Another excellent day has passed. The morning began in a most productive way, with a through investigation of the general number field sieve algorithm for classical factoring of numbers greater than 100 digits. To understand how this method of factoring works it was necessary to investigate number fields. This was a new concept to me. A number field, is a group of numbers and the addition/subtraction operators. The smallest number field is rational numbers. Irrational numbers are an expanded field of rational numbers, and complex numbers are an expanded field of irrational numbers. This investigation was a continuation of the Shor’s Algorithm paper. It is still being written.
The third lecture in the machine learning series was today. The lecture was on how to tell apart nerve signal ‘spikes’, on an electrode. This is because an electrode might (most likely does…) receive impulses from several different neurons. Each neuron has a preferred spike pattern. It might be short and fat, or wide and tall, or tall and narrow… There are many different characteristics we can look at. So, now we have these spikes with different characteristics and we want to cluster them together and say "This spike belongs to this neuron.". Or rather we want the computer to cluster them together. So at first a rather simple approach is taken. Simply pick a center to each cluster and then assign each point to the closest neighbor. But this method leaves questions about the boundaries.
We want an approach that weights the probability of each point falling within a certain cluster. To do this hidden variables are used. Each point is assumed to fall in some cluster, and a hidden variable of the probability of it falling in that point is used. At this point it became quite complicated, but the general idea was that we were maximizing the probability of each point falling in some particular location based on the influence of some hidden variables. The speaker mentioned how this is commonly used in modeling the stock markets, and it reminded me of the "risk factors" that I used to work with at my old job. This was the math behind them.
Immediately after was another talk, this time on BEC. I arrived late and missed the introduction, but I thought the discussion on optical lattices being used to contain atom’s was promising. I am going to read more of this later. At the end was a lab tour, and we walked through the optics setup for the BEC experiment. I was interested in the CCD camera, I’m going to read more about how they work.
Finally, after the BEC talk, but before the BEC lab tour, I overheard a portion of a conversation and it gave me the idea about a sun powered laser. When I googled it I did find some information on laser sam’s website about how to do this, but he said there is trouble getting a coherent beam.