complexity as theoretical applied science
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Complexity as Theoretical Applied Science. - PowerPoint PPT PresentationTRANSCRIPT
Complexity as Theoretical Applied Science Sorin Solomon,
Racah Institute of Physics HUJ Israel Director, Complex Multi-Agent Systems Division, ISI Turin
Head, Lagrange Interdisciplinary Laboratory for Excellence In Complexity Coordinator of EU General Integration Action in Complexity Science (GIACS)
Chair of the EU Expert Committee for Complexity Science
MORE IS DIFFERENT (Anderson 72)Complex “Macroscopic” properties may be the collective effect of many simple “microscopic” componentsPhil Anderson “Real world is controlled …
• by the exceptional, not the mean; • by the catastrophe, not the steady drip; • by the very rich, not the ‘middle class’.
…thus, we need to free ourselves from ‘average’ thinking.”
“MORE IS DIFFERENT” Complex Systems Paradigm
MICRO - the relevant elementary agents
INTER - their basic, simple interactions
MACRO - the emerging collective objects
Intrinsically (3x) interdisciplinary:
-MICRO belongs to one science
-MACRO to another science
-Mechanisms: a third science
Traders, investors
transactions
herds,crashes,booms
Decision making, psychology
economics
statistical mechanics, physicsmath, game theory, info
Yet with a strong collective identity and common motivation.
A science without a fixed area, moving with the frontier , much like fundamental high energy physics used to be (atoms->quarks)
In the present case feeding on the frontiers (and consuming them)
Complexity Induces a New relation Theoretical Science Real Life Applications: Traditional Applied Science applied hardware devices (results of experimental science)
to material / physical reality. Modern Complexity rather applies theoretical methods e.g. - new (self-)organization concepts and - (self-)adaptation emergence theories
to real life, but not necessarily material / physical items: - social and economic change,
- individual and collective creativity, - the information flow in life
Applications of Complexity are thus of a new brand: "Theoretical Applied Science" and should be recognized as such when evaluating their expected practical impact
I present in the sequeldata and theoretical study of Poland's 3000 counties over 15 years following the 1990 liberalization of the economy.
The data tells a very detailed story of application of multi-agents complexity to real life.
To understand it we have to go back in time more then 200 years ago in Holland.
Malthus : autocatalitic proliferation/ returns :B+AB+B+Adeath/ consumption B Ødw/dt = aw
a =(#A x birth rate - death rate)
a =(#A x returns rate - consumption /losses rate)
exponential solution: w(t) = w(0)e a t
a < 0
w= #B
a
TIME
birth rate > death rate
birth rate > death rate
Verhulst way out of it: B+B B The LOGISTIC EQUATION
dw/dt = a w – c w2 c=competition / saturation Solution: exponential ==========saturation
w = #B
almost all the social phenomena, except
in their relatively brief abnormal times obey the logistic growth. “Social dynamics and quantifying of social forces” Elliott W. Montroll US National Academy of Sciences and American Academy of Arts and Sciences 'I would urge that people be introduced
to the logistic equation early in their education…
Not only in research but also in the
everyday world of politics and economics …” Nature
Robert McCredie, Lord May of Oxford, President of the Royal Society
SAME SYSTEM Reality Models
Complex ----------------------------------Trivial
Adaptive ----------------------------------Fixed dynamical law
Localized patches -----------------------Spatial Uniformity
Survival -----------------------------------Death
Discrete Individuals Continuum Density
Development -----------------------------Decay
We show it was rather due to the neglect of the discreteness.
Once taken in account => complex adaptive collective objects. emerge even in the worse conditions
Misfit was always assigned to the neglect of specific details.
Logistic Equation usually ignored spatial distribution, Introduce discreteness and randomeness !
w.
= ( conditions x birth rate - deathx w + diffusion w - competition w2
conditions is a function of many spatio-temporal distributed discrete individual contributions rather then totally uniform and static
Phil Anderson
“Real world is controlled …
– by the exceptional, not the mean;
– by the catastrophe, not the steady drip; – by the very rich, not the ‘middle class’
we need to free ourselves from ‘average’ thinking.”
that the continuum , differential logistic equation prediction:
Time
Differential Equations
(continuum a << 0 approx)
Multi-Agent a
prediction
Is ALWAYS wrong !
Shnerb, Louzoun, Bettelheim, Solomon,[PNAS (2000)] proved by (FT,RG)
Instead: emergence of singular spatio-temporal localized collective islands with adaptive self-serving behavior
resilience and sustainability
even for a << 0!
Electronic Journal of Probability Vol. 8 (2003) Paper no. 5, pp 1–51.Branching Random Walk with Catalysts Harry Kesten, Vladas Sidoravicius
Shnerb, Louzoun, Betteleim, Solomon (2000), (2001) studied the following system of interacting particles on Zd: There are two kinds of particles, called A-particles and B-particles.
The A-particles perform continuous time simple random walks, independently of each other. The jump rate of each A-particle is DA.
The B-particles perform continuous time simple random walks with jump rate DB,
but in addition they die at rate δ and
a B-particle at x at time s splits into two particles at x during the next ds time units with a probability βNA(x, s)ds+o(ds),
where NA(x, s) (NB(x, s)) denotes the number of A-particles (respectively B-particles) at x at time s.
Using Kesten, Sidoravicius (2003) techniques, we proved (2005) that: in d dimensions, the condition for B growth is: δ / DA> 1-Pd where, the Polya constant
Pd= the probability for an A to return to origin
P1=P2=1
in terms of the Master Equation:d Pnm / dt = death of B’s: - [ m Pnm – (m+1) P n,m+1 ]
birth of B’s in the presence of n A’s - n [ m P nm – (m-1) P n,m-1] + diffusion to and from neighbors
Original Field Theory analysis: express the dynamics of Pnm (x) = the probability that there are m B’s and n A’s at the site x .
Interpret it as a Schroedinger Equation with imaginary time
and
and
+diffusionetc. (second quantization creation/anihilation operators)
where
Renormalization Group results: The systems made out of autocatalytic discrete agents (B+A B+B+A)present “Anderson” localization (in 2D, ALWAYS).
This invalidates the naïve, classical continuum differential logistic-type equation results.i-1 localization implies localized exponential growth
Interpretations of the logistic localization phase transition[conductor isolator] death life extinction survival economic decay capital autocatalytic growth
Logistic Diff Eq prediction:
Time
Differential Equations continuum
a << 0 approx)
Multi-Agent stochastic
a
prediction
w.
= a w – c w2
GDP Poland
Nowak, Rakoci, Solomon, Ya’ari
The GDP rate of Poland, Russia and Ukraine (the 1990 levels equals 100 percent)
Poland
Russia
Ukraine
Movie By Gur Ya’ari
Nowak, Rakoci, Solomon, Ya’ari
Nowak, Rakoci, Solomon, Ya’ari
“A”= education 1988
B= Number of Economic Enterprizes
per capita1994
Number of Economic Enterprizes
per capita1989
Other details of the Predicted Scenario:
First the singular educated centers WEDU develop while the others WIGN decay
Then, as WEDU >> WIGN , the transfer becomes
relevant and activity spreads from EDU to IGN and all develop with the same rate but preserve large inequality
EDU
IGN
IGN
EDU
Nowak, Rakoci, Solomon, Ya’ari
simulation
real dataEDU
EDU
IGN
IGN
Nowak, Rakoci, Solomon, Ya’ari
simulation
real data
IGN
IGN
EDU
EDU
• Case 1: low level of capital redistribution -high income inequality -outbreaks of instability (e.g. Russia, Ukraine).•Case2: high level of central capital redistribution - slow growth or even regressing economy (Latvia) but quite - uniform wealth in space and time.•Case 3 :Poland - optimal balance : - transfers enough to insure adaptability and sustainability - yet the local reinvestment is enough to insure growth.
Other predictions
Very few localized growth centers
(occasionally efficient but unequal and unstable)
Uniform distribution (inefficient but stable)
PolandRussia Ukraine
Latvia
Instability of over-localized economies
Predictionthe economic inequality (Pareto exponent) and the economic instability (index anomalous fluctuations exponent)
Forbes 400 richest by rank
400
Levy, Solomon,2003
What next?
PIEMONTE MAPPiemonte
Belarus
Piemonte
Romania
Future and on-going studies Measure chain of
changes in capital growth and transfer due to Fiat plant closure.
Enterprises creation and disappearance, etc
With Prof Terna’s group
Check alternatives
Conclusions• The logistic dynamics was believed for 200 years to be capable
to describe a very wide range of systems in biology, society, economics, etc
• The naïve continuous differential equations expression of this dynamics lead often to predictions incompatible with the empirical evidence
• We show that taking properly into account the multi-agent character of the system one predicts generically the emergence of adaptive, collective objects supporting development and sustainability.
• The theoretical predictions are validated by the confrontation with the empirical evidence and are relevant for real life economic, social and biological applications.