Transcript ISI25 - Sorin Solomon

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” components
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’.
…thus, we need to free ourselves from ‘average’ thinking.”
“MORE IS DIFFERENT”
Complex Systems Paradigm
MICRO - the relevant elementary agents
Traders, investors
INTER
transactions
- their basic, simple interactions
MACRO - the emerging collective objects
herds,crashes,booms
Intrinsically (3x) interdisciplinary:
-MICRO belongs to one science Decision making, psychology
-MACRO to another science
-Mechanisms: a third science
economics
statistical mechanics, physics
math, game theory, info
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)
Yet with a strong collective identity and common motivation.
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 sequel
data 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+AB+B+A
BØ
death/ consumption
dw/dt = a w
a =(#A x birth rate a =(#A x returns rate -
death rate)
consumption /losses rate)
exponential solution: w(t) = w(0)e a t
w=
#B
birth rate > death rate
a>0
birth rate > death rate
a<0
TIME
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
Reality
Discrete Individuals
SAME
SYSTEM
Models
Continuum Density
Complex ----------------------------------Trivial
Localized patches -----------------------Spatial Uniformity
Adaptive ----------------------------------Fixed dynamical law
Development -----------------------------Decay
Survival -----------------------------------Death
Misfit was always assigned to the neglect of specific details.
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
Logistic Equation usually ignored spatial distribution,
Introduce discreteness and randomeness !
.
w =
( conditions x birth rate - death) x w + diffusion w
conditions is a function
of many spatio-temporal
distributed discrete
individual contributions
rather then totally
uniform and static
- competition w2
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.”
Shnerb, Louzoun, Bettelheim, Solomon,[PNAS (2000)] proved by (FT,RG)
that the continuum , differential logistic equation prediction:
Is ALWAYS wrong !
Multi-Agent a << 0
prediction
resilience and sustainabilit
even for a << 0!
Differential Equations
a << 0 approx)
Time
(continuum
Instead: emergence of singular
spatio-temporal localized
collective islands with
adaptive self-serving behavior
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,
at rate δ and
a B-particle at x at time s splits into two particles at x
but in addition they die
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
(respectively B-particles) at x at time s.
of A-particles
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
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 .
in terms of the Master Equation:
d Pnm / dt = death of B’s: - m [ m Pnm – (m+1) P n,m+1 ]
birth of B’s in the presence of n A’s
- l n [ m P nm – (m-1) P n,m-1]
+ diffusion to and from neighbors
Interpret it as a Schroedinger Equation with imaginary time
where
and
+diffusion
and
etc. (second quantization
creation/anihilation operators)
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
.
2
w =aw–cw
Logistic Diff Eq prediction:
Multi-Agent stochastic
<a> << 0
prediction
Differential Equations continuum
<a> <<Time0 approx)
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
Number of
Economic
Enterprizes
per capita
1989
B= Number of
Economic
Enterprizes
per capita
1994
“A”= education
1988
Nowak, Rakoci, Solomon, Ya’ari
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
EDU
IGN
IGN
Nowak, Rakoci, Solomon, Ya’ari
EDU
simulation
IGN
EDU
IGN
real data
EDU
IGN
simulation
EDU
real data
IGN
Nowak, Rakoci, Solomon, Ya’ari
Other predictions
• 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.
Very few localized growth centers
(occasionally efficient but unequal and unstable)
Uniform distribution
(inefficient but stable)
Poland
Russia Ukraine
Latvia
Instability of over-localized
economies
Prediction
the economic inequality (Pareto exponent)
and
the economic instability
(index anomalous fluctuations exponent)
a
400
Forbes 400 richest by rank
b
Levy, Solomon,2003
What next?
PIEMONTE MAP
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.