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Our Inner Ape
Today at 11:44, I bought the book Our Inner
Ape by Frans de Waal, ISBN:9781862077959 from bookshop De Slegte for € 9.95.
Urban HPV
This morning, I went to get my new bike, a brown Urban HPV with a 7-speed transmission and frame number
C01037006. Because I am using this bike for going to work, I can
buy it with tax reduction. This bike is going to replace the
Kronan Klassik that I bought on Monday, April 4, 2005. I decided to buy a bike with a 7-speed
transmission because I expect to bike much more now that Li-Xia lives at a care home on the otherside of the town.
Topographic Atlas of Twente
Today at 16:56:42, I bought ANWB Topografische atlas Overijssel, ISBN:9789018023652
from bookshop Broekhuis
for € 9,90. It contains 111 topographic maps on
a scale 1:25,000 each covering an area of 5,5 by 8 Km.
Proof
Last Saturday, I watched the movie Proof (2005). I did find this an interesting
movie and bought the DVD second hand, which I watched last
Monday again, first only to check if it was okay, and then
having to watch it till the end.
It made me think about proving P versus NP. I have been thinking that if you want to
proof that P equals NP, you need to provide an algorithm
(Turing machine according to the official definition) that
solves an NP problem in polynomial time. There are two things
that you need to do: Proof that it runs in polynomial time
to the size of the input and proof that it is correct.
It seems that in order to proof that an algorithm runs in
polynomial time, on needs to identify a polynomial of a
certain order. It also seems that the order definines the
maximum number of nested 'loops', but that it not true. It
is possible to think of an algorithm where the number of
nested 'loops' depend on the size of the input, where each
deeper loop runs in a smaller power than the surrounding
loop.
To proof that an algorithm is correct, one needs to proof
that with any given input it calculates the correct answer.
The general way to proof that an algorithm is correct is
to provide an invariant for each step in the algorithm and
to show that the invariants are kept during each step of
the algorithm.
There are three types of algorithms solving an NP problem.
One type find a solution in case there is a solution. The
second type tells for a certain choice in the solution,
if there exists a solution or not. And the third type
simply answers if there exists a solution at all. In a
sense all three types of algorithms are equivalent. Take
for example the Exact Cover
problem where one has to select a number of binary vectors
for a given set of vectors such that for each column there
is exactly one vector that has a value true in that column.
If one has a polynomial algorithm that finds a solution,
when there is one or either not, one also has an algorithm
that answers the question whether there is a solution at
all. If one has an algorithm that for some vector can tell
if it is included in a solution or not, one can use this
to find a solution. If this algorithm establishes for some
vector that it does not occur in any solution, one can
simply remove the vector and apply the algorithm on the
remaining set of vectors. If it does occur in some solution,
one can select it and apply the algorithm on the reduced
set of vectors. If one has an algorithm that can determine
if a certain set of vectors has a solution, one can simply
use it to determine if a certain vector can be included or
not by applying the algorithm to the reduced problem where
the vector is either included or not. If for one of the types
there exists a polynomial algorithm, than one exists for each
type.
Curcumin and vitamin D-3
Today, I came across
an article about curcumin and vitamin D-3 in relation with positive effects
on Alzheimer's Disease.
For a long time I have been giving Li-Xia a supplement with curcumine. I do not know whether
it has had any positive effect on her Alzheimer's Disease. But I
do know that the amount of alergic reactions and itching has reduced
and the last year it also seems that she has less problems with feeling
cold. I do not know whether this is the result of curcumine, but it is
possible, because it does have an anti-inflammatory effect. Curcumine
is also said to have a positive effect on the liver and a relationship
between the liver and Alzheimer has been suggested. The article noticed
that for some people curcumine could have a negative effect on the
absorption of amyloid beta. But vitamin D-3 seems to have a possitive
effect on everybody. At least half a year ago, I started to give
Li-Xia vitamine D-3. In the past months I have reduced the number of
supplements that she gets, because swallowing becomes a bigger and
bigger problem. At this moment she only gets curcumin and vitamine D-3.
Geometric patterns
Today at 11:07, I bought two math related books from bookshop De Slegte and I got one book for free because of the
Boekenweek, the
Dutch national book week. I picked the (second hand) book De Erfenis
(The Inheritance) by Connie Palmen. The first book I bougth, is Het Wiskundeboek,
the Dutch translation of The Math Book, ISBN:9789089980373 by Clifford A. Pickover, which
costed € 14.95. The second book is Arabian Geometric Patterns,
ISBN:9789057681561, published by The Pepin
Press, which I bought for € 17.50. This book contains
many Arabic Geometric Patterns. Some time
ago, I was contacted by Brian Wichmann who informed me about
the Tiling Database he
maintains with assistance from Tony Lee. His site also hosts
Tony Lee's notebooks.
Lee also wrote Islamic Star Patterns. The site Taprats provides computer-generated Islamic star patterns. Many
pictures and diagrams of Islamic geometric patterns can be found
on Pattern in Islamic art.
Sitting outside
We have a lot of sunny days. Today, it is the first time
that my colleagues went outside during lunch time. Two years
ago it was March 31 when
they did so, but then they still had to put on their coats.
Magnolia in the rain
This afternoon, it started to rain for the first time after
many days with sunshine. It just started raining when I left
from the office. When I arrived at home, the rain had almost
stopped. In the garden, I noticed that some flower of Magnolia had opened. I took some pictures where you can
see the raindrops on the flower leaves.
In the past weeks, mainly while biking around the city, I
have been thinking a lot about P versus NP. I am more and more becoming convinced
that P is not equal NP. Today, I came across the paper Natural Proofs by Alexander Razborov and Steven Rudich. I had heard about this before, but now
I am actually thinking about studying the paper. I am
afraid that I have been mainly thinking about natural proofs in the past weeks.
Pioneer Anomaly Solved By 1970s Computer Graphics
Today, I read Pioneer Anomaly Solved By 1970s Computer Graphics Technique
on the Physics arXiv Blog, and decided to submit a story to
Slashdot, with a reference to
this article. It was accepted by CmdrTaco
himself. He did a little editting and added two links.
This months interesting links
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