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Robust Algorithms

You are writing a very advanced algorithm and it looks that you have noticed to every aspects of implementations, but your program does not work at all! You may become disappointed of the performance of your advanced algorithm, or you might find a very small bug in a line of your code: you had typed x++ instead of x–. The world would be a better place to live if your programs were not that sensitive to these small typos.
Not very seriously, I have thought about robust algorithm, i.e. an algorithm that is insensitive to its changes. Is it possible?! To answer this question, I must know what is an algorithm and what can be considered as an algorithm. I think (however, I am not sure), an algorithm can be considered as a thing that can be implemented by a Turing machine and vice versa. This remains the big question that is about the limits of a Turing machine. I know that it is a universal computer, but I am not sure what is the exact meaning of it: does it mean that every mathematical calculation (e.g. solving a PDE) is a “computation” task and can be implemented by a Turing machine. In addition, I want to know if there exists a problem that cannot be implemented by an algorithm (you know, I have not had any course on theory of computation or something similar).
Let’s assume that an algorithm is a sufficient framework for almost everything, including solution of a dynamical system. If the converse is true, a dynamical system is capable to present an algorithm and is its equivalent, is it possible to use the same robust analyses of the dynamical system to an algorithmic one? For instance, we may analyze a specific algorithm to see whether it is robust to some small changes or it would become unstable? If x(n) is the state of an algorithm at moment “n” and x(n+1) = F(x(n))+G(x(n),u(n)) is the next state, we may present a perturbed version of it as x(n+1)=F(x(n)) + deltaF((x(n)) + G(x(n),u(n)) + deltaG(x(n),u(n)) + du(n). These deltaF(.) and … can be considered as perturbations and the stability of the new system is dependent on their properties. For instance, for the following algorithm:

Get inputs x(1) … x(k)
Sum = 0;
for(i=1;i

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Applying Started!

I started filling the forms. I filled most parts of forms of MIT, USC, and U. of Alberta. Hmmm … Is there anybody who
can help me writing a good statement of purpose?! Anyway, hope it works!! 😀

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Life goes on

We (me and Dr.Nili) are still working on editing the paper. It is about 2.5 months from when I started writing it. It seems that it doesn’t want to be finished anyway.

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I, Robot: The Singularity Approach

I watched I, Robot a few days ago. It was of the kind of science fiction movies that pleases me much (like AI, Terminator II, and even 2001:A Space Odyssey). I don’t want to describe the movie; however, I want to say that those kinds of problems are inevitable and are side-effects of the singularity which I believe in. It is not because of disobeying those three robotics laws of Asimov, but due the fact that the agent’s designer doesn’t know what kind of intelligent behavior emerges from the interaction of an embodied system equipped with a sufficient processing power and necessary information processing software.

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Brain in a dish acts as autopilot, living computer

A University of Florida scientist has grown a living “brain” that can fly a simulated plane, giving scientists a novel way to observe how brain cells function as a network.
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To control the simulated aircraft, the neurons first receive information from the computer about flight conditions: whether the plane is flying straight and level or is tilted to the left or to the right. The neurons then analyze the data and respond by sending signals to the plane’s controls. Those signals alter the flight path and new information is sent to the neurons, creating a feedback system.
“Initially when we hook up this brain to a flight simulator, it doesn’t know how to control the aircraft,” DeMarse said. “So you hook it up and the aircraft simply drifts randomly. And as the data comes in, it slowly modifies the (neural) network so over time, the network gradually learns to fly the aircraft.”
Although the brain currently is able to control the pitch and roll of the simulated aircraft in weather conditions ranging from blue skies to stormy, hurricane-force winds, the underlying goal is a more fundamental understanding of how neurons interact as a network, DeMarse said. (quoted from EurekAlert!)

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Figure Generation Progress Report

Right now, I get my computer to generate necessary data for my figures which I will put them in my paper. Hmmm … These are necessary data:

1-Abstract Problem – Structure Learning – ZO and FO (done!)
2-Abstract Problem – Behavior/Structure Learning – ZO (done!)
3-Object Lifting – Structure Learning – ZO/FO (under preparation)
4-Object Lifting – Behavior/Structure Learning – ZO (not yet!)