Category Archives: preprint

Mean field control hierarchy

Giacomo Albi, Young-Pil Choi, Massimo Fornasier, and Dante Kalise (01/08/2016  arxiv.org/abs/1608.01728) In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE … Continue reading

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Opinion dynamics over complex networks: kinetic modeling and numerical methods

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (31/03/2016 arxiv.org/abs/1604.00421) 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 … Continue reading

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Selective model-predictive control for flocking systems

Giacomo Albi, Lorenzo Pareschi (16/03/2016 arxiv.org/abs/1603.05012) In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of the control. As a first step toward a reduction of … Continue reading

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On the optimal control of opinion dynamics on evolving networks

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (31/10/2015  arxiv.org/abs/1511.00145) In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a … Continue reading

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Biological transportation networks: modeling and simulation

Giacomo Albi, Marco Artina, Massimo Foransier, Peter A. Markowich (26/08/2015, link) We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling … Continue reading

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Invisible control of self-organizing agents leaving unknown environments

Giacomo Albi, Mattia Bongini, Emiliano Cristiani, Dante Kalise (15/04/2015  arXiv.org/1504.04064) In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We first introduce a new microscopic … Continue reading

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Boltzmann type control of opinion consensus through leaders

Giacomo Albi,  Lorenzo Pareschi, Mattia Zanella. (06/05/2014  arXiv:1405.0736) The study of formations and dynamics of opinions leading to the so called opinion consensus is one of the most important areas in mathematical modeling of social sciences. Following the Boltzmann type control … Continue reading

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Kinetic description of optimal control problems and applications to opinion consensus

Giacomo Albi, Michael Herty, Lorenzo Pareschi (30/01/2014 arXiv:1401.7798) In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under … Continue reading

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Modeling self-organized systems interacting with few individuals: from microscopic to macroscopic dynamics

Giacomo Albi, Lorenzo Pareschi (27 /09/2012 arXiv:1210.1172) In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal … Continue reading

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Binary interaction algorithms for the simulation of flocking and swarming dynamics

Giacomo Albi, Lorenzo Pareschi (04/03/2012 arXiv:1203.0721) Microscopic models of flocking and swarming takes in account large numbers of interacting individuals. Numerical resolution of large flocks implies huge computational costs. Typically for $N$  interacting individuals we have a cost of $O(N^2)$. We tackle the problem … Continue reading

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