This blog post is about 3 documents I found recently, which are both interesting and correlating.
The first is the 1998 article by Francis Crick and Christof Koch with the title : Consciousness and Neuroscience.
The second is a brochure by SIAM (Society for Industrial and Applied Mathematics) about the possibility of a carrier as a mathematician.
And finally, Wolfgang Klimesch’s article on EEG oscillations in alpha and theta band.
End of the first week here at DTU and the 66th ESGI and we already work for 2 days on the Industrial Problems.
We had to give some assignments on the end of the first part of the DCAMM Ph.D. course, so I gave one in modeling a company and another one about the use of Charpit’s Equations to solve a Geometrical Optics problem.
I’m on the problem proposed by Novo Nordisc, regarding the Protein Structure Modeling and we try to understand how we can predict the 3d structure of a protein based only on it’s amino acids sequence.
I also found an interesting game, called FoldIt, where people try to solve protein folding puzzles, which is difficult, funny and helps the science.
I’m also happy for buying a card game called SET, which I played last year in Vancouver and couldn’t find it in Greece. The day I bought it, I met some great Danish guys in Copenhagen and we played SET while drinking beers on a garbage container, in one of the most touristic places of Copenhagen. 
We also went to a thing called Kro, which means “inn”, and is a popular kind of danish pubs.
There we played a danish game with dices, which is something between Kranen and Liar’s dice (I’m not really sure).
Sunday was dedicated to sightseeing. I went to some touristic locations in Copenhagen, saw the famous Little Mermaid, tried to find the Google offices in downtown Copenhagen (no luck with that), spent some time studying at the beautiful garden of the Museum of Decoration (or something ) and then I spent the afternoon in Christiania, where I followed the music and ended up at a punk concert (no live bands at that moment) where a strange and original bike-war was taking place. The teams had modified bicycles turning them into some sort of war trucks and they were trying to destroy the opponent’s truck. It was funny and had a lot of people there.
Apart from that I walked to the beautiful deer park near DTU, found the Dyrehavsbakken, the world’s oldest amusement park (1583) and ended up to the beach, where I was able to wet my hands with the waters of Øresund. There I found a party organized by the local Gymnasium’s students which was taking place at a beautiful location. Tonight I did the same thing but with a borrowed bike, which allowed me to cover many more kilometers in a fraction of the time.
In my next post I’m going to discuss some facts about Denmark.
The IPSW week is ending today, so it is time for a new post.
I worked on the problem of modeling cancer cells growth and trying to find the best combination of anti-angiogenic drugs, chemotherapy and radiotherapy in terms of dosage, frequency, scheduling and side effects.
The problem proved to be *H*U*G*E* and extremely difficult (of course! ). We worked on many different aspects of the problem and we learned a lot in the process.
During the past week, I had the chance to learn many things about Partial Differential Equations (PDEs), since I was trying to solve a 3 coupled PDEs system. I learned how to use Maple’ s PDE features (thanks to Matt) which has A LOT of weaknesses and also the COMSOL Multiphysics program, for modeling of this kind of difficult problems. I also remembered the LaTeX Beamer presentation features.
But the last week was not only about work.
We had the chance to go for kayaking in the beautiful Wascana Center lake, I played a lot of basketball (until I turned my ankle yesterday 
) and some cards and we also watched Iron Man in an almost empty cinema where we bought some HUGE pop corn bags!
P.S. 1 : Firefox 3 was released this week, so you can see above an interesting screenshot that I was lucky to take.
P.S. 2 : Google Code Jam 2008 registration already began. First Prize $10,000 plus a free trip to the Google Headquarters in Mountain View, California for the finals! 
The first week of the GIMMC is over and there is one more week left before I go back to Greece and the exams.
The past week I have been working on the problem of snow removal for the city of Regina.
Our mentor was Dr. Ed Doolittle and we were able to categorize the problem as a Capacitated Arc Routing Problem (CARP). I performed a rough Cost Estimation to show that it probably isn’t worth of optimizing, but people should really use a relatively efficient way of solving it. You can find our presentation here.
Some highlights of the past week :
) and a Mafia game another night. )My personal suggestions for Regina :
P.S. For the last 2 days the Internet connection at the university has some problems, so I can’t upload photos now. But in the next few days, they will be posted on Facebook, so just be patient.
In 5 days from now I will be on a plane going 9000 klm across the world.
I’m going to Regina the capital of the Saskatchewan province of Canada where I will attend the 2008 PIMS Industrial Problem Solving Workshop and Graduate Industrial Mathematics Modelling Camp.
It will take place at University of Regina. It will be a good opportunity to work on some interesting problems and get to learn another city in Canada after Vancouver.
The thing is that the chaos in this wannabe civilized country called Greece has won once again.
I had to reject an offer to participate in a summer program on Mathematical Biology at the Mathematical Biosciences Institute in Ohio, USA since the exams period in our university is in a quantum state.
You never know if and when it is going to happen.
I will write soon with some photos from my first days in Regina.
Exams are over, and the 8th semester already began.
It has been a long time since my last post… In the meantime a lot of strange things happened. A general strike, a few riots etc.
I’ve been enjoying the lack of electricity for a few hours a day, which provides a peaceful and dark environment for thinking and resting your mind..
I don’t have much to say this time, but here is a gift…
The other day I needed to convert an image to pdf, so I created a simple command line utility to do so…
You can find it here. I hope you will find it useful.
So, here are a few links from OCW for some of the courses I’ll be taking this semester in case anyone takes the same courses…
Physics II (YES! Walter Lewin again! 
)
Partial Differential Equations
Signal Processing
Modeling
Optimization
Optimal Control
Logic
Theory of Probability
Background song : Molotov – Frijolero
Since when this blog migrated from my own server to the WordPress one, I always disliked some of the restrictions this implied. One of the most important ones was the lack of 
But as you may have already guessed from the previous sentence I have great news.
WordPress has a new feature, so we can write normal
So, I inaugurate this new feature, by extending a result I found at The Everything Seminar, a blog I found recently and since then reading it.
At the post Convergence of Infinite, we see a simple but strong convergence test.
Theorem.
Let 
It is easy to see that we can use this result also for a sequence of negative numbers, when 
Using this we can derive the classic result of the divergence of the harmonic series.
We can also show that the alternating harmonic series converges.
Alternating Harmonic Series
We take
So, the alternating harmonic series converges.
QED
Like the Hawking-Thorne bet, we have been talking with my good friend and fellow mathematician Primelude about the Clay Millennium Problems and if and how they are going to be solved. For a few of them we agree and for others not. So we decided to bet on that. We will post our predictions, and wait if and how some of these are going to be solved. The bet is a one year subscription to a (scientific? ) magazine of the winners choice.
So here are my predictions…
It will be proved to be True, using tools from the Etale cohomology.
Probably False. Counterexample will be found.
Probably will be proved to be False. But even if it turns out to be True,
computationally (–> practically), P will still be not equal to NP.
************************
Grigori Perelman
************************
Smooth solutions always exist for both Navier-Stokes Equations and Euler Equations.
True. I can even predict who is going to prove it, if it happens in the next 30 years.
No! I’m not telling you! 
My guess, it is going to happen by finding attributes of the distribution of the primes.
Com’ on! I almost said who!
Btw, i think that if one of the 7 problems is unsolvable,then this is the one.
There exists a theory and it can explain the mass gap… True, true true!
And now we sit and wait! Or try to win the bet (together with the 1.000.000$)
P.S.
On Goldbach conjecture :
I believe it is true, but it will take us at least 100 more years before it is being solved.
After finding out about some verses from Les Chants de Maldoror, the wonderful work of Comte de Lautréamont (1846 – 1870), I decided to translate this passage (relatively loose translation) into English (from French) so people like me who don’t speak French, can enjoy the beauty of it and the admiration of Lautréamont for the magnificent glory of mathematics.
It took me a decent amount of time, since i have no idea about French and even less about poetry and poetic translations.
So take this as a warning!
I hope that soon i will be able to present also a Greek translation.
Note : The image a bellow is the engraving Melencolia I, a work of art by the German Renaissance master Albrecht Dürer. Many books and interpretations have been written about this excellent composition, so i will not even try to describe and i will only refer you to Wikipedia or other sources of informations about it.
Le Chants de Maldoror, Comte de Lautréamont
Arithmetic! Algebra! Geometry! Grandiose trinity! Luminous triangle!
Whoever has not known you is without sense!
He would deserve to suffer the greatest tortures;
since there is blind contempt for his ignorant indifference.
but the one who has met you, never again desires the goods of the earth
and he only seeks your magic pleasure.
And concentrating on your recondite wings, only wants to elevate over a spiral staircase,
and towards the sphere ædicule (gates) of heaven.
Earth only provides moral phantasmagoria and illusions,
but you, o mathematics concise, through the rigorous and unswerving propositions and the iron consistency of your rules,
you shine in his dazzled eyes, reflecting the power of the Supreme Truth, embossed in the order of the universe.
But this surrounding order, which is revealed in the regularity of Pythagoras’s friend, the perfect square, is even greater,
since Deity (Almighty – God) has presented his existence and his attributes ultimately in this notorious work,
bringing from the bowels of chaos the treasure of your theorems and the magnificent splendors.
From ancients times to now, many people of great imagination have been enchanted by the thought of your symbols,
presented on paper, as all mysterious signs which are not understood by the profane hordes.
These symbols were only the shining revelations of eternal axioms and hieroglyphs,
which have existed before the existence of Universe and will remain true after the end of it…
Synæsthesia is the neurological condition where the stimulation of a cognitive pathway leads to the involuntary stimulation of another cognitive pathway. In simple English, it mean that when for example you see a number, your brain reacts as if you have seen a color. This also happens for shapes, letters, sounds etc.
People under the influence of psychedelic drugs can sometimes feel it (the popular “hear the colors and see the sounds” effect) or even people after a stroke.
The most common explanations are two.
1) The cross-activation of adjacent regions of the brain which are involved in the color and numbers/letters recognition.
2) The reduction in the amount of inhibition along feedback pathways (can explain the LSD/mescaline effects).
But what do all of these have to do with Algebra?
Well, last night while studying Algebra (from the wonderful textbook A First Course in Abstract Algebra – J.Fraleigh, which i highly recommend) i stopped on a phrase saying that the Dihedral D4 symmetry group is simple and beautiful.
And this is true. D4 is beautiful. But how can you see that in this Cayley table?
| o | I | T | R | R2 | R3 | RT | R2T | R3T |
|---|---|---|---|---|---|---|---|---|
| I | I | T | R | R2 | R3 | RT | R2T | R3T |
| T | T | I | R3T | R2T | RT | R3 | R2 | R |
| R | R | RT | R2 | R3 | I | R2T | R3T | T |
| R2 | R2 | R2T | R3 | I | R | R3T | T | RT |
| R3 | R3 | R3T | I | R | R2 | T | RT | R2T |
| RT | RT | R | T | R3T | R2T | I | R3 | R2 |
| R2T | R2T | R2 | RT | T | R3T | R | I | R3 |
| R3T | R3T | R3 | R2T | RT | T | R2 | R | I |
I believe that the following representation is much better for seeing the underlying beauty and symmetry.
So, i decided to create a web application for doing exactly this. You provide the Cayley table of the group, and it returns you the color representation of it.
You can find it here : http://papaya.hep.ntua.gr/projects/algebra/
For any suggestions/problems, fell free to contact me.
