COMP4001/7001 Introduction to Complex Systems

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COMP4001/7001Introduction to Complex Systems

• Jennifer Hallinan
• j.hallinan_at_imb.uq.edu.au
• 3346 2615

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Complicated Systemshave many components
interactions

• Metabolic pathways
• Plants
• Animals shell patterns, ontogeny
• Behaviour swarms
• Evolution
• Financial markets
• Traffic

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Complex Systems Sciencemodelling systems of
interacting components

• Interesting systems operate at a variety of
  temporal and spatial scales
• Similar emergent properties are found in many
  domains, such as branching structures
• Tree roots and branches
• Neurons
• Blood vessels
• Road systems
• Drainage basins
• The challenge is to understand why similar
  properties emerge across different domains.

http//photography.pauljames.de/jpg/branches.jpg
http//archive.mainroads.qld.gov.au/qldmotorwa
ys/logan.gif http//cti.itc.virginia.edu/psyc220/
neurons.gif http//www.astro.washington.edu/lab
s/clearinghouse150/labs/Mars/images/tributar.jpg
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Complicated ? Complex

• Complex systems science seeks to explain why some
  properties just seem to self-organise without any
  seeming coordination.
• The area is extraordinarily interdisciplinary
• Advances in one domain frequently provide
  insights into others with similar phenomena.

http//www.wolframscience.com/preview/set2.html
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Definition Simple Systems

• Simple systems are ones in which global
  properties are inherent in the properties of
  their component parts.
• Such systems are additive, and scale with
  increasing numbers of components.
• Consider a grain of sand. The mass of a bucket of
  sand is the sum of the masses of the individual
  grains.
• Its a simple additive process. Additive, linear,
  completely predictable.
• Can be studied top-down or bottom up by
  traditional reductional science.

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Definition Complex Systems

• They can be defined by what they are not
• Complex systems are not simple ones.
• The fundamental characteristic of a complex
  system is that it exhibits emergent properties
• Defn Emergent properties are ones that arise due
  to the interactions in a system, and are not
  inherent in the individual components
• Caveat emptor There are almost as many
  definitions of CxSys as there are CxSys
  researchers. Many definitions include a notion of
  surprise. Emergent properties can be
  surprising, but equating emergence with surprise
  is a statement about the human observer, not the
  system

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What is a Complex System? University of Michigan
Centre for the Study of Complex Systems
http//www.pscs.umich.edu/

• A complex system displays some or all of the
  following characteristics
• Agent-based
• Basic building blocks are the characteristics and
  activities of individual agents
• Heterogeneous
• The agents differ in important characteristics
• Dynamic
• Characteristics change over time, usually in a
  nonlinear way adaptation
• Feedback
• Changes are often the result of feedback from the
  environment
• Organization
• Agents are organized into groups or hierarchies
• Emergence
• Macro-level behaviours that emerge from agent
  actions and interactions

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Chaos and Complexity

• Chaos deals with deterministic systems whose
  trajectories diverge exponentially over time
• Sensitive dependence on initial conditions
• Butterfly effect
• Models of chaos generally describe the dynamics
  of one (or a few) variables which are real (ie
  represented by a decimal number). Using these
  models some characteristic behaviors of their
  dynamics can be found
• Complex systems may behave in chaotic ways
• High dimensional chaos

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Complex systems conceptshttp//necsi.org/guide/co
ncepts/

• System
• Observer
• Adaptive
• Environment
• Boundary
• Network
• Ecosystem
• Development
• Replication
• Self-organization
• Selection
• Evolution

• Randomness
• Scale
• Chaos fractals
• Linear nonlinear
• Feedback
• Response
• Dynamics
• Indirect effects
• Interdependent
• Collective
• Patterns
• Information

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Systems

• A system is a delineated part of the universe
  which is distinguished from the rest by an
  imaginary boundary
• once a system is identified (the boundary
  described) then one describes
• the properties of the system
• the properties of the universe excluding the
  system which affect the system, and
• the interactions / relationships between them

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http//necsi.org/projects/mclemens/sysrep.gif
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An Example

• The system
• A genetic regulatory network
• The boundary
• Cell membrane
• The environment
• Surrounding cells and blood
• Interactions cell ? env
• Release of peptides
• Mechanical support
• Interactions env ? cell
• Nutrients
• Temperature
• Toxins
• Interactions cell --gt cell
• Genetoc regulation
• Metabolism

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Complex adaptive systems (CAS)

• A system that changes its behavior in response to
  its environment
• Often relevant to achieving a goal or objective.
• Effects of env may be direct or indirect
• E.g. growth of a plant around an obstacle
• Learning a pattern of behavior of the system
  changes as a result of an interaction with the
  environment
• Evolution
• Adaptation requires feedback

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Feedback

• A circular process of influence where action has
  effect on the actor
• E.g. thermostat
• Essential in most systematic ideas about the
  actions of a system in its environment
• May be positive or negative
• Negative feedback is stabilizing
• Positive feedback can lead to runaway increases
  or decreases

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Nonlinearity

• Linear relationship
• 2A ? 2B
• E.g. height and weight
• Easy to analyze
• Nonlinear relationship
• Wide range of possible dependancies
• May still be monotonic
• Need more information about the system to
  elucidate
• Complex systems often follow power laws

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Power laws
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Dynamic response

• One of the powerful ways of probing the behavior
  of a complex system is observing how it responds
  to a force applied to it, especially the
  "indirect" effects that take place at different
  places or at other times than the force.
• Effects may be
• Direct
• Indirect in space
• Indirect in time
• Comparing the experimental and theoretical
  response of a system helps us determine whether
  the theory correctly describes the behavior of
  the system.

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Scale

• The size of a systemm or property
• Elementary particle
• Atom,
• Molecule,
• Cell
• Person
• City
• Planet
• Galaxy
• Universe
• The precision of observation or description
• Microscope
• Naked eye
• Telescope

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Emergence

• What parts of a system do together that they
  would not do by themselves collective behavior.
• What a system does by virtue of its relationship
  to its environment that it would not do by
  itself e.g. its function.
• The act or process of becoming an emergent
  system.
• How behavior at a larger scale of the system
  arises from the detailed structure, behavior and
  relationships on a finer scale
• Both (1) and (2) have to do with relationships,
  the relationships of the parts, or the
  relationship of the system to its environment.
• When parts of a system are related to each other
  we talk about them as a network

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Emergent properties

• The whole is greater than the sum of the parts
• Examples of properties of interacting agents
• Traffic jams are properties of many vehicles
  (cars, bicycles, aeroplanes), but not inherent in
  any one
• Robustness to random damage is a property of
  genomes, neural networks, the world wide web,
  power grids
• Molecular biologists have undertaken a
  systematic program of destroying (knocking out)
  individual genes in mice, and then looking at the
  phenotype of the mouse. Most of the knockouts
  seem to have little observable effect.
• Similarly, brains are very robust to knocking
  out individual neurons. But we all know that if
  you knockout enough neurons, clearly they do
  something.

http//www.alanturing.net/turing_archive/graphics/
realneurons.gif
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Tools to think about emergent properties

• The success stories of complex systems science
  are where we can understand an emergent property
  in terms of a relatively limited set of
  underlying rules or processes that play out over
  space and time.
• Networks
• Distributed agents
• Recursive processes grammars eg L-systems
• Simple rules give rise to complex designs

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Networks

• System components can be modelled as nodes and
  their interactions as links

• E.g.
• World wide web
• Communication systems
• Power grids
• Genetic regulatory networks
• Neural networks
• Toolkit includes network analysis, s.a. Pajek,
  Leximancer

Collaboration graph for researchers in ITEE
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Agents

• Basic building blocks are the characteristics and
  activities of individual agents
• Simple rules give rise to complex designs

• E.g.
• ant trails (pheromones)
• shell shapes and patterns
• evolutionary systems

http//www.wolframscience.com/preview/set2.html

• Toolkit includes cellular automata (CA)
  Starlogo Matlab
• University of Michigan Centre for the Study of
  Complex Systems http//www.pscs.umich.edu/

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Recursive processes

• E.g.
• fractals
• plant growth patterns (branches, roots)
• Toolkit is based on grammars, such as L-studio

http//www.cpsc.ucalgary.ca/Research/bmv/lstudio/f
lyer.pdf
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http//necsi.org/projects/mclemens/cs_char.gif
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Insights from modelling

• Simple rules and simple initial conditions can
  give rise to the most computationally complex
  behaviour (in a rigorous and formal sense).
• Insights can be gained by studying the space of
  behaviours of very simple systems

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Conclusions

• Complex systems are the rule, not the exception
• Complex systems aise from interactions between
  agents
• Complex systems are characterized by global,
  emergent properties
• Many characteristics of complex systems are
  common across problem domains
• Insights gained in economics may be applicable to
  biology
• Complex systems are usually studied using
  computational modelling approaches