Five Focus Areas for Applied Complex Systems Science

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Five Focus Areas for Applied Complex Systems
Science

• John Finnigan CSIRO

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Contents

• The Promise of Complex Systems Science
• Five new areas of application
• Matching model complexity to system complexity
• Complex dynamics of urban systems
• Dynamics of Complex Networks in Biology
• Prediction and control of social networks
• Chemical-biological reactive-transport systems
• Universal themes across these five areas
• Putting Complex Systems on the same page

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The Promise of Complex Systems Science

• Complex Systems Science offers new ways to attack
  previously intractable or wicked problems.
• The idea of CSS as a field of Science, is
  predicated, however, on the notion that there are
  universal themes that are manifested across
  systems whatever their context and that we can
  discover useful laws describing their behaviour.
• If this notion of universal themes is valid, it
  means we should be able to transfer insights and
  advances between quite different application
  areas.
• First we will survey in varying depth, five new
  application areas and then ask whether we can say
  something more general about universal themes in
  complex systems.

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Matching model complexity to system complexity

• The problem
• given observations of a complex system, how do we
  choose the appropriate model complexity to
  reproduce the system dynamics?
• What happens if an essential part of the system
  dynamics-for example, human interactions, can at
  best be poorly captured by parameterisation?
• Can we use data assimilation to keep large
  complex models of human ecosystems on-track?
• Do things get simpler if we have huge numbers of
  agents-eg. Epicast?
• The relevance
• A wide range of urgent socio-economic problems
  are being addressed by modelling, either
  explicitly or implicitly. How far can we trust
  the results of these models?

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Comparing simple ecosystem models in state space

• Nicky Grigg, CLW
• Fabio Boschetti, CMAR

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Typical features of aquatic ecosystem models

• Dynamic
• Track the flow of nutrients through sediment and
  water column processes
• Nonlinear interactions, feedbacks, hysteretic
  responses

All figures from Grigg and Boschetti (2005)
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Toy example stochastically forced food chain
qZn
Zooplankton mortality Linear mortality (n 1)
only one basin of attraction Quadratic mortality
(n 2) alternative basins of attraction, and
large flips between basins possible.
Source Edwards and Brindley (1999) after Grigg
and Boschetti (2005)
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Given observations from quadratic mortality
system Aim model the dynamics with a linear
mortality model
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Comparison of time evolution of phytoplankton
population in reconstructed state space
Parameter search resultleast squares fit
All figures from Grigg and Boschetti (2005)
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Comparison of time evolution of phytoplankton
population in reconstructed state space (Grigg
and Boschetti, 2005)
Is this a good fit?
All figures from Grigg and Boschetti (2005)
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Comparison of time evolution of phytoplankton
population in reconstructed state space
All figures from Grigg and Boschetti (2005)
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Matching model complexity to system complexity

• How does the implementation of the scientific
  method differ between a complex and a non
  complex problem?
• How does the implementation of a complex and
  a non complex problem differ?
• At what stages of a problem life-cycle does
  complexity appear and how is complexity
  manifested?
• What new concepts/methods/tools need to be
  developed to handle such complexity?

• We will address these questions in two different
  kinds of complex model
• Ecological models (see above)
• Massive agent based models (Epicast)
• And also consider how we can address gaps in
  functional knowledge by data assimilation into
  (human) ecosystem models

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Complex dynamics of urban systems

• The problem
• Urban ecosystems comprise a set of complex
  subsystems such as transport networks, energy,
  water and sewage reticulation, housing
  infrastructure and information and social
  networks.
• These interact in a landscape that can be
  described using Euclidean or other metrics and
  have impacts far beyond the urban boundary.
• Can we find effective and efficient ways of
  modelling the dynamics of whole urban ecosystem
  to guide the transition to future cities?
• The relevance
• We have passed the point at which more than half
  the worlds population lives in urban
  environments and the balance continues to shift.
  We need to be able to understand the intrinsic
  dynamics of these environments to avoid social
  disasters.

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Dynamics of Complex Networks in Biology

• The Problem
• The understanding and ultimately control, of gene
  expression in general and stem cell development
  in particular will provide very substantial and
  self-evident clinical benefits.
• The large amount of clinical and biochemical
  research activity globally is not mirrored by an
  equivalent depth of theoretical modelling, and
  simulation activity.
• This is surprising, because models provide a more
  logical path to plan and interpret
  hypothesis-driven biochemical experiments, and
  provide a rigorous framework for understanding
  the very complex and nonlinear relationships
  between stem cell components and their
  environments.

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Dynamics of Complex Networks in Biology

• Gene expression involves the interaction of many
  individual genes and gene clusters
• An obvious modeling tactic for this kind of
  system is to simulate it as a dynamic interaction
  network
• For example, in Boolean network models, nodes
  correspond to gene transcription and translation
  processes, and edges correspond to regulatory
  proteins acting as promoters and repressors.

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Genetic Regulatory Networks and Epigenetic
Emergence
While real genetic networks are complex, genes
can be approximated as binary switches they are
either on or off. Treating them this way we find
that there are strong constraints on the ways
that the 100,000 genes of higher organisms can
interact.
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Genetic Regulatory Networks as Boolean Networks
Consider a simple network of 3 genes, A, B, C,
where each gene is affected by two other genes
and possibly itself
We let the interaction between genes A, B and C
be specified by 3 of the 16 possible Boolean
functions of 2 variables. For the given values
of the 2 input variables (genes on or off) ,
these functions specify the value taken by the
output variable (target gene)
Example from Sole and Goodwin (2000)
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Genetic Regulatory Networks as Boolean Networks
Consider a simple network of 3 genes, A, B, C,
where each gene is affected by two other genes
and possibly itself
We can now specify the state transition table
that shows the values taken by A, B, C at time
T1 given the condition of the 3 genes at time T
Example from Sole and Goodwin (2000)
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Genetic Regulatory Networks as Boolean Networks
Consider a simple network of 3 genes, A, B, C,
where each gene is affected by two other genes
and possibly itself
(100) (000) (001) (110)
(111) (011) (101) (010)
Finally we can draw the kinematograph of the
system showing how the states change into one
another. One set ends at the point (110) while
the other ends in the cycle (101)?(010)
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Genetic Regulatory Networks as Boolean Networks

• Most genetic networks involve far more genes
  than 3 but Kauffman has shown that even with 1000
  genes and 21000 states, the number of end states
  for a network of connectivity k2 is 30. For a
  network of N genes, there is N1/2 end states
  (cell types?)
• Human genome N25,000? gives 160 end states
• The reason for the few end states is
  canalization. The state of only one of the two
  input genes determines the transition
• Networks with higher connectivity
  (k3,4,5,6..) have far more end states and many
  are chaotic
• However, real gene networks with kgt2 seem to
  use canalized Boolean operators.

An example of a sub-network generated from PBN
modeling applied to a set of human glioma
transcriptome data. (Hashimoto et al., 2004)
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Dynamics of Complex Networks in Biology

• The Project aims
• To develop a modular suite of programs (newly
  written and public domain) to enable
• the generation of networks from a range of types
  of data
• modelling of the dynamics of complex networks at
  the molecular, cellular and tissue levels, with a
  range of input data types, gene expression,
  protein-protein interaction etc
• a modelling layer to predict phenotype from
  biology, with genotyping and phenotyping input
• To increase the uptake of CSS and systems
  biology by molecular, cellular and tissue
  biologists in CSIRO and elsewhere through the
  demonstration of the utility of the
  methodologies.
• The different participants and collaborators
  bring a diverse range of expertise and types of
  data to the core project. These include genome
  sequences, gene expression data, whole genome
  scan datasets, epigenetic modification,
  protein-DNA, protein-protein interactions, cell
  lineage and differentiation data.

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Prediction and control of social networks

• The Problem
• This project aims at two of the hard problems in
  the analysis of the interactions within
  organisations
• Optimal estimation and prediction of the social
  interactions and strategies given incomplete
  noisy data on individual actions (e.g. email
  messages, human reports and telephone traffic).
• Optimal policy design for controlling social
  networks.
• The relevance
• In this work, an organisation is quite general,
  for example a company, a terrorist plot, a
  farming community facing a new regulatory
  environment ..
• The Approach
• Mathematical descriptions of social interactions
  within institutions have been developed by inter
  alia Crawford and Ostrom (2004), Soetevent
  (2006), and Manski (2000) 18, 19, 20.
  Despite developing the elements of grammar and
  syntax (or rules), and a typology of interactions
  (constraints, expectations and preferences) this
  work stopped short of estimating models from
  empirical data. This project aims to extend this
  work to derive dynamic models from incomplete data

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Chemical-biological reactive-transport systems

• The Problem
• There seem to be strong similarities between
  the processes that lead to emergent structures in
  fluid systems with reaction and transport,
  whether in rock formation, pollutant transport in
  porous media or atmospheric turbulence.
• The lack of a common vocabulary has been a
  major barrier to identifying the connections
  between these fields and to the transfer of
  insights.
• We will adopt a framework based in recent
  advances in non-equilibrium thermodynamics to
  investigate the bounds on instability growth and
  resultant pattern formation in geological
  processes and atmospheric shear flows to build
  this vocabulary and search for common principles.
• The Relevance
• In geology, understanding the processes leading
  to ore body formation is critical for mining
  exploration. The formation of coherent eddies
  controls turbulent exchange and transfer between
  the biosphere and atmosphere and parameterizing
  their effect is important in weather climate
  models.

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An example of emergent structure in shear flow
turbulence above a plant canopy
Unlike the boundary layer profile, the inflected
velocity profile at canopy top is inviscidly
unstable, leading to rapid growth and strong
selection for a single scale proportional to the
vorticity thickness d?. Spanwise Stuart
vortices develop which can be deflected into HU
and HD hairpins. This is the mixing layer
analogy (Raupach et al, 1996).
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A symmetry breaking mechanism comes into play
near the canopy top

• The presence of the porous canopy allows
  extensive downward deflections to form HD
  hairpins-as long as their spanwise scale is lthc
• In the canopy-top shear flow, HD hairpins are
  stretched and rotated faster than HU hairpins so
  HDs dominate
• Further from the wall, large scale upward
  deflections become dominant again so that HU
  hairpins begin to dominate
• Finally, inviscid stability analysis suggests
  that HUs and HDs should be formed in pairs as
  observed in the DNS simulations of Gerz et al.
  (1994)

Pierrehumbert and Widnall (1982)
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Convergence between the underlying ejection and
overlying sweep produces a scalar microfront.
Shear stress ltuwgt is concentrated between the
hairpin legs
The scalar is released from the canopy at a
uniform rate (independent of local wind
velocity). Within a structure, a sloping
microfront is formed with high concentration
below and in advance of the front, while low
concentration follows and is above the
microfront. Blue- ?2 isosurface Green-scalar
microfront Red- uw sweep Orange-uw ejection
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We have evidence that the Head-up and Head-Down
hairpins are formed simultaneously as the linear
instability theory suggests
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Global constraints on highly non-linear systems

• The example above shares a curious property
  with many highly non-linear physical systems.
  The spatial structure of the ensemble average
  form of the emergent eddies are well predicted by
  the eigenfunctions of linear stability theory.
  It is as if the linear eigenfunctions were
  preferred patterns for the fully turbulent
  structures.
• This observation suggests that some kind of
  minimum principle is operating but for strongly
  dissipative systems no general principles are
  agreed. One candidate-maximum entropy (eg.
  Dewar, 2005)- works well for some examples but
  the bounds on its applicability are unclear.
• In solid earth mechanics, The emergence and
  growth of instabilities resulting in pattern
  formation have been described in a framework
  based on non-equilibrium thermodynamics derived
  from the classical work of Biot, who showed that
  for many physical-chemical systems the Helmholtz
  Free Energy and the Dissipation Function are
  sufficient to define and track the growth of
  instabilities.
• We hope that comparing and contrasting these
  systems will lead to new insights.

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What common themes span these five application
areas?

• The work on matching model to system complexity
  is of immediate application to the goal of the
  urban ecosystem project
• The eduction of dynamic social networks using
  incomplete data and a formal grammar relates
  directly to current and projected work that
  derives genetic regulatory networks form data on
  cellular or whole organism response
• The work on dynamic social networks may provide
  algorithms that capture societal dynamics in the
  human ecosystem models to be studied ultimately
  in the model complexity project
• Global thermodynamical constraints that are
  applicable to continuum systems should provide
  guidance towards the major question that we face
  in agent based approaches to modelling complex
  adaptive systems
• How can we establish the connection between
  local interactions and global behaviour in
  discrete systems?

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Complex systems on one page
Social movements-the zeitgeist
Link from local interaction to emergence not
known but emergence clearly occurs
Gas laws Stat. mech.
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Complex systems on one page
Probably emergent
No guarantee of emergence Or large fluctuations
Urban Ecosystems
Madness of crowds
Social networks
Link from local interaction to emergence not
known but emergence clear
Complexity of interactions
Ecosystem models
Predictability of crowds
Low dimensional models
Biological Networks
Colonial insects
Majority view, cascading failure
Reaction-transport systems
Ising models SIR models
Understandable via conservation laws
Boids
Gas laws Stat. mech.
1 10 102 103 104 105 106 107
108 109 . . . . . .. . . .
?1026
Number of agents
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• The End