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 Solomon BIU Shnerb, Louzoun, WARSAW Nowak, Kus PARIS Weisbuch, Vignes, Ballot ROME Miceli, Cozzi PISA Dosi The Importance of Being Discrete; Life Always Wins on the Surface

SAME SYSTEM RealityModels 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 changeNo Rule change EMERGENCE OF RULE CHANGE FROM NO-RULE-CHANGE

eternal agents A, - initial uniform density a(x,t =0 )=a 0 - diffusion coefficient D a - 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 )= b 0 - diffusion rate D b

A Diffusion of A at rate D a

A

A

B Diffusion of B at rate D b

B

B

B A A+B  A+B+B; Birth of new B at rate

A B

ABAB

AB A+B  A+B+B; Birth of new B at rate

AB B A+B  A+B+B; Birth of new B at rate

ABB A+B  A+B+B; Birth of new B at rate

ABB BB A+B  A+B+B; Birth of new B at rate

ABB BB A+B  A+B+B; Birth of new B at rate

B B B  Death of B at rate 

B B B 

B B 

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 (-  + a 0 ) t - B change: b. (x,t) = (-  + a 0 )  b(x,t) < 0 The naive lore: e.g. reaction-diffusion (Partial) differential equations=> - A density a(x,t)  a o - B reproduction rate  a 0 - 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!  , D b,, etc ! - In higher dimensions, / D a > 1-P d always suffices one can prove rigorously (RG flow, Branching Random Walks Theorems) that : New theorem: for A death rate  a :  D a +  a suffices !

A Emergence of Adaptive B islands Example: single A a 0 =1/V  -  +  a 0  -    Diffusion in fact helps e (  -  ) t = e  t e -  t

A

A B diffusion

A

AA

A

A

A AA

A AA

A AA

A A A A Growth stops again when A jumps again

A A A AA

A A AAA

A A AAA Emergent Collective Dynamics: B-islands search, follow, adapt to, and exploit fortuitous fluctuations in A density.

A A AAA 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.

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= species why 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 antigen cognitive 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, oases Desert Patchy Full cover (contact to Judean Desert-Jerusalem mountains studies) ; Reclaim; PRL 90, (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 ).

Stock market shock explained Physicists model recent trading frenzy. 1 October 2002 Market makers Market 'spikes' are seen by traders as freak events. Physicists expect them, Thursday October 3, 2002

Spatial fluctuations of b between different sites  Time fluctuations in the total b Exponent of distribution of 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