LAUSR

I have read with great interest the survey [8] as I am interested in all possible applications of kinetic theory methods for active particles. The recently edited book [4] presents a broad variety of possible applications which deserve attention. The modeling of social and economical systems is definitely interesting and generates, as we learn from [8], a variety of challenging problems, not only modeling, but also analytic and computational. The mathematical tools presented in the survey refer to the kinetic theory approach proposed in [1] based on kinetic theory methods, and to the mathematical theory of collective learning reviewed in [7]. In addition, one has to bear in mind also alternative approaches such as that of hybrid deterministic-stochastic models [9] or swarm modeling [5]. My education has been mainly addressed to the study of the sixth Hilbert problem which was originally studied for the dynamics of classical particles versus fluid dynamics [11]. However, Hilbert’s visionary idea has been recently focused on the study on living systems constituted to many interacting living entities [6]. The method leads to the derivation of macroscopic quantities from the description at the microscopic scale. This process has been viewed by Hilbert as an important step towards the unifications of physical theories. This problem has been recently studied for multicellular systems [3], [10] as well as to the derivation of crowd dynamics [2]. However, humans are not cells, while their functions are not simply limited to those of pedestrians. However, we are aware that social and economical dynamics induces movement in a territory. Hence it should also be interesting to derive models with a space structure. Accordingly a micro-macro derivation approach might be developed. A more general reasoning is as follows: