Post on 10-Jun-2020
Methoden van Wetenschappelijk Onderzoek
Les 2:Complexity and Complex Systems
Joachim De Beule
Every Day Science...
donderdag 25 september 2008 | Bron: belga
Vlaming geeft Waal elk jaar bijna 1.000 euro
Bert Verhoeff
De Vlaming geeft elk jaar 967 euro aan de Walen. De Brusselaar legt daar nog eens 211 euro bovenop. Het levert elke Waal jaarlijks 1.783 euro op. Dat blijkt uit een studie van de Nationale Bank van België, die voor het eerst de transfers in ons land in kaart brengt. Dat schrijft De Tijd donderdag.Vlaming geeft Waal elk jaar bijna 1.000 euro
Nationale Bank Wallonië ontvangt jaarlijks 6 miljard euro solidariteit
“Classical” science● Equilibrium: Systems tend towards equilibrium states
– no change of macroscopic values in the absence of external stimuli
– often ignorance of dynamical aspect of equilibrium at microscopic level
● Linear causality: small perturbations produce small effects
● Negative Feedback: when distorted, the system will react to return to the (same) equilibrium state
ActualTemperature T
Linear thermostat:Heating H proportionalto difference
DesiredTemperature D
Difference =(DT)
Complex Systems
A new way of looking at things:
1. Nonequilibrium: a complex system lives “at the edge of chaos” [1]
2. Nonlinear interactions among constituents
3. Positive feedback: small fluctuations can cause large scale rearrangements (emergence of new properties)
Can selforganize itself, i.e. “acquire a functional, spatial or temporal structure without specific interference from the outside” [2].
[1] C . G. Langdon, Physica 42D, 12 (1990)
[2] E. Haken, Information and selforganisation: a macroscopic approach to complex systems, Springer Verlag, Berlin, 1988
Complex Systems Science
More is different!
P..W. Anderson Science 177 393396 (1972)
quantitatively larger systems
are
qualitatively different
Emergence of complexity is related to
1) Microscopical interactions
2) Coevolution
3) SelfOrganization
A Physical Complex System
Atoms do not show the electrical features of macroscopic materials. Complex rearrangement of electrons in crystals determine these new properties.
A Social Complex System
A seller and a buyer do not behave as a stock market. We cannot deduce the behavior of a stock market looking at only one or two of them.
A Technological Complex System
Router connections at microscopical level produce the complex Internet structure.
A “Hot” Complex System
Networks and Statistics
Statistics again...
Statistics 1. Uniform distribution
Statistics 2. Gaussian distribution
Statistics 3. powerlaw distribution
Statistics 3. powerlaw distribution
Linear scale Logarithmic scale
slope h/b =
h
b=1
~ log(c)
Statistics 3. powerlaw distributionPower law ( ) Pareto distribution( )
Statistics 3. powerlaw distribution
“The rth largest city has n inhabitants”
~ “r cities have n or more inhabitants
Ziph's law ( )
Examples of power laws in nature
Properties of powerlaw distributions● pdf:
● Example, => pdf
● Complementary cdf
● Moments
● => Only well defined for !!!
● All moments diverge!!!
Power law with power
Power law distributions are “scalefree”
Scaleinvariant systems in nature
Power laws often point to a simpler underlying (microlevel) mechanism
● If every individual tries to be with the same mobilephone company as his closest friends then the popularity of companies (rank/frequency plot) will follow a power law
● And if think you this does not happen, what about the “Timberlake effect”?
● If every individual moves only if in his current neighborhood he is part of a relatively small minority then subpopulations will form with powerlaw distributed sizes.
● ...
“Is Justin Timberlake a Product of Cumulative Advantage?” By DUNCAN J. WATTS, New York Times, April 15, 2007
A Case study: income distribution (Pareto)
Originally proposed by Italian economist Vifredo Pareto to describe the allocation of wealth
“8020 rule”: 20% of the population controls 80% of the wealth
Research Questions:
1) What is the distribution of income?
2) Can a simple underlying (microlevel) mechanism be found that explains this distribution?
A Case study: income distribution (Pareto)
First step: gathering data ...
“The World Distribution of Household Wealth”, James B. Davies, S. Sandstrom, A. Shorrocks, and E.N. Wolff, July 2007 http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1068&context=cgirs
A Case study: income distribution (Pareto)
First step: gathering data ... ... beware of the bias!
“The Super Rich Are Out of Sight” Micheal Parenti in 2002 on CommonDreams.org http://www.commondreams.org/views02/122706.htm
– December 1997: from U.S. Census Bureau data it was concluded that the average income of the top 20 percent earners was $117,500
– But the bureau never interviewed anyone who had an income higher than $300,000. – Or if interviewed, they were never recorded as above the "reportable upper limit" of
$300,000, the top figure allowed by the bureau's computer program. – Why? An official said that :
the Census Bureau's computers could not handle higher amounts highincome respondents usually understate their investment returns since the super rich are so few, they are not likely to show up in a national sample.
A Case study: income distribution (Pareto)
Statistics...
A Case study: income distribution (Pareto)
The bottom half of wealth owners own less then 0.8% of all the
available wealth
Statistics...
A Case study: income distribution (Pareto)
Or, a fraction of 0.01 of all the people in the world own almost half of all the available wealth
Statistics...
A Case study: income distribution (Pareto)
If you have less then 178 dollar, then you belong to the 10% poorest people in the world
Statistics...
A Case study: income distribution (Pareto)
Or, you need more than 61288$ to belong to the top 10% of wealth
owners
Statistics...
A Case study: income distribution (Pareto)
Of all the 10% poorest people,0.2% live in North America, 27.1%
in Africa, etc...
Statistics...
A Case study: income distribution (Pareto)
Statistics...
6.1% of the world population lives in North America. They own 34.4% of all wealth.
22.8% of the world population lives in China. They own 2.6% of all wealth.
A Case study: income distribution (Pareto)
Graphs...
A Case study: income distribution (Pareto)
Graphs...
A Case study: income distribution (Pareto)
And power laws...
!
A Case study: income distribution (Pareto)Just the beginning ...What about question 2?“Temporal evolution of the “thermal” and “superthermal” income classes in the USA
during 1983–2001” A. Christian Silva and Victor M. Yakovenko http://www2.physics.umd.edu/~yakovenk/papers/EPL693042005.pdf
“If This Is Such a Rich Country, Why Are We Getting Squeezed?”, Heather Boushey and Joshua Holland, AlterNet, 2007
More to read (Gini coefficient of inequality): http://en.wikipedia.org/wiki/Pareto_distribution
Assignment: perform a similar case study for Belgium If you don't find appropriate data to support findings about income distribution, can you say something about e.g. city size
Belgian bureau for statistics: http://www.statbel.fgov.be/figures/download_nl.asp
four pages electronic report (pdf or ps) according to “scientific standards” (see next class); due before Christmas
!