Τρίτη, 11 Απριλίου 2017

A "Solution" to Riemann Hypothesis


Riemann hypothesis is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12". The Riemann zeta function is conventionally represented as the sum:
ζ(z)=k=11kz
Recently, I read in Peter Woit's blog that some researchers have published a paper that describes a  Hamiltonian operator H that can be used to possibly solve this problem. This operator has the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function! The paper is also available as a preprint. In a sense, this paper says that one can set up a quantum system whose evolution "solves" Riemann hypothesis. To me this is a reasonable approach to the solution of the problem. And it reminds me of the work of  Leonard Adlemam.

Κυριακή, 22 Ιανουαρίου 2017

Multiverse and Computation

The idea that quantum computation is a manifestation of the multiverse is not new. For example, David Deutsch believes that quantum computers can be used to test its existence. Personally I believe that the multiverse is good for scripts of scifi series (e.g., the Fringer) but that's all. But I think that something is also logically wrong with this idea.

Roughly, the multiverse is the idea that there many copies of our universe (or some universe) and each evolves differently, yet in each one of them there is a copy of me but all these copies are different pairwise. Obviously, at each moment many things happen that can have different outcomes so in one universe a spermatozoon fuses with an ovum while in another this never happens but in another universe a different spermatozoon fuses with it. Practically, this means that in the first universe person A will be born, in the second nothing will happen while in the third person B will be born. If all these things are quite possible (!), I wonder how and why a quantum computer would synchronize all these universes? In most of these universes there is no parallel of myself so who is going to participate in the computation that I just started?

In my opinion, hypercomputation is the idea that we do not know enough physics to definitely say that the Turing machine dictates what can and what cannot be computed. On the other hand, the multiverse, in general, and Deutsch's ideas, are about the certitude that
  • the multiverse exists
  • there are different forms of ourselves in parallel universes
  • quantum computation takes place simultaneously in a number of universes 
Some call this science but I call it pseudoscience!

Παρασκευή, 19 Φεβρουαρίου 2016

Memcomputing

Memcomputing is a new computing paradigm that is based on the idea that the memory can and should be used to compute. The idea is based on the functionality of the brain where neurons are used to both store information and process it.  In particular the following drawing shows the way a memecomputer operates. The zigzag arrow specifies that  a signal is sent.  All other arrows designate flow of information.


Now compare this architecture with the "traditional" von Neumann architecture:

I think the difference is obvious. The interesting thing with me memcomputing is that the people who designed this computer architecture published a paper where they claim that memcomputers can solve NP-complete problems. In particular, they claim that their machine can solve instances of the subset sum problem. This problem can be phrased as follows:  Consider a finite set G of integers  having n elements, is there a non-empty subset K of G whose elements sum up to s? As happens in this and other similar cases, a number of people com forward just to question the last claim without reconizing the general contribution of people. The Shtetl-Optimized blog is such a medium. What is really annoying with such media is that their authors completely ingore Socrates's dictum: I know that I know nothing…


Creator of EAC implementation passed away

Today I was informed that  Jonathan Wayne Mills, the creator of an implementation of the Extended Analog Machine passed away on January 27, 2016 at the age pf 64 after a six month fight against cancer. I am really saddened when I hear such tragic news.
on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf
on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf

Jonathan Wayne Mills

Jonathan Wayne Mills

Jonathan Wayne Mills
Jonathan Wayne Mills

Πέμπτη, 11 Δεκεμβρίου 2014

Deep Neural Networks are Easily Fooled!

In an article that was recently posted to the arXiv and is entitled Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images, the authors discuss how Deep neural networks (DNNs) can be fooled when performing visual classification. In particular, the show how  easy it is to produce images that are completely unrecognizable to humans yet that  DNNs believe they are recognizable objects with 99.99% confidence...!

Σάββατο, 20 Σεπτεμβρίου 2014

A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...