requires m steps. Also here the trick of covering two points can be used, if the square grid graph with the largest number of simultaneous steps can be filled at the side. For this reason we define S(n,m,g) as an upper limit for the Symple Number of the graph PnxPm that is calculated by joining two smaller square grid graphs with a Pm graph or extending a single square grid graph with such a graph. For such a graph it is true that either a vertex at the top or at the bottom can be filled as a last step. Which means that a rotated form can be used as a candidate for reduction for a larger square grid graph. The program produces the following table for S(n,m,g) where the minimum Symple Number and the smallest number of groups for which it occurs are given:

         1      2      3      4      5      6      7      8      9     10     11     12     13     14     15     16     17     18     19
 1:   1, 1   2, 1   3, 1   3, 2   4, 2   4, 2   5, 2   5, 2   6, 2   6, 2   6, 3   7, 2   7, 3   7, 3   8, 3   8, 3   8, 3   8, 4   9, 3
 2:   2, 1   4, 1   5, 2   6, 2   7, 2   8, 2   9, 2  10, 2  11, 2  12, 2  13, 2  13, 3  14, 3  15, 3  15, 3  16, 3  16, 4  17, 3  17, 4
 3:   3, 1   6, 1   7, 2   8, 3  10, 2  11, 3  12, 3  13, 3  14, 4  16, 3  17, 4  19, 3  19, 3  20, 4  20, 4  21, 5  22, 4  23, 4  23, 4
 4:   3, 2   7, 2   9, 2  10, 3  12, 4  13, 5  15, 4  16, 4  17, 5  18, 5  19, 5  20, 6  21, 6  22, 6  23, 6  25, 5  26, 5  27, 6  27, 6
 5:   4, 2   9, 2  11, 2  12, 3  14, 4  16, 3  17, 4  19, 4  20, 4  21, 5  22, 6  24, 6  25, 8  28, 5  29, 6  31, 4  32, 4  32, 5  33, 6
 6:   4, 2  10, 2  12, 4  14, 3  16, 4  18, 5  20, 4  21, 5  23, 5  24, 5  25, 6  27, 6  28, 6  29, 8  31, 6  32,11  34, 6  36, 6  37, 6
 7:   5, 2  12, 2  14, 4  16, 3  18, 4  20, 5  22, 4  24, 5  25, 6  27, 5  28, 6  29, 7  31, 6  32, 7  33, 8  35, 7  36, 8  40, 7  41, 8
 8:   5, 2  13, 2  15, 4  18, 3  20, 4  22, 5  24, 6  26, 5  28, 6  29, 7  31, 8  32, 9  34, 8  35, 9  37, 8  38, 9  39,10  42, 9  43,10
 9:   6, 2  15, 2  17, 4  20, 3  22, 4  24, 6  27, 4  29, 6  30, 6  32, 7  33, 8  35, 7  37, 7  38, 8  39, 8  41,10  42,10  44, 8  45, 8
10:   6, 2  16, 2  18, 4  22, 3  24, 4  27, 5  29, 6  31, 6  33, 6  34, 9  36, 8  37, 9  39, 8  41, 9  42,10  44, 9  46, 8  47,10  48,10
11:   6, 3  17, 3  20, 4  24, 3  26, 4  29, 6  31, 7  33, 6  35, 6  37, 7  38, 8  40, 9  42, 9  43,11  45, 8  47,10  48,10  50,11  51,12
12:   7, 2  19, 2  21, 4  26, 3  28, 4  32, 5  33, 8  36, 6  38, 6  40, 7  41, 8  43,10  44,11  46,13  48,10  50, 9  51,10  53,11  54,12
13:   7, 3  20, 3  23, 4  28, 3  30, 4  33, 5  35, 6  37, 8  40, 6  42, 7  43, 8  45,10  47,10  49, 9  50,10  52,12  54,10  55,12  57,10
14:   7, 3  21, 3  24, 4  30, 3  32, 4  35, 6  37, 8  40, 7  42, 8  45, 8  46,12  48,10  50, 8  51,13  53,10  55,12  56,13  58,15  60,12
15:   8, 3  23, 3  26, 4  31, 5  33, 6  36, 6  39, 8  41,10  44, 8  47, 7  49, 8  50,10  52,10  54,11  55,12  57,14  59,10  61,12  62,12
16:   8, 3  24, 3  27, 4  33, 5  35, 6  39, 5  41, 6  43, 8  46,10  49, 7  51, 8  53,10  54,11  56,13  58,14  60,16  62,12  64,14  65,12
17:   8, 3  25, 3  28, 6  34, 6  37, 6  40, 6  43, 8  46, 8  48,10  52, 7  53, 8  55,10  57,12  59,11  61,12  63,14  65,11  66,13  67,14
18:   8, 4  26, 4  30, 4  36, 5  38, 6  42, 6  45, 8  48, 9  51, 8  53, 9  55,10  58,10  60,12  63,13  65,10  66,12  67,13  69,15  70,16
19:   9, 3  28, 3  31, 6  37, 6  40, 6  44, 6  46, 8  49, 9  52, 8  55,10  58, 8  60,10  62,12  65,10  67,11  68,12  69,14  71,15  72,16

An interesting case is 16,6 where the minimum number of groups, 11, is larger than all it surrounding values. There are more such cases, but this seems to the largest in the table. Notice that there are also cases that are only surrounded by larger numbers, such as 13,14. The break down of S(16,6,11) based on output printed by the program is:

Which could be made graphical in the following figure, where '#' is used for groups, '-' and '|' for the connecting path graphs, and '+' the points that act as a reduction point.

###|###|###|+###
###|###|###|####
-------|+-------
##+####|###+####
##|+---|---|+---
##|####|###|####

That this can be filled in 32 steps is shown in the following, where the steps are marked with 'a' to 'z' and 'A' to 'F':

almqblmCclmrrdlm
noprnopBnopsnopq
uvtwxyzAAuvtwxyz
eltflmnDglmthlmn
mnrropqEnoprropq
opsilmnFjlmsklmn


Wednesday, October 27, 2010

c.2272delG

Today, we received a letter informing us that a c.2272delG mutation has been found in the MLL2 gen/enzyme of Andy. It is a new mutation because it is not found with Li-Xia or me. Of course, it could be possible that either of us caries a cell line in our sex cells that has this mutation. The mutation consists of a single deletion of a base pair at position 2272. To see the consequences for this appearent small mutation in the amino acid sequence, look here.

Watching Go

This evening, Li-Xia and I went to the university for meeting the people of the Go club. We met Taco and Huub. I showed them the four Go books that I had bought this summer. I did not want to play, not knowing how long I could stay, so I watched Taco and Huub play. Afterwards, we analyzed a game that I played on the internet and I added some of remarks being made.


Sunday, October 31, 2010

Super Symple

In the past weeks the rules of the abstract game Symple have slightly changed. The first is that the original game Symple has been renamed into Symplex, and that Symple is now the variant that is played on a square board with an odd size. Also a solution for the advantage for the first player has been found, namely, that the second player has the right, if nobody has grown yet to create a new group and grow in one turn. Another change that has been made is that the penalty for the number of groups has changed from two to four. Although this seems to be a small change, it might be bigger than one would expect. The motivation behind it, is that at the end of the game, you could still create new groups in the territorium of your opponents, because if the penalty is two, even if you can only create a group of two stones, you can take away points from your opponent without cost. With a penalty of four, this is less easy. Only if you can create a group of three stones, there is some gain. That group has a negative score of one, but you take away three points of your opponent, creating a net score of plus two.

Although, the rules of Symple are rather simple, I feel that they still could be made simpler. One of the problems when playing the game (without computer support) is that you often forget which groups you already have grown. And also the rule that if two groups grow on a shared field that it counts as if both groups have grown, is rather complicated. What would happen if all restrictions on where you can grow are removed? Simply stating that you can grow as many stones as you have groups. That means that if you want to grow in a certain move, you simply take a number of stones equal to the number groups you have. Would this game, that I would brand Super Sympe, be substantial different from Symple? And how different would it be? Whether invasions at the end of the game are possible, depends on the number of groups the opponent has. Interesting.


This months interesting links


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