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dvonn (2) overload

In the
[previous post](https://lievenlb.local/index.php?p=309) we have
seen that it is important to have lots of mobile pieces around in the
endgame and that it is hard for a computer-program to evaluate a
position correctly. In fact, we illustrated this with a position which
‘clearly’ looks much better for Black (the computer) whereas it is
already lost! In fact, the computer lost this particular game already 7
plies earlier. Consider the position

$\xymatrix@=.3cm @!C
@R=.7cm{.& & & & & & & & & & & & & \\ & & & \SBlack \connS & &
\bull{d}{5} \conn & & \bull{e}{5} \conn & & \bull{f}{5} \conn & &
\bull{g}{5} \conn & & \bull{h}{5} \conn & & \SWhite \connS & & \SWhite
\connS & & \SWhite \conneS & & & \\ & & \SBlack \connS & & \SBlack
\connS & & \Black{6} \connS & & \bull{e}{4} \conn& & \bull{f}{4} \conn &
& \bull{g}{4} \conn & & \bull{h}{4} \conn & & \SWhite \connS & &
\SWhite \connS & & \SWhite \conneS & & \\ & \SBlack \connbeginS & &
\SBlack \connS & & \BDvonn{2} \connS & & \bull{d}{3} \conn & & \SBlack
\connS & & \BDvonn{3} \connS & & \White{4} \connS & & \SWhite \connS &
& \Dvonn \connS & & \SWhite \connS & & \SWhite \connendS & . \\ & &
\Black{5} \connbeginS & & \SBlack \connS & & \SBlack \connS & &
\bull{d}{2} \conn & & \SBlack \connS & & \bull{f}{2} \conn & &
\bull{g}{2} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite
\connendS & & \\ & & & \bull{a}{1} \con & & \bull{b}{1} \con & &
\Black{5} \conS & & \bull{d}{1} \con & & \bull{e}{1} \con & &
\bull{f}{1} \con & & \bull{g}{1} \con & & \bull{h}{1} \con & & \White{2}
& & & \\ .& & & & & & & & & & & & & } $

Probably, Black lost the
game with its last move d1-f3 thereby disconnecting its pieces into two
clusters. White (the human player) must already have realized at this
moment he had a good chance of winning (as indicated in the previous
post) by letting Black run out of moves by building large stacks on the
third row, White building a stack of the appropriate size which then
jumps on the largest Black stack on the final move. Btw. this technique
is called *sharpshooting* in Dvonn-parlance

The concept
of manipulating the height of a stack so that it can land precisely on a
critical space. It’s a matter of counting and one-digit addition. Notice
that this doesn’t necessarily mean putting your own stacks atop one
another – the best sharpshooting moves are moves which also neutralize.
To counter a sharpshooting move is called “spoiling”.

But
for this strategy to have a chance, White must keep the Black stacks
containing the Dvonn pieces on the third row. At the moment the stack on
c3 can move to c1 or to c5 and with his next move White counters this
by *overloading* the stack, that is

To spoil a move or
prevent a lifting move by moving atop the enemy stack. Even if the
opponent has enough control to retake the stack, he cannot move it
because it has become taller.

So, White sacrifies his
height 4 stack on g3 with the move g3-c3. Black must take back
immediately (if not, White moves c3-i3 and all Black’s material in the
farmost right cluster is lost) but now the previously mobile Black
height 2 stack at c3 has become an immobile (or *old stack*) height 7
stack which has no option but to stay on c3 (clearly Black will never
move it to j3…). Next, White performs a similar startegy to
neutralize the *young* height 3 Black stack on f3 by overloading it by 2
and hence after the forced recapture it becomes a height 6 Black stack
which must remain on f3 forever. Here are the actual moves 1) g3-c3
b2-c3 2) h2-h3 b4-c5 3) h3-f3 e2-f3 and we end up with the
situation we analyzed last time, that is

$\xymatrix@=.3cm @!C
@R=.7cm{.& & & & & & & & & & & & & \\ & & & \Black{2} \connS & &
\bull{d}{5} \conn & & \bull{e}{5} \conn & & \bull{f}{5} \conn & &
\bull{g}{5} \conn & & \bull{h}{5} \conn & & \SWhite \connS & & \SWhite
\connS & & \SWhite \conneS & & & \\ & & \bull{b}{4} \conn & & \SBlack
\connS & & \Black{6} \connS & & \bull{e}{4} \conn& & \bull{f}{4} \conn &
& \bull{g}{4} \conn & & \bull{h}{4} \conn & & \SWhite \connS & &
\SWhite \connS & & \SWhite \conneS & & \\ & \SBlack \connbeginS & &
\SBlack \connS & & \BDvonn{7} \connS & & \bull{d}{3} \conn & & \SBlack
\connS & & \BDvonn{6} \connS & & \bull{g}{3} \conn & & \bull{h}{3}
\conn & & \Dvonn \connS & & \SWhite \connS & & \SWhite \connendS & . \\
& & \Black{5} \connbeginS & & \bull{b}{2} \conn & & \SBlack \connS & &
\bull{d}{2} \conn & & \bull{e}{2} \conn & & \bull{f}{2} \conn & &
\bull{g}{2} \conn & & \bull{h}{2} \conn & & \SWhite \connS & & \SWhite
\connendS & & \\ & & & \bull{a}{1} \con & & \bull{b}{1} \con & &
\Black{5} \conS & & \bull{d}{1} \con & & \bull{e}{1} \con & &
\bull{f}{1} \con & & \bull{g}{1} \con & & \bull{h}{1} \con & & \White{2}
& & & \\ . & & & & & & & & & & & & & } $

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the efficient academic

Can
software help mathematicians to keep up with the neverending (sic) flood
of new research material? In the past I touched this already… Recently, there is a new fairly active Google group
the
efficient academic
which describes its interests as

Professors, Instructors, and Graduate Students
interested in getting things done more easily and quickly. We discuss
organization, task management, and tools that helps us to be more
productive and not procrastinate. We tend to discuss David Allen’s
GTD system but not exclusively. (278 members)

Personally, I think GTD is far too management-driven to be useful in
research, but I’m equally convinced that there are nice programs
around that I have to delve deeper into, in particular DevonThinkPro.
Fortunately, Serkan Cabi has
written two interesting posts on applications of DevonThink to
physics-research :

which can help me a bit. In the second post
appears another useful resource for the average desperate present-day
ringtheorist. Joanna Karczmarek
can help you to put the Hep-th
on Your Harddrive
. A mere 8Gb containing all material published on
hep-th over the years, just waiting to be put in a database-tool like
DevonThink or, if you still need an excuse to buy one, on your iPod to
read on your daily commute…

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Latexrender and dvonn boards

In order
to blog a bit about Dvonn-strategy, I made myself a simple Dvonn
LaTeX-template which works very well on paper but which gets mutilated
by Latexrender, for example the first situation of the looks
like

$~\xymatrix@=.3cm @!C @R=.7cm{ & & \Black{2} \connS & &
\bull{d}{5} \conn & & \bull{e}{5} \conn & & \bull{f}{5} \conn & &
\bull{g}{5} \conn & & \bull{h}{5} \conn & & \SWhite \connS & & \SWhite
\connS & & \SWhite \conneS & & \\ & \bull{b}{4} \conn & & \SBlack
\connS & & \Black{6} \connS & & \bull{e}{4} \conn& & \bull{f}{4} \conn &
& \bull{g}{4} \conn & & \bull{h}{4} \conn & & \SWhite \connS & &
\SWhite \connS & & \SWhite \conneS & \\ \SBlack \connbeginS & &
\SBlack \connS & & \BDvonn{7} \connS & & \bull{d}{3} \conn & & \SBlack
\connS & & \BDvonn{6} \connS & & \bull{g}{3} \conn & & \bull{h}{3}
\conn & & \Dvonn \connS & & \SWhite \connS & & \SWhite \connendS \\ &
\Black{5} \connbeginS & & \bull{b}{2} \conn & & \SBlack \connS & &
\bull{d}{2} \conn & & \bull{e}{2} \conn & & \bull{f}{2} \conn & &
\bull{g}{2} \conn & & \bull{h}{2} \conn & & \SWhite \connS & & \SWhite
\connendS & \\ & & \bull{a}{1} \con & & \bull{b}{1} \con & & \Black{5}
\conS & & \bull{d}{1} \con & & \bull{e}{1} \con & & \bull{f}{1} \con & &
\bull{g}{1} \con & & \bull{h}{1} \con & & \White{2} & &} $

The
reason behind this unwanted clipping is that Latexrender uses
**convert** to take the relevant part of a ps-page containing only the
TeXed formula on an empty page by performing clipping and then converts
it into a GIF-file (or any other format you desire). The obvious way
round this is to enlarge my template by adding two additional rows and
columns and putting visible nonsense there (such as dots) to enlarge the
relevant part so that no clipping is done of essential info. But then
(1) the picture generated becomes even larger than that above and (2) I
don’t want you to see the extra nonsensical dots… The essential line
in the **class.latexrender.php** file is

$command =
$this->_convert_path." -density ".$this->_formula_density.
" -trim -transparent \"#FFFFFF\" ".$this->_tmp_filename.".ps ".
$this->_tmp_filename.".".$this->_image_format;

So
I needed to delve into the [manual pages for the convert command](http://amath.colorado.edu/computing/software/man/convert.html)
of the ImageMagick-package. To my surprise, the *-trim* option (which I
thought to adjust somewhat by adding parameters) doesn’t exist! Still, I
got around my second problem using the *crop* option and around the
first by using the very useful *geometry* option. The latter is also
useful if you find that the size of the output of Latexrender is not
compatible with the size of your regular text. Of course you can amend
this somewhat by using the *extarticle* documentclass (as suggested) but
if you want to further adjust it, use for example

-geometry
86%

to size the output to exactly 86% (or whatever you need).
So, whenever I want to do some Dvonn-blogging from now on I’ll change my
class.latexrender.php file as follows

$command =
$this->_convert_path." -crop 0x0-10% -crop 0x0+10% -density
".$this->_formula_density. " -geometry 80%
-transparent \"#FFFFFF\" ".$this->_tmp_filename.".ps ".
$this->_tmp_filename.".".$this->_image_format;

which
produces the output

$\xymatrix@=.3cm @R=.7cm{.& & & & & & & & & &
& & & \\ & & & \Black{2} \connS & & \bull{d}{5} \conn & & \bull{e}{5}
\conn & & \bull{f}{5} \conn & & \bull{g}{5} \conn & & \bull{h}{5} \conn
& & \SWhite \connS & & \SWhite \connS & & \SWhite \conneS & & & \\ & &
\bull{b}{4} \conn & & \SBlack \connS & & \Black{6} \connS & &
\bull{e}{4} \conn& & \bull{f}{4} \conn & & \bull{g}{4} \conn & &
\bull{h}{4} \conn & & \SWhite \connS & & \SWhite \connS & & \SWhite
\conneS & & \\ & \SBlack \connbeginS & & \SBlack \connS & &
\BDvonn{7} \connS & & \bull{d}{3} \conn & & \SBlack \connS & &
\BDvonn{6} \connS & & \bull{g}{3} \conn & & \bull{h}{3} \conn & &
\Dvonn \connS & & \SWhite \connS & & \SWhite \connendS & . \\ & &
\Black{5} \connbeginS & & \bull{b}{2} \conn & & \SBlack \connS & &
\bull{d}{2} \conn & & \bull{e}{2} \conn & & \bull{f}{2} \conn & &
\bull{g}{2} \conn & & \bull{h}{2} \conn & & \SWhite \connS & & \SWhite
\connendS & & \\ & & & \bull{a}{1} \con & & \bull{b}{1} \con & &
\Black{5} \conS & & \bull{d}{1} \con & & \bull{e}{1} \con & &
\bull{f}{1} \con & & \bull{g}{1} \con & & \bull{h}{1} \con & & \White{2}
& & & \\ . & & & & & & & & & & & & & } $

which (I hope) you will
find slightly better…

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