Comment on "Self segregation versus clustering in the Evolutionary Minority Game"

This is a comment on a paper by S. Hod and E. Nakar, published in Phys. Rev. Lett. 88, 238702 (2002)Comment: 1 page (PRL-like), 1 Figure. Some changes in the text. Accepted for publication in Phys.Rev. Let

2-local triple homomorphisms on von Neumann algebras and JBW∗^*-triples

We prove that every (not necessarily linear nor continuous) 2-local triple homomorphism from a JBW$^*$-triple into a JB$^*$-triple is linear and a triple homomorphism. Consequently, every 2-local triple homomorphism from a von Neumann algebra (respectively, from a JBW$^*$-algebra) into a C$^*$-algebra (respectively, into a JB$^*$-algebra) is linear and a triple homomorphism

Local triple derivations on C*-algebras

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.Comment: 12 pages, submitte

Thermal treatment of the minority game

We study a cost function for the aggregate behavior of all the agents involved in the Minority Game (MG) or the Bar Attendance Model (BAM). The cost function allows to define a deterministic, synchronous dynamics that yields results that have the main relevant features than those of the probabilistic, sequential dynamics used for the MG or the BAM. We define a temperature through a Langevin approach in terms of the fluctuations of the average attendance. We prove that the cost function is an extensive quantity that can play the role of an internal energy of the many agent system while the temperature so defined is an intensive parameter. We compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the MG or BAM in the limit of very low temperature.Comment: 9 pages in PRE format, 6 figure