Compilation of Email Discussion on the topic of Multi Agent Oriented Constraint Satisfaction CSCE976 Spring'2002 ===================================================================== Date: Fri, 3 May 2002 00:21:07 -0500 (CDT) From: "Berthe Y. Choueiry" To: cse976-ml@cse.unl.edu Subject: CSCE 976: discussion In his minutes on the last talk (Xu Lin's) Dan related the "energy system" to the idea of entropy. I am not really sure this is correct (as I am not comfortable with the notion of entropy). Instead, I meant the following. Sometimes (i.e., when you are lucky), you can derscribe the behavior of a *dynamic* system using an energy function (a.k.a. Lyapunov function). As the system (remember, it is a dynamic system) progresses towards an equilibirum, you can characterize this equilibirum point as the point with minimal energy. This is the minimun of the Liyapunov function. When it is a "good" minimum, the system is said to be *stable* (i.e., when you move it a little bit from its equilibrium point and leave it there, it will go back to the point of minimal energy, possibly after a few oscillations). When you have a Liyapunov function, you compute the point where the derivative is nul to get the equilibrium point. I am not sure how this relates to entropy, but a Lyapunov function can be thought of an optimization function, and equilibrium as a minimization problem. Does this make sense? -Berthe Y. Choueiry choueiry@cse.unl.edu ===================================================================== Date: Fri, 3 May 2002 09:51:14 -0500 From: Daniel Buettner To: cse976-ml@cse.unl.edu Subject: Re: CSCE 976: discussion Well, I was thinking of entropy in the context of molecular configuration where atoms will arrange themselves to reduce the energy in the system. This sounds like a process that could be modeled with a Lyapunov function, but I don't think we ever talked about that in chemistry or physics. -- ~ ~ ~ "Daniel Buettner" line 4 of 4 --100%-- ===================================================================== Date: Fri, 3 May 2002 10:46:22 -0500 (CDT) From: Lin Xu Subject: Re: CSCE 976: discussion To: cse976-ml@cse.unl.edu In chemistry, each molecular has different stage. For each stage, it has different energy level. Normally, the lowest energy level is more stable, but when the tempture is high or under UV, they may become high energy level. Sometimes between two low energy stage, there is a big hill. So heat may cause something become complete different. Lin .'* :`...' `.,' ' `. ' .**. ; ; ': ` ``:`****,' .' : ..::. ``**":.'' `. .: `: ; `,' : For everyone you love and love you! `: ` : ; : : : ; : : : .: : : :..,' ``::. Lin Xu `....:..' ..:;'' .: . ...:::: ,'''''``::::::: `:::: `::. `:: ===================================================================== Date: Mon, 6 May 2002 19:50:58 -0500 (CDT) From: "Berthe Y. Choueiry" To: cse976-ml@cse.unl.edu Subject: Re: CSCE 976: discussion Lin> In chemistry, each molecular has different stage. For each stage, it Lin> has different energy level. Normally, the lowest energy level is Lin> more stable, Yes, this is the "physical" justification for simulating annealing as an approach to optimization. Lin> So heat may cause something become complete different. You mean heat allows us to discover new stable configurations because we can go from one local minimum to the other. Correct? Indeed, a Liyapunov function can have several "attractors" (zones where the energy is minimal) some of them are stable, others are not. Does this make sense?? Thanks, -Berthe Y. Choueiry choueiry@cse.unl.edu =====================================================================