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  

9 9.5 10 10.5 11 11.53750

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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