Abstract
This chapter presents some on research perspectives. Various topics are treated focusing on the following issues: further analysis of the modeling of welfare policy in the case of interactions in a network and in open systems; generalization of the modeling approach to various systems of social sciences, for instance opinion formation; modeling the interplay of different types of dynamics also viewed as a tool for predicting rare events; and analytic problems posed by the application of models to the study of social phenomena.
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References
Acemoglu, D., Robinson, J.A.: A theory of political transitions. American Economic Review 91(4), 938–963 (2001)
Acemoglu, D., Robinson, J.A.: Economic Origins of Dictatorship and Democracy. Cambridge University Press (2006)
Agrawal, A., Cockburn, I., McHale, J.: Gone but not forgotten: knowledge flows, labor mobility, and enduring social relationships. Journal of Economic Geography 6(5), 571–591 (2006)
Ajmone Marsan, G.: New paradigms towards the modelling of complex systems in Behavioral Economics. Mathematical and Computer Modelling 50(3–4), 584–597 (2009)
Ajmone Marsan, G.: On the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition. Computer & Mathematics with Applications 57(5), 710–728 (2009)
Aletti, G., Naldi, G., Toscani, G.: First-order continuous models of opinion formation. SIAM Journal on Applied Mathematics 67(3), 837–853 (2007)
Arlotti, L., Bellomo, N.: Solution of a new class of nonlinear kinetic models of population dynamics. Applied Mathematics Letters 9(2), 65–70 (1996)
Arlotti, L., De Angelis, E.: On the initial value problem of a class of models of the kinetic theory for active particles. Applied Mathematics Letters 24(3), 257–263 (2011)
Arlotti, L., De Angelis, E., Fermo, L., Lachowicz, M., Bellomo, N.: On a class of integro-differential equations modeling complex systems with nonlinear interactions. Applied Mathematics Letters 25(3), 490–495 (2012)
Azoulay, P., Zivin, J.S.G., Sampat, B.N.: The diffusion of scientific knowledge across time and space: Evidence from professional transitions for the superstars of medicine. Working Paper 16683, National Bureau of Economic Research (2011)
Bagarello, F., Oliveri, F.: A phenomenological operator description of interactions between populations with applications to migration. Mathematical Models and Methods in Applied Sciences 23(3), 471–492 (2013)
Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., Viale, M., Zdravkovic, V.: Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences 105(4), 1232–1237 (2008)
Barabási, A.L.: The Science of Networks. Perseus, Cambridge MA (2022)
Barabási, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272(1), 173–187 (1999)
Barbera, S., Maschler, M., Shalev, J.: Voting for voters: A model of electoral evolution. Games and Economic Behavior 37(1), 40–78 (2001)
Barrat, A., Bathélemy, M., Vespignani, A.: The Structure and Dynamics of Networks. Princeton University Press, Princeton NJ (2006)
Bastolla, U., Fortuna, M.A., Pascual-García, A., Ferrera, A., Luque, B., Bascompte, J.: The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009)
Bellomo, N., Bellouquid, A., Nieto, J., Soler, J.: On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives. Mathematical Models and Methods in Applied Sciences 22(1), 1130,001 (37 pages) (2012)
Bellomo, N., Herrero, M.A., Tosin, A.: On the dynamics of social conflicts looking for the Black Swan. Kinetic and Related Models 6(3), (2013)
Bellouquid, A., Delitala, M.: Mathematical modeling of complex biological systems: A kinetic theory approach. Modeling and Simulation In Science, Engineering and Technology. Birkhäuser, Boston (2006)
Berinsky, A.J., Burns, N., Traugott, M.W.: Who votes by mail?: A dynamic model of the individual-level consequences of voting-by-mail systems. Public Opinion Quarterly 65(2), 178–197 (2001)
Bertotti, M.L.: Modelling taxation and redistribution: A discrete active particle kinetic approach. Applied Mathematics and Computation 217(2), 752–762 (2010)
Bertotti, M.L.: On a class of dynamical systems with emerging cluster structure. Journal of Differential Equations 249(11), 2757–2770 (2010)
Bertotti, M.L., Delitala, M.: From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences. Mathematical Models and Methods in Applied Sciences 14(7), 1061–1084 (2004)
Bertotti, M.L., Delitala, M.: Conservation laws and asymptotic behavior of a model of social dynamics. Nonlinear Analysis: Real World Applications 9(1), 183–196 (2008)
Bertotti, M.L., Delitala, M.: On a discrete generalized kinetic approach for modelling persuader’s influence in opinion formation processes. Mathematical and Computer Modelling 48(7), 1107–1121 (2008)
Bertotti, M.L., Delitala, M.: On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders. Mathematical Models and Methods in Applied Sciences 18(6), 913–934 (2008)
Bertotti, M.L., Delitala, M.: Cluster formation in opinion dynamics: a qualitative analysis. Zeitschrift für angewandte Mathematik und Physik 61(4), 583–602 (2010)
Bertotti, M.L., Modanese, G.: From microscopic taxation and redistribution models to macroscopic income distributions. Physica A 390(21–22), 3782–3793 (2011)
Bisi, M., Spiga, G., Toscani, G.: Kinetic models of conservative economies with wealth redistribution. Communications in Mathematical Sciences 7(4), 901–916 (2009)
Borjas, G.J.: Economic theory and international migration. International Migration Review 23(3), 457–485 (1989)
Bressan, A.: Bifurcation analysis of a non-cooperative differential game with one weak player. Journal of Differential Equations 248(6), 1297–1314 (2010)
Bressan, A.: Noncooperative differential games. A tutorial (2010). URL http://descartes.math.psu.edu/bressan/PSPDF/game-lnew.pdf. Lecture Notes for a Summer Course
Bursik, R.J.: Social disorganization and theories of crime and delinquency: Problems and prospects. Criminology 26(4), 519–551 (1988)
Camilli, F., Capuzzo Dolcetta, I., Falcone, M.: Preface. Networks and Heterogeneous Media 7(2), i–ii (2012). Special Issue on Mean Field Games
Cebula, R.J., Vedder, R.K.: A note on migration, economic opportunity, and the quality of life. Journal of Regional Science 13(2), 205–211 (1973)
Comincioli, V., Della Croce, L., Toscani, G.: A Boltzmann-like equation for choice formation. Kinetic and Related Models 2(1), 135–149 (2009)
Crescenzi, R., Rodriguez-Pose, A.: Innovation and Regional Growth in the European Union. Springer, Berlin, Heidelberg (2011)
Cushing, B., Poot, J.: Crossing boundaries and borders: Regional science advances in migration modelling. Papers in Regional Science 83(1), 317–338 (2004)
De Lillo, S., Delitala, M., Salvatori, C.: Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles. Mathematical Models and Methods in Applied Sciences 19(1), 1405–1425 (2009)
Dobson, D., St. Angelo, D.: Party identification and the floating vote: some dynamics. The American Political Science Review 69(2), 481–490 (1975)
Galam, S.: Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate. Physica A 390(17), 3036–3054 (2011)
Gauvin, L., Vannimenus, J., Nadal, J.P.: Phase diagram of a Schelling segregation model. The European Physical Journal B 70(2), 293–304 (2009)
Gerber, A., Karlan, D.S., Bergan, D.: Does the media matter? A field experiment measuring the effect of newspapers on voting behavior and political opinions. Discussion paper 12, Yale University, Department of Economics (2006). Yale Working Papers on Economic Applications and Policy
Granovetter, M.S.: The strength of weak ties. American Journal of Sociology 78(6), 1360–1380 (1973)
Guéant, O., Lasry, J., Lions, P.: Mean field games and applications. In: Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Mathematics, vol. 2003, pp. 205–266. Springer, Berlin, Heidelberg (2011)
Helbing, D.: Quantitative sociodynamics: Stochastic methods and models of social interaction processes. Springer Verlag (2010)
Helbing, D., Sigmeier, J., Lämmer, S.: Self-organized network flows. Networks and Heterogeneous Media 2(2), 193–210 (2007)
Jensen, M.B., Johnson, B., Lorenz, E., Lundvall, B.Å.: Forms of knowledge and modes of innovation. Research Policy 36(5), 680–693 (2007)
Knopoff, D.: On the modeling of migration phenomena on small networks. Mathematical Models and Methods in Applied Sciences 23(3), 541–563 (2012)
Langer, P., Nowak, M.A., Hauert, C.: Spatial invasion of cooperation. Journal of Theoretical Biology 250(4), 634–641 (2008)
Lasry, J.M., Lions, P.L.: Mean field games. Japanese Journal of Mathematics 2(1), 229–260 (2007)
Maldarella, D., Pareschi, L.: Kinetic models for socio-economic dynamics of speculative markets. Physica A 391(3), 715–730 (2012)
Markus, G.B., Converse, P.E.: A dynamic simultaneous equation model of electoral choice. The American Political Science Review 73(4), 1055–1070 (1979)
Nowak, M.A.: Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)
Nowak, M.A., Ohtsuki, H.: Prevolutionary dynamics and the origin of evolution. Proceedings of the National Academy of Sciences 105(39), 14,924–14,927 (2008)
Nuño, J.C., Herrero, M.A., Primicerio, M.: A mathematical model of a criminal-prone society. Discrete and Continuous Dynamical Systems - Series S 4(1), 193–207 (2011)
OECD: Regional Outlook, Building Resilient Regions for Stronger Economies. OECD Publishing (2011)
Ohtsuki, H., Pacheco, J.M., Nowak, M.A.: Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology 246(4), 681–694 (2007)
Olson, M.: Dictatorship, democracy, and development. American Political Science Review 87(3), 567–576 (1993)
Piff, P.K., Stancato, D.M., Côté, S., Mendoza-Denton, R., Keltner, D.: Higher social class predicts increased unethical behavior. Proceedings of the National Academy of Sciences 109(11), 4086–4091 (2012)
Rand, D.G., Arbesman, S., Christakis, N.A.: Dynamic social networks promote cooperation in experiments with humans. Proceedings of the National Academy of Sciences 108(48), 19,193–19,198 (2011)
Sah, R.K.: Social osmosis and patterns of crime. Journal of Political Economy 99(6), 1272–1295 (1991)
Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., van Nes, E.H., Rietkerk, M., Sugihara, G.: Early-warning signals for critical transitions. Nature 461, 53–59 (2009)
Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G.E., Brantingham, P.J., Bertozzi, A.L., Chayes, L.B.: A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences 18(S1), 1249–1267 (2008)
Taleb, N.N.: The Black Swan: The Impact of the Highly Improbable. Random House, New York City (2007)
Taleb, N.N.: Force et fragilité. Réflexions philosophiques et empiriques. Les Belles Lettres, Paris (2010)
Van Kempen, E.T.: The dual city and the poor: social polarisation, social segregation and life chances. Urban Studies 31(7), 995 (1994)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)
Wood, A.J., Ackland, G.J., Dyke, J.G., Williams, H.T.P., Lenton, T.M.: Daisyworld: A review. Reviews of Geophysics 46(1), RG1001 (23 pages) (2008)
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© 2013 Nicola Bellomo, Giulia Ajmone, Andrea Tosin
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Ajmone Marsan, G., Bellomo, N., Tosin, A. (2013). Forward Look at Research Perspectives. In: Complex Systems and Society. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7242-1_5
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