Category Archives: Kinetic modelling

Hydrodynamic models of preference formation in multi-agent societies

by Mattia Zanella

Lorenzo Pareschi, Giuseppe Toscani, Andrea Tosin, Mattia Zanella

Journal of Nonlinear Science, 29(6): 2761-2796, 2019.  Preprint arXiv,

In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal preference. This variable describes an opinion-driven polarisation process, leading finally to a choice among some possible options, as it happens e.g. in referendums or elections. Like in the kinetic theory of rarefied gases, the derivation of hydrodynamic equations is essentially based on the computation of the local equilibrium distribution of the opinions from the underlying kinetic model. Several numerical examples validate the resulting model, shedding light on the crucial role played by the distinction between opinion and preference formation on the choice processes in multi-agent societies.

Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles

by Mattia Zanella

Andrea Tosin, Mattia Zanella

Multiscale Modeling and Simulation, 17(2): 716-749, 2019. (Preprint arXiv)

We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of vehicle-to-vehicle interactions and then upscaled to the global flow via a kinetic approach based on a Boltzmann-type equation. Then first and second order hydrodynamic traffic models, which naturally embed the microscopic control strategies, are consistently derived from the kinetic-controlled framework via suitable closure methods. Several numerical examples illustrate the effectiveness of such a hierarchical approach at the various scales.

 

Opinion modeling on social media and marketing aspects

by Mattia Zanella

Giuseppe Toscani, Andrea Tosin, Mattia Zanella

Physical Review E, 98(2): 022315, 2018. (Preprint arXiv)

We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisement of their products.

Related popularization article for the Italian blog Madd:Math!: La popolarità delle opinioni

 

 

Kinetic models of collective decision-making in the presence of equality bias

by Mattia Zanella

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Lorenzo Pareschi, Pierluigi Vellucci, Mattia Zanella 

Physica A: Statistical Mechanics and its Applications, 10(1):1-32, 2017. (Preprint arXiv)

We introduce and discuss kinetic models describing the influence of the competence in the evolution of decisions in a multi-agent system. The original exchange mechanism, which is based on the human tendency to compromise and change opinion through self-thinking, is here modified to include the role of the agents’ competence. In particular, we take into account the agents’ tendency to behave in the same way as if they were as good, or as bad, as their partner: the so-called equality bias. This occurred in a situation where a wide gap separated the competence of group members. We discuss the main properties of the kinetic models and numerically investigate some examples of collective decision under the influence of the equality bias. The results confirm that the equality bias leads the group to suboptimal decisions.

Opinion dynamics over complex networks: kinetic modelling and numerical methods

by Mattia Zanella

CC2D_0

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella

Kinetic and Related Models, 10(1): 1-32, 2017. (Preprint arXiv)

In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents’ distribution over the evolving network is considered which combines an opinion update based on binary interactions between agents with a dynamic creation and removal process of new connections. The number of connections of each agent influences the spreading of opinions in the network but also the way connections are created is influenced by the agents’ opinion. The evolution of the network of connections is studied by showing that its asymptotic behavior is consistent both with Poisson distributions and truncated power-laws. In order to study the large time behavior of the opinion dynamics a mean field description is derived which allows to compute exact stationary solutions in some simplified situations. Numerical methods which are capable to describe correctly the large time behavior of the system are also introduced and discussed. Finally, several numerical examples showing the influence of the agents’ number of connections in the opinion dynamics are reported.