the emergence of macroscopic complex adaptive objects from microscopic simple random agents d...
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The emergence of Macroscopic Complex Adaptive Objects from Microscopic Simple Random Agents
D Mazursky (Soc. Sci., Bus. Adm.)
Henri Atlan (biology), Irun Cohen (immunology),
Hanoch Lavee (desert/ecology)
H and M Levy (finance econo),
J Goldenberg (marketing),
ISI SolomonBIU Shnerb, Louzoun, WARSAW Nowak, KusPARIS Weisbuch, Vignes, BallotROME Miceli, CozziPISA Dosi
The Importance of Being Discrete; Life Always Wins on the Surface
SAME SYSTEM Reality Models
Complex ----------------------------------Trivial
Adaptive ----------------------------------Fixed dynamical law
Localized patches -----------------------Spatial Uniformity
Survival -----------------------------------Death
Discrete Individuals Continuum Density
Development -----------------------------Decay
Misfit was always assigned to the neglect of specific details.We show it was rather due to the neglect of the discreteness.
SCOTT!Rule change No Rule change
EMERGENCE OF RULE CHANGE FROM NO-RULE-CHANGE
eternal agents A,
- initial uniform density a(x,t=0)=a0
- diffusion coefficient Da
- death rate µ: B
- birth rate B + A B + B + A[when at the same location with a "catalyst," A],
mortals B - initial uniform density b(x,t=0)= b0
- diffusion rate Db
A
Diffusion of A at rate Da
A
Diffusion of A at rate Da
A
Diffusion of A at rate Da
B
Diffusion of B at rate Db
B
Diffusion of B at rate Db
B
Diffusion of B at rate Db
B
A
A+B A+B+B; Birth of new B at rate
A B
A+B A+B+B; Birth of new B at rate
AB
A+B A+B+B; Birth of new B at rate
AB
A+B A+B+B; Birth of new B at rate
ABB
A+B A+B+B; Birth of new B at rate
ABB
A+B A+B+B; Birth of new B at rate
ABBBB
A+B A+B+B; Birth of new B at rate
ABBBB
A+B A+B+B; Birth of new B at rate
B
B Death of B at rate
B
B Death of B at rate
B Death of B at rate
Interpretations in Various Fields:
- A= proteins
- B=DNA
Origins of Life:
Genetic Evolution: - Sites: various genomic configurations. - B= individuals; Jumps of B= mutations. - A= advantaged niches (evolving fitness landscape).
Immune system: - sites = shapes / strains of antigens and antibodies - B = cells, antibodies;
- A = antigen B cells that meet corresponding antigen multiply.
Interpretations in Various Fields:
Desert / Vegetation: B = plants,
A= water / light / nutrients
Finance:
sites= investors, investment instruments / strategies
B = wealth, capital units, shares, companies
A= profit opportunities / jobs, strategies, customers
Also gene copying on DNA chains; Internet links, etc
What will happen?
b (x,t) decays as
b (x,t) ~e (-+a0)
t
- B change:b.(x,t) = (-+a0)b(x,t) < 0
The naive lore:
e.g. reaction-diffusion (Partial) differential equations=>
- A density a(x,t) ao
- B reproduction rate a0
- B death rate
Angels and Mortals by my students
Eldad Bettelheim and Benny Lehmann
-On a large enough 2 dimensional surface, the B population always grows!
, Db, < a(x,t) >, etc !
- In higher dimensions, /Da > 1-Pd
always suffices
one can prove rigorously (RG flow, Branching Random Walks Theorems)
that:
New theorem: for A death rate a : Da + a
suffices !
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Emergence of Adaptive B islands
Example: single A
a0=1/V-
+a0-
Diffusion in fact helps
e ( - ) t =e
t e - t
A
A
B diffusion
A
A A
A
A
AAA
AAA
B diffusion
AAA
AA AA
Growth stops again when A jumps again
AA AAA
A AA A A
A AA A A
Emergent Collective Dynamics:B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density.
A AA A A
This is in apparent contradiction to the “fundamental laws” where
individual B don’t follow anybody
Emergent Collective Dynamics:B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density.
Emergent Collective Dynamics:B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density. This is in apparent contradiction to
the “fundamental laws” where individual B don’t follow anybody
The strict adherence of the elementary particles A and B to the
basic fundamental laws and the emergence of complex adaptive entities with self-serving behavior do not interfere one with another.Yet they determine one another.
Emergent Collective Dynamics:B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density.
Is this a mystery? Not in the AB model where all is on the table !
This is in apparent contradiction to the “fundamental laws” where
individual B don’t follow anybody
Collaborations that identified and studied
systems
in biology, finance and social sciences that
•are naively non-viable (decay to extinction) when viewed macroscopically
•but perfectly viable in reality
•(and when simulated / analyzed correctly at the
microscopic individual level).
- spatial patches = first self-sustaining proto-cells.even with very low protein density and very low reproduction capability and very unstable structure, self–copying DNA would have survived if earth was large enough!
Interpretations in Various Fields:
- individuals =chemical molecules,
Origins of Life:
Genetic Evolution: - Sites: various genomic configurations. - B= individuals; Jumps of B= mutations. - A= advantaged niches - emergent adaptive patches= specieswhy are there not a continuum of creatures between snails and salamanders (both are partenogenetic).
Ordinary miracles Michael Brooks, New Scientist magazine, May 2000<< According to John Beringer, an expert on microbial biology at the University of Bristol:
"Microbes that need oxygen will be found close to the surface of soil, and microbes that are very fastidious about oxygen concentration will be found in bands at the appropriate oxygen concentration."
Microbes concentrating on a two-dimensional resource may have been more successful than their cousins who tried exploiting a three-dimensional feast.>>
Immune system: - B cells; A antigencognitive immunology : acquiring immunity by
learning antigen classes (patches)
B cells that meet antigen with complementary shape multiply. (later in detail the AIDS analysis)
New strains appear and are destroyed within weeks.
Many new small strains accumulate and destroy many immune system cells. The system collapses
The strains of the first invasion are completely wiped out
REALITY
SIMULATION
Desert / Vegetation: - B = plants,
- A= water / light / nutrients- patches- patterns, stripes, oasesDesert <-> Patchy <-> Full cover
(contact to Judean Desert-Jerusalem mountains studies) ; Reclaim; PRL 90, 38101 (2003)
s
Measurements of organic matter distribution (Lavee and Sarah)
Mediterranean; uniform 500mm
Semi-arid; patchy
Desert; uniform
200mm
Finance/Economics:- sites: investment instruments / strategies B = capital units, investors, shares, companies A= profit opportunities / strategies, market, customers
patches= “herds”, rallies, booms, crashes power laws, Levy stable distributions, clustered volatility, deviations from B-S
Polish spatial economic map since 89 (Andrzej Nowak ).
Polish spatial economic map since 89 (Andrzej Nowak ).
Polish spatial economic map since 89 (Andrzej Nowak ).
Stock market shock explained
Physicists model recent trading frenzy. 1 October 2002
Market makersMarket 'spikes' are seen by traders as freak events.
Physicists expect them, Thursday October 3, 2002
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Spatial fluctuations of b between different sitesTime fluctuations
in the total b
Exponent of distributionof individual wealth= (Prediction)Exponent of distribution of market fluctuations
M. Levy S.S
WWW DATA
WWW MODEL
GENETIC NETWORK MODEL Proteomics data
Genetic model
NODE DEGRE vs AGE
AGE