THINKING OUTSIDE THE BOX: KNOWLEDGE POWER

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THINKING OUTSIDE THE BOX KNOWLEDGE POWER

• Alan Wilson
• Centre for Advanced Spatial Analysis
• University College London

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Two objectives for the seminar

• To make some general observations about
  generating good ideas as a researcher and in
  particular, thinking outside the box
• To offer some specific examples from personal
  experience
• Invite everyone to transpose the general argument
  into their experience

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KNOWLEDGE POWER

• where does knowledge power come from?
• academic disciplines
• combinations of disciplines - interdisciplinary
  work often inhibited by the social coalitions,
  especially in the sciences
• practical experience

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• the power derives from
• concepts and theories
• superconcepts that transcend disciplines
• capabilities for handling difficulty and
  complexity
• systems thinking beyond reductionism
• capabilities for handling complexity
• problem-solving, issue-resolving capabilities
• analysis, design and policy capabilities

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• intuitively this suggests that we need depth and
  breadth
• THINKING OUTSIDE THE BOX involves some kind of
  breadth
• are there superconcepts which can help us with
  the development of knowledge power?
• how can we assemble an intellectual toolkit that
  gives us knowledge power? (A very individual
  thing of course.)

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BUILDING AN INTELLECTUAL TOOLKIT

• one personal view
• think of authors who have particularly influenced
  you and who become part of your toolkit
• learn to identify superconcepts and generic
  problems
• know something about most disciplines?
• examples from my own experience follow

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Weavers classification of problems

• Weaver (of Shannon and Weaver) was Science VP of
  the Rockefeller foundation in the 50s he wanted
  to think through where the Foundation should be
  investing in a very perceptive way he argued
  that there were three kinds of problem
• simple
• of disorganised complexity
• of organised complexity
• and that the biggest challenges for science would
  be the third ...and how right he was so locate
  your problem on that spectrum a super concept
  perspective

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Newtons Law of Gravity Weaver - 1

• Yij KXiZj/cij2
• simple because essentially a two-body problem
• was used in transport modelling in the 1950s

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Boltzmanns entropy Weaver - 2

• S klogW
• mostly seen as the basis of the second law of
  thermodynamics essentially statistical physics
  works for gases because of statistical
  averaging
• transport modelling in cities in the 50s being
  treated as a Newtonian system
• shift to a Boltzmann perspective and the
  averaging works brilliantly. the models work
• achieved through (a) a change of perspective,
  Weaver-style-disorganised systems and (b) taking
  a concept entropy from an entirely different
  discipline

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Boltzmann with Lotka and Volterra Weaver - 3

• NB the power of combination here
• Physics
• classical gases - Boltzmann
• lattices generalised modelling methods
• Geography
• transport flows (Boltzmann)
• the evolution of cities and a shift now to
  complex systems (B and L-V)
• Boltzmann fast dynamics combines with
  Lotka-Volterra slow dynamics

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• Biology and epidemiology
• L-V and virus populations
• Ecology
• dealing with space L-V with B-flows added
• Economics
• consumer and retailer behaviour (B)
• retail structure and dynamics (L-V)
• evolutionary and complex economics
• the physical chemistry of mixtures

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• what are the common features?
• retailers competing for customers
• viruses competing for targets and resources
• species competing for resources
• industries (e.g.) competing for both resources
  and markets
• chemicals competing for energy

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A CURRENT EXAMPLE NETWORK ANALYSIS

• There has been an explosion of interest in the
  study of the evolution of spatial structures,
  particularly of so-called scale free networks
  (SFNs)1. Using the ideas above, we can show
  that the BLV methodology is under-used by
  researchers in this area and facilitates further
  development.

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• We need to bring together the concepts of
  equilibrium statistical mechanics to model flows
  (Boltzmann) and hypotheses to represent dynamics,
  building on Lotka and Volterra, together with a
  more general representation of networks. Given
  these historical associations, the integrated
  models can be characterised as BLVN models.

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• The SFN literature appears to be based almost
  wholly on a topological approach that
  characterises networks as a single set of nodes
  and a corresponding set of edges. The measure of
  spatial structure is the distribution of N(k),
  the number of nodes connected to others by k
  edges. (A measure of clustering of nodes is also
  sometimes used.)

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Figure 1
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• The more general characterisation used in urban
  science employs three sets of nodes
• a set i that can represent the origins of some
  activity
• a set j that can represent destinations
• and an underlying network with nodes h and
  edges e that carry the interactions or flows
  between origins and destinations.

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Figure 2
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• Prominence is then given to the modelling of real
  networks in space. The deployment of BLVN methods
  in urban and regional geography is well
  established2 and it has recently been shown
  that they can be extended into ecology3. This
  perspective and the associated models have been
  largely neglected by scientists from other
  disciplines working in network analysis.

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• To fix ideas, consider the origin nodes to be
  centroids of zones which are residential areas of
  a city, the destination nodes to be retail
  centres, and the network to be an urban transport
  system a mixture of roads and separate public
  transport links. There is then, potentially, an
  interaction, Yij, between each origin zone,
  Xi, and each destination zone, Zj, measured,
  for example, as either a flow of people or a flow
  of money spent in retail centres.

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• For simplicity, consider the flows of people.
  These flows are then carried on the underlying
  network. The flow from i to j will be carried on
  one or more routes of the network subsets of
  h and e. One measure of the significance of a
  retail centre is then the sum of the flows into
  it, and this is potentially much more sensitive
  than a count of edges.

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Figure 3
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• It can be shown6 that by maximising an entropy
  term the Boltzmann part of the argument S
  klogW - subject to suitable constraints,
• Yij AiXiZjaexp(-ßcij) (1)
• where
• Ai 1/SkZkaexp(-ßcik) (2)
• We can now calculate the total inflow into each
  j
• Dj SiYij (3)

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• A key point is that modelling flow totals into
  nodes gives a much richer picture of spatial
  structure - and this in turn is a broader notion
  than network structure.

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• We now consider the Zj changing on the basis of
  a slow dynamics hypothesis. The flows into j
  have been attracted by a pulling power, Zja. We
  can now hypothesise that if Dj gt Zj, then Zj
  should grow, and vice versa7
• ?Zj e(Dj Zj)Zj (4)
• for a suitable parameter, e. These equations are
  recognisably related to the Lotka and Volterra
  equations, albeit in this case, with the
  populations being spatially distributed but a
  single species.

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• The key variable which is used in SFN analysis is
  the number of edges at each node and p(k) is
  taken as the probability that a node has k-edges
  connected to it.
• It is found empirically that this distribution
  often takes the form of a power law, p(k) k-?,
  for some parameter ?. The network, in this
  case, can be considered to be equivalent to
  either our i or j sets.
• For definiteness consider the j set. Then if we
  measured Zj by the number of edges which might
  be flows above some threshold at j, then the
  size distribution of the Zj, say P(Z), would be
  equivalent to the p(k) distribution.

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• However, the flows form the basis of a much
  richer concept and there is a method for then
  articulating network structure45. The dynamic
  model that represents the evolution of centres,
  the Zj, can be seen as a network generator and
  as the basis for SFN modelling.
• The BLVN formulation can offer explanations for
  the spatial structure and the size distribution
  (and this is typically not the case in the SFN
  analysis) and, potentially, the basis of a power
  law.
• There is a wide range of application that
  embraces many scale-free networks but locating
  them within a richer methodology.

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• There are many possible applications. These are
  wide-ranging in all aspects of urban and regional
  analysis10 and there are examples in
  demography11, economics1213 and
  ecology14.
• There is huge potential in all areas of the
  scale-free networks enterprise
  epidemiology15, chemistry16, physics17,
  biology18, geomorphology19 and the world-wide
  web2021. There is a tremendous programme of
  further exploration to be implemented.

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CONCLUDING COMMENTS

• while most of you are properly and fully rooted
  in your own disciplines and tool kits, I am
  arguing that you could find it fruitful to
  explore concepts and problems elsewhere
• there is a continual tension between breadth and
  depth. If you are doing research, then depth is
  the key if you want to expand your capability to
  be original, then a touch of breadth is a good
  thing!
• that is what the knowledge power idea is about!

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Super concepts

• I have a list of around 60......some more super
  than others
• system, system representation, location,
  interaction, accounts, scales, hierarchy,
  information, flight simulators, conservation
  principles, optimisation, pattern recognition,
  networks, entropy, equilibrium, critical points,
  initial conditions, path dependence, emergence,
  microsimulation
• What would your own examples be??

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Final comment Weinberg on research Be
ambitious!

• No one knows everything, and you dont have to.
  Jump in, sink or swim.....pick up what you need
  as you go along
• While you are swimming and not sinking, aim for
  rough water....go for the messes.
• ...forgive yourself for wasting time.
  Supervisors may not like this, but its saying
  that if youre being ambitious, youll have to
  explore territory which sometimes turns out to be
  unfruitful
• but your growing intellectual toolkit will help
  you to navigate

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References.

• 1 Newman, M., Barabasi, A-L, Watts, D. J.
  (2006) (eds.) The structure and dynamics of
  networks, Princeton University Press, Princeton,
  N. J.
• 2 Wilson, A. G. (2000) Complex spatial systems,
  Addison-Wesley-Longman, Harlow.
• 3 Wilson, A. G. (2006) Ecological and urban
  systems models some explorations of similarities
  in the context of complexity theory, Environment
  and Planning, A, pp. 633-646.
• 4 Nystuen, J. D. and Dacey, M. F. (1961) A
  graph theory interpretation of nodal regions,
  Papers, Regional Science Association, 7, pp.
  29-42.

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• 5 Rihll, T. E. and Wilson, A. G. (1987) Spatial
  interaction and structural models in historical
  analysis some possibilities and an example,
  Histoire et Mesure II-1, 5-32.
• 6 Wilson, A. G. (1970) Entropy in urban and
  regional modelling, Pion, London.
• 7 Harris, B. and Wilson, A. G. (1978)
  Equilibrium values and dynamics of attractiveness
  terms in production-constrained
  spatial-interaction models, Environment and
  Planning, A, 10, 371-88.

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• 8 Wilson, A. G. and Oulton, M. J. The corner
  shop to supermarket transition in retailing the
  beginnings of empirical evidence, Environment and
  Planning, A, 15, pp 265-74, 1983.
• 9 Clarke, M. and Wilson, A. G. (1985) The
  dynamics of urban spatial structure the progress
  of a research programme, Transactions, Institute
  of British Geographers, NS 10, 427-451.
• 10 Birkin, M., Clarke, G. P., Clarke, M. and
  Wilson, A. G. (1996) Intelligent GIS location
  decisions and strategic planning, Geoinformation
  International, Cambridge.

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• 11 Rees, P. H. and Wilson, A. G. (1977) Spatial
  population analysis, Edward Arnold, London.
• 12 Roy, J. R. and Hewings, G. J. D. (2005)
  Regional input-output with endogenous internal
  and external network flows, Discussion paper REAL
  05-T-9, Regional Economics Applications
  Laboratory, University of Illinois, Urbana.

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• 13 Rosser, J. B. Jr. (1991) From catastrophe to
  chaos a general theory of economic
  discontinuities, Kluwer Academic Publishers,
  Boston.
• 14 Smith, C. H. (1983) A system of world
  mammal faunal regions. I. Logical and statistical
  derivation of the regions, Journal of
  Biogeography, 10, pp. 455-466.
• 15 Moreno, Y. and Vazquez, A. (2003) Disease
  spreading in structured scale-free networks,
  European Physical Journal, B, 31, pp. 265-271.

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• 16 Gray, P. and Scott, S. (1990) Chemical
  oscillations and instabilities, Oxford University
  Press, Oxford.
• 17 Thurner, S. (2005) Nonextensive statistical
  mechanics and complex scale-free networks,
  Europhysics News, November/December.
• 18 Albert, R. (2005) Scale-free networks in
  cell biology, Journal of Cell Science, 118, pp.
  4947-4957.

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• 19 Rinaldo, A. Banavar, J. R., Colizza, V. and
  Maritan, A. (2004) On network form and function,
  Physica, A, 340, pp. 749-755.
• 20 Pastor-Satorras, R. and Vespigniani, A.
  (2004) Evolution and structure of the internet a
  statistical physics approach, Cambridge
  University Press, Cambridge.

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• 21 Tomlin, J.A. (2003) A new paradigm for
  ranking pages on the World Wide Web, WWW2003, May
  20-24, 2003, Budapest, Hungary.