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Not a progress report

Walkability as an example

Godel’s incompleteness theorem

Hamiltonian Complexity Theory to show the limit of Model-ability!!

How to model without direct rational assumptions about the real phenomena?

An inversion in paradigm of experiments and observation

The second advantage is that from the mathematical analysis of the Markov chain it is possible to infer hidden properties of the underlying road network which can be hardly revealed even by tailored ad-hoc simulations.

Encapsulating the properties in relations

How to model without direct rational assumptions about the real phenomena?

An inversion in paradigm of experiments and observation

- 1. svm@arch.ethz.ch SEC Markovian Modeling of Urban Traffic Flows in Coexistence With Urban Data Streams Vahid Moosavi Simulation platform, Future Cities Lab, ETHZ Supervisor: Professor Ludger Hovestadt Chair for Computer Aided Architectural Design, Department for Architecture, ETH Zürich 26 April 2013 1
- 2. Multi-layer modeling and the curse of dimensionality… 2 We take different layers (dimensions) and want to mimic the behavior. For example in Traffic modeling: • Shortest Path and rationality??!! • Traffic congestions?! • Traffic Lights?!! • Lots of other unknown elements that we don’t know yet and in fact manipulate. …Curse of Dimensionality …Complicated models, but not complex
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- 5. 5 Rational (Specific ) Models Complex (Pre-specific ) Models Properties of the system for modeling PossibleRelations (typesandnumbers) Multi-Agent Systems Urban Cellular automata Urban Dynamics Basic Statistics (Hypothesis Testing) Urban Metabolism Natural (Deterministic) Models Urban Scaling Social Physics Fractal Models Complexity and the Limits of Model-ability in Rational Way It is not about more data or more computing power, we need an abstraction from the concept of rational modeling.
- 6. An inversion in the concept of modeling 6 X Y X Y Model Reality Analysis Synthesis Model Reality Celebration of Computation Celebration of Connectedness Celebration of Analysis If not then,
- 7. An inversion in the concept of modeling 7 X Y X Y Celebration of Computation Celebration of Connectedness Celebration of Analysis If not then, Logic or rationale Or (descriptive theories) ObservationsObservations Celebration of Computation supports
- 8. An example From Language modeling… Problems • Sentiment Analysis • Translation • Communication • … 8 Approaches for dealing with these problems 1. Based on Grammar, Logic and Model of the language. (Noam Chomsky) 2. Based on data-driven probabilistic models. (Originally by Markov and now in Google Translate) … And maybe be a dialectical approach too... On Chomsky and the Two Cultures of Statistical Learning: http://norvig.com/chomsky.html
- 9. Relational Model Classic SpaceSyntax, London “The social logic of space,(1984)” 33,000+ taxicabs GPS Trajectory of Taxicabs, Beijing, 2012 Inversion in Modeling 9 Rational Model X Y X Y Celebration of Computation Celebration of Connectedness
- 10. Video 10
- 11. An Experiment : Markovian Models in coexistence with data streams (using Taxi cabs GPS trajectories) 11 • Each Taxi produces a sequence of symbols. …It is telling its own story. • Symbols could be road names, units of space, district names,… • Sequence can be based on any time resolution. … we can construct a Markov Network encapsulating the transitions between states (symbols) • Remark: The Markov network construction can be based on a specific time period (e.g. rush hours, weekends,…) or specific part of the city. Possible functions • Simulation of traffic flow • Stationary distribution of cars • Road clustering • Road Engineering and scenario planning – Finding critical roads – Road network sensitivity analysis – … – As an opposing or complementary view to Chomsky, Linell presented interactionism: The sense-making ability of humans is rooted in social interaction; the mind is interactive, dialogical, social, shared, extended, distributed, etc.
- 12. Video : A sample Sequence 12
- 13. Experiment : Markovian Models in coexistence with data streams 13 0 0.5 0.5 0 0 0 0 0.5 0 0.5 0 0 0 0 0.450.45 0 0.1 0 0 0 0 0 0.5 0 0.5 0 0 0 0 0 0.1 0 0.45 0.45 0 0 0 0 0.5 0 0.5 0 0 0 0 0.5 0.5 0 CarID,Date,Lon,Lat,Symbol 100,2008-02-02 21:22:11,116.36263,39.93097,374 100,2008-02-02 21:24:56,116.36708,39.92274,405 100,2008-02-02 21:29:57,116.34696,39.92226,403 100,2008-02-02 21:32:14,116.34557,39.91717,403 100,2008-02-02 21:34:59,116.33843,39.92169,402 100,2008-02-02 21:37:16,116.32875,39.92175,401 100,2008-02-02 21:40:01,116.31468,39.9225,400 100,2008-02-02 21:42:18,116.29511,39.92328,398 100,2008-02-02 21:45:02,116.29542,39.9306,368 …,374,405,403,403,402,401,400,398,368,… A sample stream of the data A row stochastic Markov Matrix 1 2 3 4 5 6 7 1 2 3 4 5 6 7
- 14. Some Properties of Markov Chain in Urban road network Quantity / Markov Network Trafic Network Perron Eigenvector (dual) Vehicular density in the city network Mean First Passage Times Average travel times for a pair of origin/destination Kemeny constant Average travel time for a random trip Perron Eigenvector (primal) Congested junctions in the network Second Eigenvector (dual) Associates nodes to traffic sub-communities 141.Crisostomi, E., Kirkland, S., Shorten, R. (2011), A Google-like model of road network dynamics and its application to regulation and control. International Journal of Control
- 15. Future Steps • Time series prediction for individuals • MCMC for multi-agent based simulation if needed : Data-Driven Simulation no more direct theory or logic, but in principle we no longer need simulation but just analysis on top of data-driven models. For example, there is no need to be able mimicking the behavior of one day of a city, with urban data streams, we can watch it. We should go back to the history of simulation as a numerical approximation to Analytical models, which was the celebration of computing power, but now the issue is not about the computing power, it is about the limit of the thing (model based on theories) which are being computed. It is a limit of model-ability. Then, urban data streams brings a new capability for us. 15
- 16. • Markov Modeling of Singapore Ezlink Data • Based on important link in the Kemeny Analysis, run again the steady state probability without that area. • Validation: Use power k of Markov and then compare with the result in K steps based on empirical data • Predicting the future states by power of Markov Chain • Caclulating and visualizing the other network measures • Accessibility analysis using Mean first passage time: one measure can be just a an average and deviation • Use SOM to compare different features such as Kemeny constant effect, First Eig, Average Mean First Paassage time, Other features such closeness, betweenness, other network features 16
- 17. Results 17
- 18. Thanks! 18
- 19. Urban Data Streams Planning Interventions Markov Chain (MC) Construction Updating MC periodically Urban Segments Regional Scale Transition Time Selected Time Period Traffic Community Detection Real Time Traffic Flow Road network Engineering Expected Empirical Travel Times Network Analytics City Mining and Analysis Modeling
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