CO.ST.C.A.R.E. · Continuum State Cellular Automata and Random Equations - Applications to urban growth and traffic models
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2005-06-15 → 2006-06-14
- EU contribution
- €40,000
- Participants
- 1
- Scheme
- ERG
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Results in brief
Final Activity Report Summary - CO.ST.C.A.R.E. (Continuum State Cellular Automata and Random Equations - Applications to urban growth and traffic models)
The first aim of our project was to start the development of a new axiomatic theory of complex systems of interacting entities including meaningful examples (e.g. cellular automata, CA, and multi-agents systems, MAS) and with good mathematical properties. In the first year of the project we precisely defined the axioms of this new mathematical structure called Interaction Spaces (IS). Defining these axioms we included as IS: systems with behaviour depending on the past history (systems with memory, i.e. non-Markovian), CA (both deterministic and stochastic; in general with time dependant neighbourhoods), multi-agents systems, CA with non-local interactions, etc. A first example of IS developed in detail has been a decisions support mathematical model for urban growth processes. An important second example is work in progress and consists in a trans-disciplinary project (together with urban planners, environmental protection officers, architects, physicists and mathematicians) for a traffic model coupled with a urban growth model and used as a decision support system for the management of urban projects of new big traffic generators (e.g. shopping centres, free time centres, tourists attraction sites, monopolistic activities, etc.). After a sufficiently detailed study of the scientific literature we chose to focus our future attention on the following examples of IS: models of housing markets, models of Wikipedia and open-source software, pedestrian movement, patterns formation, Darwinian evolution and behavioural finance. During the first year project new validation ideas of these type of complex systems has been developed. The scientific project is underdevelopment (3 years remaining). Objectives to complete: Development of mathematical models from other fields, proof that every extensive observable in an IS verifies both an ordinary differential equation (ODE) and a random differential equation (RDE); numerical solution of the RDE; numerical study of bifurcations in IS using RDE and ODE.
Data: CORDIS, © European Union
Project objective
The proposed research project focuses on a generalization of Cellular Automata (CA) describable using both ODE and random differential equations (RDE). They are models capable of quantitative forecast as well as the same modelling flexibility of classical CA.The use of a continuum state space permits to use new ideas about model’s calibration and validation e.g. defining a meaningful distance on the configuration space and using optimization techniques. We shall call them Interaction Based Dynamical Systems (IBDS), because they seems useful to model complex systems formed by agents locally interacting.Objectives of the project are:- Mathematical definition of IBDS generalizing the work done by the reintegration research group about continuum state CA modelling of urban growth- Construction of the probability space associated to an IBDS. This is the mathematical framework where to prove the following objectives- Study of the related differential equations. Every IBDS can be described using both an ODE, in case of infinitesimal standard deviation, and an infinite system of RDE (one for each moment of the state variables)- Numerical solution of this system of RDE5.- Construction of a traffic model using IBDS6.- Numerical study of bifurcations using ODE and RDE7.- Analysis of the possibility to generalize the MCF work of the proposal’s researcher to extend the real field adding random infinitesimal fluctuations.- Use of this extension to study IBDS.These objectives will be achieved using standard probability theory methods, the infinitesimals of researcher’s MCF, programming in Matlab and interdisciplinary work at the host institute.The possibility to introduce a new and flexible type of modelling tool for the study of complex systems is of great importance both for EU and for the possibility of the researcher to obtain further future fundings for research projects, an important task of the ERG. The research project will last 4 years.
Original text from CORDIS.
Participants
- UNIVERSITÀ DELLA SVIZZERA ITALIANA · LUGANOCoordinatorSwitzerland
Links
Data: CORDIS, © European Union