STOCHASTIC MOBILITY MODELS IN SPACE AND TIME

An interesting fact in nature is that if we observe agents (neurons, particles, animals, humans) behaving, or more precisely moving, inside their environment, we can recognize - tough at different space or time scales - very specific patterns. The existence of those patterns is quite obvious, since not all things in nature behave totally at random, especially if we take into account thinking species like human beings. If a first phenomenon which has been deeply modeled is the gas particle motion as the template of a totally random motion, other phenomena, like foraging patterns of animals such as albatrosses, and specific instances of human mobility wear some randomness away in favor of deterministic components. Thus, while the particle motion may be satisfactorily described with a Wiener Process (also called Brownian motion), the others are better described by other kinds of stochastic processes called Levy Flights. Minding at these phenomena in a unifying way, in terms of motion of agents – either inanimate like the gas particles, or animated like the albatrosses – the point is that the latter are driven by specific interests, possibly converging into a common task, to be accomplished. The whole thesis work turns around the concept of agent intentionality at different scales, whose model may be used as key ingredient in the statistical description of complex behaviors. The two main contributions in this direction are: 1. the development of a “wait and chase” model of human mobility having the same two-phase pattern as animal foraging but with a greater propensity of local stays in place and therefore a less dispersed general behavior; 2. the introduction of a mobility paradigm for the neurons of a multilayer neural network and a methodology to train these new kind of networks to develop a collective behavior. The lead idea is that neurons move toward the most informative mates to better learn how to fulfill their part in the overall functionality of the network. With these specific implementations we have pursued the general goal of attributing both a cognitive and a physical meaning to the intentionality so as to be able in a near future to speak of intentionality as an additional potential in the dynamics of the masses (both at the micro and a the macro-scale), and of communication as another network in the force field. This could be intended as a step ahead in the track opened by the past century physicists with the coupling of thermodynamic and Shannon entropies in the direction of unifying cognitive and physical laws.