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Spring School Complexity Science
Introduction to
Complexity Science
Working with Systems
Systems
Systems science is clearly concerned with systems. Two
kinds are relevant here…
We can think of the things in the world that provide the
demand for systems science: problem systems…
genomes, cities, corporations, the health service
Sometimes the things that we build to solve these
problems are also thought of as systems…
databases, simulation models, virtual environments, etc.
The word system is clearly a very general term that can be
applied to many, many things. What do we mean by it?
Seth Bullock, 2006
What is a System?
At root a system is a set of individual components that are
linked by relationships of some kind to form a whole.
A graph representation can capture
the structure of a simple system.
+ive
-ive
Nodes might represent road junctions,
arcs the roads connecting them…
…or firms connected by supply and
demand relationships…
City
Web
Genetic
Centre
of Component
Regulatory
One-Way
…or genes involved in a network of
Network
System
Supply
+ive and –ive genetic regulation.
Other definitions exist, but this captures the various levels
of description involved studying any system: part and
whole, system and its surroundings, etc.
Seth Bullock, 2006
A Biological Example
sample
sample
sample
sample
level
Many genes code for proteins that either promote or
inhibit the transcription of other genes. Together, such
genes form genetic regulatory networks.
can we infer the structure of these networks from microarray data, samples of transcription factor levels?
1
2
3
4
time
is the data too noisy or
irregular for this to work?
could we simulate a
particular real network?
could we use simulations to discover how these types of
genetic regulatory network behave in general ?
Seth Bullock, 2006
A Geographical Example
One of the main factors influencing the design of built
environments such as airports, museums, libraries, etc., is
the way in which pedestrians move through these spaces.
How can designers structure environments such that the
behaviour of pedestrians is appropriate or desirable?
ensuring safe & timely exit and escape behaviour
avoiding bottlenecks, congestion, crowding, etc.
maximising impact of advertising space, facilities, etc.
Virtual environments and models of pedestrian movement
can provide designers with feedback before bricks are laid.
How can we ensure that these computational solutions are
fit for purpose – usable, accurate, flexible?
Seth Bullock, 2006
An Engineering Example
Many engineered products are complex assemblies of subcomponents manufactured by many different companies.
For example, JPL, Lockheed, and Boeing, among others,
collaborated on the design of the Genesis 11 spacecraft.
Effectively tracking design changes
and their ramifications requires
understanding how the relations
between components of the system
reflect the relations between the
firms collaborating to build it.
How might complexity science improve the management
of this information?
Seth Bullock, 2006
A Medical Example
In 2001, an outbreak of foot & mouth (a disease that
affects several species of livestock) cost the UK ~£5bn:
within 14 days it had covered the entire country
at its height nearly 50 cases a day were being detected
millions of animals were slaughtered
hundreds of farmers lost their livelihoods
the rural & tourism industries lost billions of pounds
A poor understanding of livestock transportation, disease
behaviour, and vaccination, coupled with bureaucratic
delays & poor co-ordination created a rapacious epidemic.
Could we have reduced the impact of foot & mouth?
Seth Bullock, 2006
A Science of Systems
There have been several attempts to develop tools to help
solve problems like the ones listed on the previous slides.
Such efforts are kinds of systems science:
cybernetics, systems theory, dynamical systems theory,
complexity, control theory, information theory, etc.
Each of these approaches attempts to provide frameworks
for thinking about and analysing systems in general.
Motivating these endeavours is an assumption that the
systems mentioned in earlier slides are fundamentally
similar – their differences are merely superficial.
If this is true, is there something to be gained from
studying such systems in general, rather than individually?
Seth Bullock, 2006
Levels of Description
It is important to appreciate the subjectivity of a systems
perspective – there is no single “correct” level of analysis.
For instance, human DNA can be understood as…
a set of genes, a string of bases, a large molecule, etc.
Each perspective is valid, but each differs from the others
in important respects, and is relevant at different times.
Often the success of a particular approach is crucially
dependent on choosing an appropriate level of description:
detailed enough to capture critical system behaviour
yet abstract enough to avoid unnecessary complexity
Which aspects to visualize, model, etc., depends on the
nature of the problem that is being solved.
Seth Bullock, 2006
Describing System Structure
The implications of a system’s structure will tend to be
domain-specific, but there are also general considerations:
types of atomic entity: how many? what kind?
e.g., herds of cattle & sheep, diseases, vaccines
types of interaction: how many? what kinds?
e.g., transportation, infection, vaccination, etc.
type of connectivity: sparse (rural) vs. dense (city)
e.g., road & rail networks, infection vectors, etc.
degree of uniformity: homogeneous vs. heterogeneous
e.g., random or grid-like vs. structured in some way
inputs & outputs: how many? what kind?
Seth Bullock, 2006
e.g., open system vs. closed system?
Sub-systems & Coupling
It is often useful to consider an entire system as divided
into parts, e.g., because they seem relatively independent.
E.g., the eye & brain can be considered to be a single
cognitive system, or to be distinct sub-parts of the system.
They exchange signals via nervous tissue,
the eye supplying sensation while the brain
Entire
S
Cognitive &
controls the ocular muscles.
R
B
Visual System
Likewise, robot and environment interact in
M
many ways, e.g., via sensors and motors.
Sub-systems that influence one another in this way are
said to be coupled.
E
Seth Bullock, 2006
The Eye of the Beholder
Like choosing a level of description, deciding what counts
as inside or outside a system, or how to divide one into
sub-systems is a subjective issue. For example…
…it may be useful to consider a tool to be part of the
agent, or a robot’s wheels part of the environment, etc.
We often treat an external system as a part of our body…
prosthetic devices such as eye-glasses, pacemakers
tools (e.g., a hammer), vehicles (e.g., a bicycle, a car)
…or sometimes consider a body part to be external to us…
e.g., when a body part is anaesthetised or fails somehow
Indeed, sub-systems tend to be noticed as separate only
when they fail in some manner…
Seth Bullock, 2006
Hierarchy vs. Anarchy
An important distinction separates systems that exhibit a
hierarchical structure from those that are disordered.
Many man-made systems feature central controllers, or
higher authorities that organise lower-level entities.
Structures like these are intended to
Boss
generate well-ordered behaviour.
Team
Team
In contrast, many natural systems
Leader
Leader
are not structured in this way, yet
are still capable of generating wellTeam Members
Team Members
organised, coordinated behaviours.
For example, the self-organisation of
Many Identical Team Members
ant colonies, or traders at the New
York stock exchange.
Seth Bullock, 2006
Describing System Behaviour
It is typically more important to characterise a system’s
actual behaviour, rather than it’s structure.
Some systems have no behaviour (e.g., a fixed
classification system), but most do.
some systems are static until acted upon in some way
many man-made computational systems, for instance
in contrast, some systems have an intrinsic dynamic
a brain? an ant-colony? economy? online community?
Like structure, what behaviour is attended to is subjective.
long-term, short-term, low-level, high-level, etc., etc.
In what ways can we classify system behaviour?
Seth Bullock, 2006
Stability
In many cases, we wish to understand under what
conditions a system will remain stable.
will a newsgroup remain robust as new users are added?
will an ecology remain stable as new species are added?
is the economy crashing? will a stock retain its value?
is the market for our product changing? how?
In fact, it is often not stability per se that is of interest, but
the extent to which a system has departed from stability.
How is the system being perturbed? How is this
perturbation being coped with? What results from it?
Are we able to alter the system? Can we effectively
change it in desired ways?
Seth Bullock, 2006
Emergence
The behaviour that a system exhibits at one level of
description may be very different from that at other levels.
Systems that appear disordered at a low level (such as ant
colonies, crowds, economies, etc.) may never-the-less
exhibit ordered behaviour at a higher level. For example:
Jupiter’s Great Red Spot: a huge gas cloud
termite mounds, bee hives, wasp nests
efficient market prices: the “invisible hand”
traffic jams, crowd behaviour, fashion cycles
When high-level ordered behaviour arises from the uncoordinated actions of lower-level entities, it is termed selforganization or emergent behaviour.
Seth Bullock, 2006
Adaptation
Adaptive systems change over time such that they come to
suit their environment – they adapt to their surroundings.
Evolution by natural selection is the primary example of an
adaptive process, but many other types exist:
Learning: e.g., shaping an organism’s tastes, fears, etc.
Imitation: e.g., trading behaviour on a stock exchange
Competition: e.g., pop bands compete for an audience
Even a system as simple as a
lawn can exhibit adaptive
behaviour, “coevolving” with
pedestrians until stable paths
are achieved.
Seth Bullock, 2006
Behaviour from Structure?
So far we have talked about structure and behaviour
separately, but it is clear that they are intimately linked.
How does a company’s management structure influence
its behaviour? It’s flexibility, quality control, creativity?
How does Soton’s traffic network influence rush hour?
How does the human genome influence morphogenesis?
Will a particular virtual reality encourage collaboration?
Can we confidently make changes to a system’s structure
in order to bring about desirable changes in behaviour?
In order to answer this type of question, we need to do
more than just describe a system’s structure & behaviour.
Seth Bullock, 2006