Systems Biology (Methods in Molecular Biology)

4 Conclusion

Following the Newtonian track, originated in the realm of celestial

mechanics and immediately generalized to any kind of time-

dependent events, dynamical simulations are traditionally obtained

by mathematical models based upon numerical integration of dif-

ferential equations. The chaotic behavior of complex systems, how-

ever, provides severe limitations to any long-term prediction by

deterministic models and opens the door to an alternative approach

based upon qualitative, stochastic models. It is worth stressing that

the latter remains the only possible approach whenever the phe-

nomena of interest concern the collective behavior of large popula-

tions of relatively simple elements.

On these premises, Multi Agent Systems (MAS) perform reli-

able simulations of population-dynamics phenomena depending

upon the interactions of the population members among each

other and with the environment. Thus, the utility of MAS is to be

primarily appreciated in the design of mechanistic models account-

ing for some collective behavior. Another, more ambitious, context

deals with the quantitative refinement of the model’s parameters, in

the aim to fit the experimentally observed dynamics. All in all, as

compared to the traditional approach based on approximated

-30

-10

10

30

-30

-10

10

30

1 51 101 151 201 251

T = 2.27 (a.u.)

Area3 Area9 Area15

Area3 Area9 Area15

Area3 Area9 Area15

1 101 201 301 401 501

T = 2.27 (a.u.)

-30

-10

10

30

1 251 501 751 1001 1251 1501 1751 2001 2251 2501 2751 3001 3251 3501 3751 4001 4251 4501 4751 5001

T = 2.27 (a.u.)

Fig. 12Arising of stable and highly correlated activity trends in brain areas under default state. All conditions
are the same as in Figs.10 and 11. The table on therightcontains the correlation coefficient at the considered
temperature (T) and time span (t)

324 Alfredo Colosimo