May 5, 2006


It has been a long time since my last post. The reason is that I was making arrangements for moving to UK to work in the Neural Computation Research Group in Aston University, Birmingham. Well, I'm in Aston now. But after my arriving I had to solve a lot of problems. The most bizarre one was that I needed to open a bank account to receive my salary, but to open a bank account in UK you need a permanent address. When I arrived here, I was living in a hotel, therefore I didn't have a permanent address. I started to look for a flat to rent, but to my surprise the agencies asked me for a bank account number in order to rent a flat! I could not rent because I didn't have a bank account and I could not open a bank account because I didn't have a permanent address!

The circle was broken by a kind landlord who agreed in renting his flat even without a bank account. So, I could rent the flat, open the bank account and receive my salary. Everything is fine now (at least at the moment...) and I've already started to work.

I'm working here with Statistical Mechanical (SM) approaches to Information Theory (IT). What does it mean? Well, IT is an important area because it deals with exchange and storing of information, coding and decoding and everything else you can imagine you can do with information. There is even a feeling that some fundamental laws of the universe are based on informational concepts. IT was born with french engineer Claude Shannon, although I think I've already said this a lot of time in other posts. Shannon proved a lot of theorems finding bounds to some important quantities like how many information you can transmit when you have noise. This means that the results always are related to worst case situations.

However, sometimes you just want to know what is typical, not the worst case. Let me give an example. Let us say you need to save money to buy a car and you want to know how much money you need to save. Well, the worst case would be a Ferrari or a Porsche, but it will not help cause you (at least most of us) will not be able to save that amount. What you need to know is how much a car 'typically' costs, so you can have an idea of how much you have to save even without choosing the car in advance.

It turns out that SM has the appropriate techniques to do that. The most important one is a technical matter that I'll explain someday named 'Replica Theory'. How is it used in IT? Well, IT deals with transmitting information. We can choose do that bit by bit. We can encode, decode, compress and do a lot of things with information, bit by bit. In practical issues, we deal with a lot of information, that's why your HD has more than 80G today. When we do calculations, this amount of bits can be very well approximated by saying that we have an infinite number of bits. Now we arrived at the point: SM calculations always use the so-called 'thermodynamical limit' (TL), or the limit of an infinite number of components in the system. So, treating each bit as a component of the system formally, we can use SM to analyze what happens in the limit of infinite information! The results obtained can give typical behaviours that approximate very well the cases of practical interest!

Now, I need to come back and study broadcast, multiple access and relay network channels. I'll take some time to talk about them someday, when I learn them better...

On my desk:

  • Remarks on gravity, entropy, and information, Robert Carroll (physics/0602036)

  • Unknown Quantum States and Operations, a Bayesian View, Christopher A. Fuchs, Ruediger Schack (quant-ph/0404156)

  • Why can states and measurement outcomes be represented as vectors?, Piero G. L. Mana (quant-ph/0305117)

  • Quantum Theory From Five Reasonable Axioms, Lucien Hardy (quant-ph/0101012)

  • The Born Rule in Quantum and Classical Mechanics, Paul Brumer, Jiangbin Gong (quant-ph/0604178)

Picture taken from:

1 comment:

Osame Kinouchi said...

Oi roberto,
Porque vc nao coloca uma versão em portugues deste post no SEMCIENCIA?
Preciso do seu numero blogger para colocar o link na lista de contribuidores, vc conhece esse numero? Abraços, Osame