Video Lectures (25)

A curated collection of 25 video lectures on urban complex systems, ecology, climate change, pollution, and environmental governance — providing the scientific and policy context for the mathematical models in this course.

Cities as Complex Systems

References

Scaling Laws & Urban Science (Modules 1, 9)

  • Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C. & West, G. B. (2007). Growth, innovation, scaling, and the pace of life in cities. PNAS 104(17), 7301–7306.
  • Bettencourt, L. M. A. (2013). The origins of scaling in cities. Science 340(6139), 1438–1441.
  • West, G. B., Brown, J. H. & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science 276(5309), 122–126.
  • Batty, M. (2008). The size, scale, and shape of cities. Science 319(5864), 769–771.

Urban Growth & Reaction-Diffusion (Module 2)

  • Fisher, R. A. (1937). The wave of advance of advantageous genes. Annals of Eugenics 7(4), 355–369.
  • Kolmogorov, A., Petrovskii, I. & Piskunov, N. (1937). Étude de l’équation de la diffusion. Moscow Univ. Math. Bull. 1, 1–25.
  • Murray, J. D. (2002). Mathematical Biology I: An Introduction. Springer.
  • Glansdorff, P. & Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley.

Cellular Automata & Land Use (Module 3)

  • Clarke, K. C., Hoppen, S. & Gaydos, L. (1997). A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area. Environment and Planning B 24(2), 247–261.
  • Liu, X., Liang, X., Li, X. et al. (2017). A future land use simulation model (FLUS). Global Change Biology 23(11), 5415–5427.
  • White, R. & Engelen, G. (1993). Cellular automata and fractal urban form. Environment and Planning A 25(8), 1175–1199.

Agent-Based Models (Module 4)

  • Schelling, T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology 1(2), 143–186.
  • Alonso, W. (1964). Location and Land Use. Harvard University Press.
  • Helbing, D. & Molnár, P. (1995). Social force model for pedestrian dynamics. Physical Review E 51(5), 4282–4286.
  • Muth, R. F. (1969). Cities and Housing. University of Chicago Press.

Stochastic Dynamics & Fokker-Planck (Module 5)

  • Risken, H. (1996). The Fokker-Planck Equation. Springer.
  • Gardiner, C. W. (2009). Stochastic Methods: A Handbook. Springer, 4th ed.
  • Nelson, E. (1966). Derivation of the Schrödinger equation from Newtonian mechanics. Physical Review 150(4), 1079–1085.
  • Léonard, C. (2014). A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete and Continuous Dynamical Systems 34(4), 1533–1574.

Network Analysis (Module 6)

  • Boeing, G. (2017). OSMnx: New methods for acquiring, constructing, analyzing, and visualizing complex street networks. Computers, Environment and Urban Systems 65, 126–139.
  • Newman, M. E. J. (2010). Networks: An Introduction. Oxford University Press.
  • Molloy, M. & Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures & Algorithms 6(2–3), 161–180.

Traffic & Lattice Gases (Modules 10–11)

  • Derrida, B., Evans, M. R., Hakim, V. & Pasquier, V. (1993). Exact solution of a 1D asymmetric exclusion model using a matrix formulation. J. Phys. A 26(7), 1493–1517.
  • Lighthill, M. J. & Whitham, G. B. (1955). On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. R. Soc. London A 229, 317–345.
  • Parmeggiani, A., Franosch, T. & Frey, E. (2003). Totally asymmetric simple exclusion process with Langmuir kinetics. Physical Review E 70, 046101.
  • Kardar, M., Parisi, G. & Zhang, Y.-C. (1986). Dynamic scaling of growing interfaces. Physical Review Letters 56(9), 889–892.
  • Tracy, C. A. & Widom, H. (1994). Level-spacing distributions and the Airy kernel. Communications in Mathematical Physics 159(1), 151–174.

Mean Field Games & Optimal Control (Modules 12–13)

  • Lasry, J.-M. & Lions, P.-L. (2007). Mean field games. Japanese Journal of Mathematics 2(1), 229–260.
  • Huang, M., Malhamé, R. P. & Caines, P. E. (2006). Large population stochastic dynamic games. Communications in Information and Systems 6(3), 221–252.
  • Achdou, Y. & Capuzzo-Dolcetta, I. (2010). Mean field games: Numerical methods. SIAM J. Numer. Anal. 48(3), 1136–1162.
  • Pontryagin, L. S. et al. (1962). The Mathematical Theory of Optimal Processes. Wiley.

Synchronization & Topology (Modules 14–15)

  • Kuramoto, Y. (1984). Chemical Oscillations, Waves, and Turbulence. Springer.
  • Strogatz, S. H. (2000). From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D 143(1–4), 1–20.
  • Edelsbrunner, H. & Harer, J. (2010). Computational Topology: An Introduction. AMS.
  • Carlsson, G. (2009). Topology and data. Bulletin of the AMS 46(2), 255–308.

Canyon Pollution & SUMO (Modules 16–18)

  • Berkowicz, R. (2000). OSPM — A parameterised street pollution model. Environmental Monitoring and Assessment 65, 323–331.
  • Vardoulakis, S. et al. (2003). Modelling air quality in street canyons: A review. Atmospheric Environment 37(2), 155–182.
  • Soulhac, L. et al. (2011). The model SIRANE for atmospheric urban pollutant dispersion. Atmospheric Environment 45(40), 7379–7395.
  • Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings 11(1–3), 103–113.
  • Lopez, P. A. et al. (2018). Microscopic traffic simulation using SUMO. IEEE ITSC 2018, 2575–2582.
  • Krajzewicz, D. et al. (2012). Recent development and applications of SUMO. Int. J. Adv. Syst. Meas. 5(3&4), 128–138.
  • Peaceman, D. W. & Rachford, H. H. (1955). The numerical solution of parabolic and elliptic differential equations. J. SIAM 3(1), 28–41.
  • WHO (2021). Global Air Quality Guidelines. World Health Organization, Geneva.
  • EEA (2022). Air quality in Europe 2022. European Environment Agency Report 05/2022.

Fractals, Memory & Quantum (Modules 7–8)

  • Witten, T. A. & Sander, L. M. (1981). Diffusion-limited aggregation, a kinetic critical phenomenon. Physical Review Letters 47(19), 1400–1403.
  • Metzler, R. & Klafter, J. (2000). The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Physics Reports 339(1), 1–77.
  • Eisert, J., Wilkens, M. & Lewenstein, M. (1999). Quantum games and quantum strategies. Physical Review Letters 83(15), 3077–3080.
  • Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman.

General Urban Science & Complexity

  • Batty, M. (2013). The New Science of Cities. MIT Press.
  • Barthelemy, M. (2016). The Structure and Dynamics of Cities. Cambridge University Press.
  • Bettencourt, L. M. A. & West, G. B. (2010). A unified theory of urban living. Nature 467, 912–913.
  • Wilson, A. G. (2000). Complex Spatial Systems. Pearson.
  • Pumain, D. (2006). Hierarchy in Natural and Social Sciences. Springer.

About These Resources

The 25 video lectures cover the scientific and policy foundations for understanding cities as complex systems. The references span the key literature across all 18 modules — from Bettencourt’s urban scaling theory through TASEP exact solutions, Mean Field Games, topological data analysis, and SUMO microsimulation.

All video content is publicly available on YouTube. References are organized by module to complement the course material.