Modeling Techniques for Self-Organizing Systems

Modeling Techniques for Self-Organizing Systems - Group 1

In general: Three methodologies for designing (self-organizing) systems.

• Bottom up modeling
  • System consists of units
  • Modeling structure and dynamics of units (agents), topology, and interaction
    • Model I/O behavior of agents
      • Transfer function
      • Local rule set
    • Topology
      • Network, connections between agents
      • Spatial environment, e.g. 2d grid, defining a continuous neighborhood
    • Interaction between agents
      • Transfer function linear or non-linear
  • Advantage: straightforward implementation
  • Disadvatage: Emergenct properties cannot been foreseen from local rules
  • Examples:
    • Conway's Game of Life e(Cellular Automaton
    • Micro economics

• Top down modeling
  • Model entire system from observations
  • Observe time series and predict behavior by finding regularities in pattern's using for instance:
    • Markov Models
    • Neural Networks
  • Advantage: Covers emergence and goal orientation
  • Disadvantage: Analyzing system as black box, difficult to verify obtained system model
  • Example:
    • Chart Analysis in stock market

• Recursive bootstrapping
  • Cyclic adaptation of both models
  • Increase understanding in each iteration

Modeling the Structure, Dynamics and Quantification - Group 2

Looked at modeling the topology and connections between agents.

Techniques for dynamic processes (microscopic rules of behaviour) and their strengths/weaknesses regarding robustness:

• Cellular Automaton
  • Easy to form a broad range of patterns
  • But: Dependence on synchronization

• Evolutionary Algorithms
  • Genetic Algorithms
    • Efficient search through high dimensional state
    • However: Need to specify a "fitness landscape" a priori (need to know what to find a good solution to)
    • History dependence (can converge to different solutions)
    • Good, but not optimal solution
    • Discussion mentioned that this may be more design than modeling (since it designs the solution/fitness landscape)

• UML (Modelling specification language)
• Finite State Machines / Hidden Markov Models
  • Flexible
  • Model at the system level (macroscopic)

• Control Theory
  • Real-Time, but has some centralized, global requirements

• Agent-based approaches
  • Local synch. algorithms
  • Local geometric constructions
  • Game theory (high complexity once N>2)
  • Swarm behaviour / intelligence (scalable, but has limited modeling capabilities)
  • Robustness of individual agent versus collective species (micro vs macro)

• Reaction-diffusion equations

Universal aspect to all the techniques:

• How to quantify structure?
  • Information Theory
  • Fourier transforms
  • Computational mechanics

• Tradeoffs: Model complexity versus robustness

Modeling Self-Organisation - Group 3

In the group work we discussed modeling in a bit general way. There doesn't seem to be consensus about how to model self-organizing systems specifically. So, the approach that was presented was along the lines of the bottom-up approach as defined by group 1. Of identifying identities, local interactions, global behaviour (or goal).

It is assumed that modeling in this case refers to an already existing system or network that shows self-organization. Not about engineering one. This system has to be analyzed in such a way that an abstract model can be defined, that represents the both the global behaviour and the local individual interactions, and the pathway between those. So, techniques in this sense, as we more or less established in the group is defined as the way to reach at this predefined "emergent" property from local interactions systematically.

Most of the group members did see simulation not as a modeling technique and the discussion was for a while about graphs and e.g. petri nets. Those are representations of the real world. The corresponding theories, like graph theory might provided some clues about actually modeling relations between local-level and global-level behaviour. A random walker on a graph was not seen by the group as a technique to establish this types of relationships. However, there were no ideas about what parts of graph theory actually are describing self-organization.

Reaction-diffusion models, autocatalytic sets, etc. all those systems can be found on the wikipedia page on self-organization. However, there doesn't seem to be some general modeling technique that combines all those different tacks on the problem...

Group Work - Group 4

• Modeling Techniques
  • Use differential/difference equations to model Self Organizing Systems that correlate at some point e.g. for synchronization
    • Lyapunov-Exponent – evaluate how different start points change the systems evolution through a phase space
    • Sensitivity to the initial conditions of the differential equations
  • (Hidden) Markov models
• Properties
  • Emergent properties are often not easy to measure/understand
  • Sensitivity to the initial conditions of the differential equations might help with adaptivness
  • Adaptivness/goal-orientedness: in Markov models we can remove some nodes and re-evalute. Can give us an idea about effectiveness etc.
• Limitations/Potentials
  • “classical methods” are well researched and evaluated but not specifically tailored towards SOS
  • very hard to measure