What Is the Role of Node j in the Consensus Equation for Agent i?

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Homework Help Overview

The discussion revolves around understanding a consensus equation related to agents in a network, specifically focusing on the role of node j in the equation for agent i. The context involves concepts from graph theory and dynamics of agent interactions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to clarify why the summation limit involves node j as a neighbor of agent i and questions the necessity of taking a derivative of the term x_j(t). Other participants express confusion regarding the explanations provided and seek further details.

Discussion Status

The discussion is ongoing, with participants actively seeking clarification and additional information. Some have attempted to provide insights into the equation's implications, but there is no clear consensus or resolution yet.

Contextual Notes

Participants are working with a specific equation from a presentation, and there are indications of varying levels of understanding among them. The original poster emphasizes the importance of this understanding for their research.

asd1249jf
http://img112.imageshack.us/img112/2433/consensusequationdv9.jpg

I am having the most trouble understanding this equation. Why is the limit of summation, declared as a node j in a member of the neighbors of agents i (Which is a set of nodes and links, taken from disk graphs)? Why is it that by the term [tex]x_j(t)[/tex], a derivative of X(of the i index) must be taken? Can anyone explain how this equation works?

I am sure that this is a very difficult question and may take time to answer it, but I would heavily appreciate it if anyone can explain it well, as my research is at stake here.

More information about this equation can be found on slide #11 of powerpoint presentation.

http://www.piaggio.ccii.unipi.it/Bertinoro%202007/Materiale%20Didattico/EgerstedtTalk.pdf
 
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If i=1, N1= {1} so [itex]\overdot{x}[/itex]1= x1- x1= 0.
If i= 2, N2= {1, 2} so [itex]\overdot{x}[/itex]2= (x32- x1)+ (x2- x2= x2- x1
If i= , N3= {1,2,3} so [itex]\overdot{x}[/itex]= (x3- x1)+ (x3)+ (x3- x2)+ x3- x1)= 2x3- x1-x2.
etc.
 
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Ok, I stared at what you said for 10 minutes but failed to understand it. Can you please provide additional details?
 
anyone?
 
:( anyone?
 
Please?
 
l46kok said:
http://img112.imageshack.us/img112/2433/consensusequationdv9.jpg

I am having the most trouble understanding this equation. Why is the limit of summation, declared as a node j in a member of the neighbors of agents i (Which is a set of nodes and links, taken from disk graphs)? Why is it that by the term [tex]x_j(t)[/tex], a derivative of X(of the i index) must be taken? Can anyone explain how this equation works?

I am sure that this is a very difficult question and may take time to answer it, but I would heavily appreciate it if anyone can explain it well, as my research is at stake here.

More information about this equation can be found on slide #11 of powerpoint presentation.

http://www.piaggio.ccii.unipi.it/Bertinoro%202007/Materiale%20Didattico/EgerstedtTalk.pdf
My non-technical understanding is that the change in node i is an average of the distances between i and its neighbors. So, if node i is agnostic in its beliefs, and its distance to node 1i (who is atheist) is x1i - xi = d1i, and its distance to node 2i (who is religious) is x2i - xi = d2i, then i's beliefs will change in proportion to the average distance to its neighbors: (d1i + d2i)/2. If i's initial distance to 1i is greater than its initial distance to 2i, d1i > d2i, then in the next period (or iteration) i's beliefs will get closer to 1i.
 
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