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Confinement for repulsiveattractive kernels
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Preface to special issue on mathematics of social systems
1.  University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 900951555 
For more information please click the “Full Text” above.
References:
[1] 
A. B. T. Barbaro and P. Degond, Phase transition and diffusion among socially interacting selfpropelled agents, Discrete and Continuous Dynamical Systems, 34 (2014), 12491278. 
[2] 
D. Balagué, J. A. Carrillo and Y. Yao, Confinement for repulsiveattractive kernels, Discrete and Continuous Dynamical Systems, 34 (2014), 12271248. 
[3] 
J. Bedrossian and N. Rodríguez, Inhomogeneous PatlakKellerSegel models and aggregation equations with nonlinear diffusion in $R^d$, Discrete and Continuous Dynamical Systems, 34 (2014), 12791309. 
[4] 
J. Bedrossian, N. Rodríguez and A. L. Bertozzi, Local and global wellposedness for aggregation equations and KellerSegel models with degenerate diffusion, Nonlinearity, 24 (2011), 16831714. doi: 10.1088/09517715/24/6/001. 
[5] 
M. Burger, M. Di Francesco, P. A. Markowich and M. T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics, Discrete and Continuous Dynamical Systems, 34 (2014), 13111333. 
[6] 
Y. S. Cho, A. Galstyan, P. J. Brantingham and G. Tita, Latent selfexciting point process model for spatialtemporal networks, Discrete and Continuous Dynamical Systems, 34 (2014),13351354. 
[7] 
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Transactions on Automatic Control, 52 (2007), 852862. doi: 10.1109/TAC.2007.895842. 
[8] 
M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi and L. Chayes, Selfpropelled particles with softcore interactions: patterns, stability and collapse, Phys. Rev. Lett., 96 (2006), 104302. doi: 10.1103/PhysRevLett.96.104302. 
[9] 
R. Ghosh and K. Lerman, Rethinking Centrality: The role of dynamical processes in social network analysis, Discrete and Continuous Dynamical Systems, 34 (2014), 13551372. 
[10] 
R. A. Hegemann, E. A. Lewis and A. L. Bertozzi, An estimate & Score Algorithm for simultaneous parameter estimation and reconstruction of incomplete data on social networks,, Security Informatics, 2 (): 1. doi: 10.1186/2190853221. 
[11] 
T. Kolokolnikov, H. Sun, D. Uminsky and A. L. Bertozzi, Stability of ring patterns arising from twodimensional particle interactions, Phys. Rev. E, 84 (2011), 015203. doi: 10.1103/PhysRevE.84.015203. 
[12] 
T. Kolokolnikov, M. J. Ward and J. Wei, The stability of steadystate hotspot patterns for a reactiondiffusion model of urban crime, Discrete and Continuous Dynamical Systems, 34 (2014), 13731410. 
[13] 
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for twospecies competition models, J. Math. Biol., 45 (2002), 219233. doi: 10.1007/s002850200144. 
[14] 
A. Mackey, T. Kolokolnikov and A. L. Bertozzi, Twospecies particle aggregation and stability of codimension one solutions, Discrete and Continuous Dynamical Systems, 34 (2014), 14111436. 
[15] 
S. G. McCalla, Paladins as predators: Invasive waves in a spatial evolutionary adversarial game, Discrete and Continuous Dynamical Systems, 34 (2014), 14371457. 
[16] 
M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models. Meth. Appl. Sci., 18 (2008), 12491267. doi: 10.1142/S0218202508003029. 
[17] 
M. B. Short, A. L. Bertozzi and P. J. Brantingham, Nonlinear patterns in urban crime  hotpsots, bifurcations, and suppression, SIAM J. Appl. Dyn. Sys., 9 (2010), 462483. doi: 10.1137/090759069. 
[18] 
M. B. Short, P. J. Brantingham, A. L. Bertozzi and G. E. Tita, Dissipation and displacement of hotpsots in reactiondiffusion models of crime, Proc. Nat. Acad. Sci., 107 (2010), 39613965. 
[19] 
M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society, Phys. Rev. E, 82 (2010), 066114. doi: 10.1103/PhysRevE.82.066114. 
[20] 
M. B. Short, G. O. Mohler, P. J. Brantingham and G. E. Tita, Gang rivalry dynamics via coupled point process networks, Discrete and Continuous Dynamical Systems, 34 (2014), 14591477. 
[21] 
A. Stomakhin, M. B. Short and A. L. Bertozzi, Reconstruction of missing data in social networks based on temporal patterns of interactions, Inverse Problems, 27 (2011), p. 115013. doi: 10.1088/02665611/27/11/115013. 
[22] 
T. Vicsek, A. Czirók, E. BenJacob, I. Cohen and O. Shochet, Novel type of phase in a system of selfdriven particles, Phys. Rev. Lett., 75 (1995), 12261229. 
[23] 
X.S. Wang, H. Wang and J. Wu., Traveling waves of diffusive predatorprey systems: Disease outbreak propagation, Discrete Contin. Dyn. Syst., 32 (2012), 33033324. doi: 10.3934/dcds.2012.32.3303. 
[24] 
J. R. Zipkin, M. B. Short and A. L. Bertozzi, Cops on the dots in a mathematical model of urban crime and police response, Discrete and Continuous Dynamical Systems, 34 (2014), 14791506. 
show all references
References:
[1] 
A. B. T. Barbaro and P. Degond, Phase transition and diffusion among socially interacting selfpropelled agents, Discrete and Continuous Dynamical Systems, 34 (2014), 12491278. 
[2] 
D. Balagué, J. A. Carrillo and Y. Yao, Confinement for repulsiveattractive kernels, Discrete and Continuous Dynamical Systems, 34 (2014), 12271248. 
[3] 
J. Bedrossian and N. Rodríguez, Inhomogeneous PatlakKellerSegel models and aggregation equations with nonlinear diffusion in $R^d$, Discrete and Continuous Dynamical Systems, 34 (2014), 12791309. 
[4] 
J. Bedrossian, N. Rodríguez and A. L. Bertozzi, Local and global wellposedness for aggregation equations and KellerSegel models with degenerate diffusion, Nonlinearity, 24 (2011), 16831714. doi: 10.1088/09517715/24/6/001. 
[5] 
M. Burger, M. Di Francesco, P. A. Markowich and M. T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics, Discrete and Continuous Dynamical Systems, 34 (2014), 13111333. 
[6] 
Y. S. Cho, A. Galstyan, P. J. Brantingham and G. Tita, Latent selfexciting point process model for spatialtemporal networks, Discrete and Continuous Dynamical Systems, 34 (2014),13351354. 
[7] 
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Transactions on Automatic Control, 52 (2007), 852862. doi: 10.1109/TAC.2007.895842. 
[8] 
M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi and L. Chayes, Selfpropelled particles with softcore interactions: patterns, stability and collapse, Phys. Rev. Lett., 96 (2006), 104302. doi: 10.1103/PhysRevLett.96.104302. 
[9] 
R. Ghosh and K. Lerman, Rethinking Centrality: The role of dynamical processes in social network analysis, Discrete and Continuous Dynamical Systems, 34 (2014), 13551372. 
[10] 
R. A. Hegemann, E. A. Lewis and A. L. Bertozzi, An estimate & Score Algorithm for simultaneous parameter estimation and reconstruction of incomplete data on social networks,, Security Informatics, 2 (): 1. doi: 10.1186/2190853221. 
[11] 
T. Kolokolnikov, H. Sun, D. Uminsky and A. L. Bertozzi, Stability of ring patterns arising from twodimensional particle interactions, Phys. Rev. E, 84 (2011), 015203. doi: 10.1103/PhysRevE.84.015203. 
[12] 
T. Kolokolnikov, M. J. Ward and J. Wei, The stability of steadystate hotspot patterns for a reactiondiffusion model of urban crime, Discrete and Continuous Dynamical Systems, 34 (2014), 13731410. 
[13] 
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for twospecies competition models, J. Math. Biol., 45 (2002), 219233. doi: 10.1007/s002850200144. 
[14] 
A. Mackey, T. Kolokolnikov and A. L. Bertozzi, Twospecies particle aggregation and stability of codimension one solutions, Discrete and Continuous Dynamical Systems, 34 (2014), 14111436. 
[15] 
S. G. McCalla, Paladins as predators: Invasive waves in a spatial evolutionary adversarial game, Discrete and Continuous Dynamical Systems, 34 (2014), 14371457. 
[16] 
M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models. Meth. Appl. Sci., 18 (2008), 12491267. doi: 10.1142/S0218202508003029. 
[17] 
M. B. Short, A. L. Bertozzi and P. J. Brantingham, Nonlinear patterns in urban crime  hotpsots, bifurcations, and suppression, SIAM J. Appl. Dyn. Sys., 9 (2010), 462483. doi: 10.1137/090759069. 
[18] 
M. B. Short, P. J. Brantingham, A. L. Bertozzi and G. E. Tita, Dissipation and displacement of hotpsots in reactiondiffusion models of crime, Proc. Nat. Acad. Sci., 107 (2010), 39613965. 
[19] 
M. B. Short, P. J. Brantingham and M. R. D'Orsogna, Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society, Phys. Rev. E, 82 (2010), 066114. doi: 10.1103/PhysRevE.82.066114. 
[20] 
M. B. Short, G. O. Mohler, P. J. Brantingham and G. E. Tita, Gang rivalry dynamics via coupled point process networks, Discrete and Continuous Dynamical Systems, 34 (2014), 14591477. 
[21] 
A. Stomakhin, M. B. Short and A. L. Bertozzi, Reconstruction of missing data in social networks based on temporal patterns of interactions, Inverse Problems, 27 (2011), p. 115013. doi: 10.1088/02665611/27/11/115013. 
[22] 
T. Vicsek, A. Czirók, E. BenJacob, I. Cohen and O. Shochet, Novel type of phase in a system of selfdriven particles, Phys. Rev. Lett., 75 (1995), 12261229. 
[23] 
X.S. Wang, H. Wang and J. Wu., Traveling waves of diffusive predatorprey systems: Disease outbreak propagation, Discrete Contin. Dyn. Syst., 32 (2012), 33033324. doi: 10.3934/dcds.2012.32.3303. 
[24] 
J. R. Zipkin, M. B. Short and A. L. Bertozzi, Cops on the dots in a mathematical model of urban crime and police response, Discrete and Continuous Dynamical Systems, 34 (2014), 14791506. 
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