M. Abdellahi, M. Zahri
Department of Mathematics
College of Science
Taibah University
P.O. Box 30002, Madinah, KINGDOM OF SAUDI ARABIA

Abstract. For a fixed initial discrete positive measure, we define the corresponding global energy, which we call it collective intelligence energy. Since this energy map is not a continuous function of measure, we introduce an intensity function to extend it to a continuous mass operator. Moreover, by using nonlinear programming methods, we present some interesting results on maximizing such self-organizing behavior of the collective. We also show that the support structure of the measure -collection of individuals- influences the energy of collective intelligence. Therefore, characterizing the distribution of this agents based model in form of active autonomous individuals is worth to be analyzed.

Received: May 15, 2012

AMS Subject Classification: 92D50, 92D25, 91D30

Key Words and Phrases: energy of collective intelligence, self-organizing agents, emergence, measure metric space, nonlinear optimization

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