BeLoged

Well I am in Oklahoma....on a project :) Finally managed to fix the pictures. There was a problem with the webserver configurations. Updates killed the server configuration. Fixed now though. Will try to post something substantial this week. Especially on my MultiScale data thresholding research. I have a working code, just need to make some changes to get nicer results.

Fun With Prime Numbers

Many interesting algorithms to calculate prime numbers. Very exciiting....

I added some more articles and information to Technology and Mathematics
categories. My research on Multiscale Data Thresholding is coming along.
I will start putting some intermediate results soon.

I like simple, basic mathematics. I like theories which can be explained with simple tools. I believe that good ideas should be able to be presented in simple ways. If something can only be described in such a way that a few experts can understand it then it means there is still some work needed in that area to convert it to a simpler form. I am planning to talk about things like Prime Numbers, Encryption, Number Theory, Linear Algebra and Differential Equations and methods to solve these problems using numerical techniques. I hope some of these will turn into lecture notes at some point.

Some of the interesting books I read or am reading currently on math and engineering:

The Code Book by Simon Singh If you are interested in the history of encryption and codes this is a great book. Many interesting ideas about how to attack certain type of combinatorial problems without killing yourself with raw complexity.

Prime Obsession The story of Prime Numbers and the famous Riemann Hypothesis (Short description by Wolfram Research) There is also a proof which is not validated yet (Proof of Riemann Hypothesis)

I am mostly interested in Process Control, Model Predictive Control, Adaptive Control and Nonlinear Control. I am planning to put here classic links and basic theory. Some Matlab files and relevant book infos.

Some links:

Statistical Process Control from NASA

What is PID (simple and short)?

Other Interesting Tuning Algorithms

Interactive online education site from McMaster

More on PID

• A good starting point for the terms: Evaluation Stocks http://stocks.about.com/od/evaluatingstocks/
• Collection of introductory articles on Stock Picking http://www.investopedia.com/university/stockpicking/
• Golden ratio and Fibonacci Numbers in Stock Market http://goldennumber.net/stocks.htm
• Data Mining Techniques: How to extract useful information from big amount of data: MIT Course on Datamining
  
  

Chaos, control and controlling chaos are all very interesting topics. This article in NewScientist gives a great example of the use if chaos in control. They designed a robot to be controlled by chaotic functions. It is just a simulation but I believe it is a great start. There is a big gap between computer scientist who develop the algorithms and the people who apply them on real robots or systems. Genetic Algorithms sound very nice on paper, so does simulated annealing, but who wants to wait 5 hours before a single step is calculated. A great read...

Very interesting article on combinatorial Chemistry and drug discovery methods.

Technology Review: Bridging the Genomic Divide



That small molecules have more chance to interact with proteins and that there are only very small number of them identified is amazing. Production of small molecules is much easier and thus many more of them can be tested in a combinatorial way. The article also mentiones that NIH is planning to make the results available to public and acedemia.

Interesting technology...Magnetic Propulsion



I remember that in high school I was thinking about using Bogazici channel (connects Black Sea to Marmara Sea, so it is salty water) and the earths magnetic field to generate electricity. If you calculate between the coasts of the channel there is a mV range difference in potential. If you have very large metal plates you can generate electricity. THe oposite works too : You pump electricity to those plates and with the help of the magnetic field of earth (perpendicular to earth) you can move the water.

I added a new category on Technology. I am going to add links and ideas
about computers, software, technology and science in general to that
category.

Check this site: Prisoner's Dilemma

It is about the Prisoner's Dilemma competition. The new winner is a set of cooperating agents. Very clever. The rules are so simple but yet the results are so interesting.

I am planning to use this space to write about computers, software and technology in general.

An interesting article on this new finding. Unfortunately gene therapy is still far away from being reality, but it is interesting to play with genes in this way to prevent cancer or similar health issues. The question is though the side effects. How specific can one get in preventing cell division?

Started working on some new algorithms to test my ideas on event

identification using multiscale thresholding. Check it out at my mathematics category.

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A signal consists of multiple components occurring at different frequencies. Current analysis methods analyze signals either in time or frequency domain but not in both at the same time. Time series analysis is major topic in signal processing. Any control engineer spends endless nights studying the Fourier transformations which convert a time series into the frequency domain and you can draw fancy graphs and shape your frequency response of your controller. These methods work very nicely for linear systems, meaning if you can open a valve infinitely :).

I am interested in analyzing signals in both domains at the same time. This would enable the use of methodologies from both domains, like constrains and events in time, and data smoothing (multiband frequency filters). Wavelets provide a nice framework for this type of research.

I currently work on simple multiscale threshholding algorithms. The idea and underlying math is extremely simple:

• Convert the signal into multiscale domain using Haar wavelets (http://cnx.rice.edu/content/m10764/latest/)
• Threshold the difference components (i.e. if less then epsilon set it to zero)
• Reconstruct the signal

Next steps are going to be

• Use a moving window for the threshholding algorithm to get multiple reconstructed values for the same data points
• Analyze these points for variance
• Establish an event detection algorithm

I will post some of my results soon.

ScienceWorld is a very rich scientific treasure box. I recommend everyone to go and take a look.

My thesis was based on Multiscale Modelling. The building blocks of this methodology are a type of filters called Wavelets. Using wavelets it is possible to transform a first order system to time-frequency domain. In this domain the model representation is not anymore the simple linear time line but a tree structure where both time line (horizontal) and scales (frequency bands - vertical) are represented.

Once the model is transformed into this new domain it is also possible to create algorithms to solve a QR Programming problem based on this first order system. Instead of solving the problem globally it is possible to solve a subset which is a close approximation. This fast solution represents fine resolution at the beginning of the time line and a coarser resolution in the future where uncertainity in most physical systems make finer calculations obsolote anyhow.

I am going to go into more details in the comments section of this post in the next couple days. I will formulate a sample case and demonstrate the solution algorithm. I hope to have some links ready at some point too. Please send comments if you have any.

UPDATE: What is QR? (click here for the source)

The quadratic programming problem involves minimization of a quadratic function subject to linear constraints. Most codes use the formulation

where is symmetric, and the index sets and specify the inequality and equality constraints, respectively.

The difficulty of solving the quadratic programming problem depends largely on the nature of the matrix Q.