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Collective learning dynamics in behavioral crowds
JID:PLREV AID:764 /DIS
[m3SC+; v1.233; Prn:12/07/2016; 9:15] P.1 (1-2)
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ScienceDirect Physics of Life Reviews ••• (••••) •••–••• www.elsevier.com/locate/plrev
Comment
Collective learning dynamics in behavioral crowds Comment on “Human behaviours in evacuation crowd dynamics: From modeling to “big data” toward crisis management” by Nicola Bellomo et al. D. Burini Department of Mathematical Sciences, Politecnico di Torino, 10129 Torino, Italy Received 27 June 2016; accepted 4 July 2016
Communicated by J. Fontanari
A recent literature on crowd dynamics [9,10] has enlightened that the management of crisis situations needs models able to depict social behaviors and, in particular, the spread of emotional feelings such as stress by panic situation. I wish to mention that propagation of emotional behaviors can be described by models of collective learning dynamics, where interactions involve a whole populations rather than individual entities [6]. The survey of Bellomo et al. [4] presents an overview and critical analysis of the literature on the modeling of learning dynamics. The authors propose their own approach, based on suitable development of methods of the kinetic theory and theoretical tools of evolutionary game theory, with the objective of developing a mathematical theory of perception and learning in view of their application to modeling complex systems, which can develop a collective intelligence. The approach can be viewed as an extension of the concept of population thinking and of the theory of evolution and the important motivations to the contents of this paper are induced by the idea that the mathematical structure might include features which could make it interesting in different field of life sciences, see also [7]. The survey [4] enlightens the aforementioned topics and after a critical analysis of the existing literature proposes a crisis management approach based on modeling of crowd dynamics by kinetic theory methods [1–3,5] with interactions modeled by a stochastic development of evolutionary games [8]. Crowd dynamics is a relevant example of learning dynamics where walkers learn from other walkers their own bias, indeed the mathematical tools proposed in [4] show common features with those presented in [6,7]. The result is the following structure: ∂t f (t, u) = A[f ](t, u) + B[f ](t, u) η(u∗ , u∗ )A(u∗ → u|u∗ , u∗ )f (t, u∗ )f (t, u∗ ) du∗ du∗ = Du ×Du
− f (t, u)
η(u, u∗ ) f (t, u∗ ) du∗
Du
DOI of original article: http://dx.doi.org/10.1016/j.plrev.2016.05.014. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.plrev.2016.07.002 1571-0645/© 2016 Published by Elsevier B.V.
JID:PLREV AID:764 /DIS
[m3SC+; v1.233; Prn:12/07/2016; 9:15] P.2 (1-2)
D. Burini / Physics of Life Reviews ••• (••••) •••–•••
2
+
ν[f ](u∗ ) B[f ](u∗ → u|u∗ , E1 [f ])f (t, u∗ ) du∗
Du
− f (t, u)ν[f ](u),
(1)
where the internal variable u denotes the level of learning within the population and square brackets have been used to denote the dependence on the distribution functions which highlight the nonlinear nature of interactions. In eq. (1) the first term A[f ](t, u) is referred to individual-based learning of walkers with interaction rate η and transition probability density A. The second term B[f ](t, u), instead, is due to micro–macro learning of a walker from the mean value of the activity E1 (macrostate) of the group of individuals which the walker interacts with. The interaction rate ν and the transition probability density B are supposed to depend on the macrostate of the population. The structure of eq. (1) highlights that human behaviors in pedestrian flow and in more critical cases such as rapid evacuation in danger situations, is not only influenced by their own strategy, but also depends on interactions, mechanical and social, with the surrounding walkers (behavioral crowd). The survey [4] has given evidence that future research activity in the field of crowd modeling should look ahead to future developments where propagation of emotional state are carefully taken into account. It would be nice having the authors’ opinion on the use of learning dynamics over the modeling approach to behavioral crowds. My idea is that indeed, it has to be regarded as an important tool to be used toward the aforementioned objective. On the other hand, I am aware that the main difficulty is that the titles examined in [6] refer to systems where the role of space is not relevant, while it is essential in crowd dynamics. I argue that the role of the space variable needs the introduction of a sensitivity domain to perceive signals that might change, or not, individual emotional states. This feature induces nontrivial conceptual difficulties that suggest further developments of Sigmund theory of evolutionary games [8]. Hopefully, the opinion on this topic by the authors of [4] can contribute to tackle this matter. References [1] Ajmone Marsan G, Bellomo N, Gibelli L. Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics. Math Models Methods Appl Sci 2016;26(6):1051–93. [2] Bellomo N, Bellouquid A. On multiscale models of pedestrian crowds from mesoscopic to macroscopic. Commun Math Sci 2015;13(7):1649–64. [3] Bellomo N, Bellouquid A, Knopoff D. From the micro-scale to collective crowd dynamics. Multiscale Model Simul 2013;11:943–63. [4] Bellomo N, Clarke D, Gibelli L, Townsend P, Vreugdenhil BJ. Human behaviours in evacuation crowd dynamics: from modelling to “big data” toward crisis management. Phys Life Rev 2016. http://dx.doi.org/10.1016/j.plrev.2016.05.014 [in this issue]. [5] Bellomo N, Gibelli L. Toward a behavioral-social dynamics of pedestrian crowds. Math Models Methods Appl Sci 2015;25:2417–37. [6] Burini D, De Lillo S, Gibelli L. Collective learning modeling based on the kinetic theory of active particles. Phys Life Rev 2016;16:123–39. [7] Burini D, De Lillo S, Gibelli L. Learning dynamics towards modeling living systems: reply to comments on “Collective learning modeling based on the kinetic theory of active particles”. Phys Life Rev 2016;16:158–62. [8] Hofbauer J, Sigmund K. Evolutionary game dynamics. Bull Am Math Soc 2003;40:479–519. [9] Vermuyten H, Belien J, De Boeck L, Reniers G, Wauters T. A review of optimisation models for pedestrian evacuation and design problems. Saf Sci 2016;87:167–78. [10] Wijermans N, Conrado C, van Steen M, Martella C, Li JL. A landscape of crowd management support: an integrative approach. Saf Sci 2016;86:142–64.
[m3SC+; v1.233; Prn:12/07/2016; 9:15] P.1 (1-2)
Available online at www.sciencedirect.com
ScienceDirect Physics of Life Reviews ••• (••••) •••–••• www.elsevier.com/locate/plrev
Comment
Collective learning dynamics in behavioral crowds Comment on “Human behaviours in evacuation crowd dynamics: From modeling to “big data” toward crisis management” by Nicola Bellomo et al. D. Burini Department of Mathematical Sciences, Politecnico di Torino, 10129 Torino, Italy Received 27 June 2016; accepted 4 July 2016
Communicated by J. Fontanari
A recent literature on crowd dynamics [9,10] has enlightened that the management of crisis situations needs models able to depict social behaviors and, in particular, the spread of emotional feelings such as stress by panic situation. I wish to mention that propagation of emotional behaviors can be described by models of collective learning dynamics, where interactions involve a whole populations rather than individual entities [6]. The survey of Bellomo et al. [4] presents an overview and critical analysis of the literature on the modeling of learning dynamics. The authors propose their own approach, based on suitable development of methods of the kinetic theory and theoretical tools of evolutionary game theory, with the objective of developing a mathematical theory of perception and learning in view of their application to modeling complex systems, which can develop a collective intelligence. The approach can be viewed as an extension of the concept of population thinking and of the theory of evolution and the important motivations to the contents of this paper are induced by the idea that the mathematical structure might include features which could make it interesting in different field of life sciences, see also [7]. The survey [4] enlightens the aforementioned topics and after a critical analysis of the existing literature proposes a crisis management approach based on modeling of crowd dynamics by kinetic theory methods [1–3,5] with interactions modeled by a stochastic development of evolutionary games [8]. Crowd dynamics is a relevant example of learning dynamics where walkers learn from other walkers their own bias, indeed the mathematical tools proposed in [4] show common features with those presented in [6,7]. The result is the following structure: ∂t f (t, u) = A[f ](t, u) + B[f ](t, u) η(u∗ , u∗ )A(u∗ → u|u∗ , u∗ )f (t, u∗ )f (t, u∗ ) du∗ du∗ = Du ×Du
− f (t, u)
η(u, u∗ ) f (t, u∗ ) du∗
Du
DOI of original article: http://dx.doi.org/10.1016/j.plrev.2016.05.014. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.plrev.2016.07.002 1571-0645/© 2016 Published by Elsevier B.V.
JID:PLREV AID:764 /DIS
[m3SC+; v1.233; Prn:12/07/2016; 9:15] P.2 (1-2)
D. Burini / Physics of Life Reviews ••• (••••) •••–•••
2
+
ν[f ](u∗ ) B[f ](u∗ → u|u∗ , E1 [f ])f (t, u∗ ) du∗
Du
− f (t, u)ν[f ](u),
(1)
where the internal variable u denotes the level of learning within the population and square brackets have been used to denote the dependence on the distribution functions which highlight the nonlinear nature of interactions. In eq. (1) the first term A[f ](t, u) is referred to individual-based learning of walkers with interaction rate η and transition probability density A. The second term B[f ](t, u), instead, is due to micro–macro learning of a walker from the mean value of the activity E1 (macrostate) of the group of individuals which the walker interacts with. The interaction rate ν and the transition probability density B are supposed to depend on the macrostate of the population. The structure of eq. (1) highlights that human behaviors in pedestrian flow and in more critical cases such as rapid evacuation in danger situations, is not only influenced by their own strategy, but also depends on interactions, mechanical and social, with the surrounding walkers (behavioral crowd). The survey [4] has given evidence that future research activity in the field of crowd modeling should look ahead to future developments where propagation of emotional state are carefully taken into account. It would be nice having the authors’ opinion on the use of learning dynamics over the modeling approach to behavioral crowds. My idea is that indeed, it has to be regarded as an important tool to be used toward the aforementioned objective. On the other hand, I am aware that the main difficulty is that the titles examined in [6] refer to systems where the role of space is not relevant, while it is essential in crowd dynamics. I argue that the role of the space variable needs the introduction of a sensitivity domain to perceive signals that might change, or not, individual emotional states. This feature induces nontrivial conceptual difficulties that suggest further developments of Sigmund theory of evolutionary games [8]. Hopefully, the opinion on this topic by the authors of [4] can contribute to tackle this matter. References [1] Ajmone Marsan G, Bellomo N, Gibelli L. Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics. Math Models Methods Appl Sci 2016;26(6):1051–93. [2] Bellomo N, Bellouquid A. On multiscale models of pedestrian crowds from mesoscopic to macroscopic. Commun Math Sci 2015;13(7):1649–64. [3] Bellomo N, Bellouquid A, Knopoff D. From the micro-scale to collective crowd dynamics. Multiscale Model Simul 2013;11:943–63. [4] Bellomo N, Clarke D, Gibelli L, Townsend P, Vreugdenhil BJ. Human behaviours in evacuation crowd dynamics: from modelling to “big data” toward crisis management. Phys Life Rev 2016. http://dx.doi.org/10.1016/j.plrev.2016.05.014 [in this issue]. [5] Bellomo N, Gibelli L. Toward a behavioral-social dynamics of pedestrian crowds. Math Models Methods Appl Sci 2015;25:2417–37. [6] Burini D, De Lillo S, Gibelli L. Collective learning modeling based on the kinetic theory of active particles. Phys Life Rev 2016;16:123–39. [7] Burini D, De Lillo S, Gibelli L. Learning dynamics towards modeling living systems: reply to comments on “Collective learning modeling based on the kinetic theory of active particles”. Phys Life Rev 2016;16:158–62. [8] Hofbauer J, Sigmund K. Evolutionary game dynamics. Bull Am Math Soc 2003;40:479–519. [9] Vermuyten H, Belien J, De Boeck L, Reniers G, Wauters T. A review of optimisation models for pedestrian evacuation and design problems. Saf Sci 2016;87:167–78. [10] Wijermans N, Conrado C, van Steen M, Martella C, Li JL. A landscape of crowd management support: an integrative approach. Saf Sci 2016;86:142–64.