Executive Abstract Logistic dynamics has been recognized since 200 years to govern a wide range of social, economic, biological and cognitive systems. In the past the predictions of the logistic equation have been invalidated almost systematically in many occasions. In particular they predicted often falsely the decay of the dynamics in adverse conditions. We show that the correct accounting for the discrete character of the elementary components of the system leads to dramatically different predictions: –In particular the emergence of adaptive collective objects that insure survival and development in conditions in which the naïve continuous/ global treatment would predict complete and uniform decay. –The emergence of stable Pareto-Zipf power laws even in very non-stationary conditions. We review a series of applications, predictions and their validation.

Complexity Sorin Solomon, Racah Institute of Physics HUJ Israel Director, Complex Multi-Agent Systems Division, ISI Turin MORE IS DIFFERENT (Anderson 72) (more is more than more) Complex “Macroscopic” properties are often the collective effect of many simple “microscopic” components (and independent on their details) Director, Lagrange Interdisciplinary Lab for Excellence In Complexity 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.

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. Once taken in account => complex adaptive collective objects. emerge even in the worse conditions

“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 orders, transactions herds,crashes,booms Decision making, psychology Financial economics statistical mechanics, physics math, game theory, info

95 0 C 1Kg 1cm 97 1cm 1Kg 99 1Kg 101 The breaking of macroscopic linear extrapolation ? Extrapolation? BOILING PHASE TRANSITION More is different: a single molecule does not boil at 100C 0 Simplest Example of a “More is Different” Transition Water level vs. temperature

Example of “MORE IS DIFFERENT” transition in Finance: Instead of Water Level: -economic index (Dow-Jones etc…) Crash = result of collective behavior of individual traders

Statistical Mechanics Phase Transition Atoms,Molecules Drops,Bubbles Anderson abstractization Complexity MICRO MACRO More is different Biology Social Science Brain Science Economics and Finance Business Administration ICT Semiotics and Ontology Chemicals E-pages Neurons Words people Customers Traders Cells,life Meaning Social groups WWW Cognition, perception Markets Herds, Crashes

Instead of temperature (energy / matter): Exchange rate/ interest rate Value At Risk / liquid funds Equity Price / Dividends Equity Price / fundamental value Taxation (without representation)/ Tea

Reality curves DVD VCR CARS in USA Product Propagation Bass extrapolation formula vs microscopic representation Actual sales Extrapolation

Microscopic view of a water drop: a network of linked water molecules

The water drop becomes vapors: the network splits in small clusters

Boiling is not a physical property of particular molecules but a generic property of the cluster geometry To understand, one does not need the details of the interactions. Rather one can prove theorems on what is the density of links that ensures the emergence or disintegration of clusters Phase Transition

Product Propagation BASS VCR SALES Bass extrapolation formula vs microscopic representation VCR Extrapolation Actual sales

Product Propagation BASS VCR SALES Bass extrapolation formula vs microscopic representation VCR Extrapolation Actual sales Also Belief Propagation

Reality curves DVD VCR CARS in USA Extrapolation Product Propagation Bass extrapolation formula vs microscopic representation Actual sales Also Belief Propagation

Propagation effects: - product propagation - spread of ideas - epidemics - Internet viruses - Social ills: drugs, violence, terror - Credit networks and bankruptcy avalanches - production / trade practices - real estate valuation - tax paying habits

Potential Adopters Rejectors The Square Lattice is just for clarity The effects demonstrated are much more general

Density of potential adopters: 26/48>50% What Percent will actually adopt?

The Buyers are split in small clusters

The epidemics, bankruptcy avalanche, idea, product spread is limited to one cluster

Density of potential adopters: 26/48>50% What Percent will actually adopt? 7/48 < 15 %

Only 15 % will actually adopt! But what if add one more potential adopter?

If adds one more potential adopter 22 out of 27 potential adopters adopt 22/48~46%

Adopters Density 55% This is not just a fortuitous case; for larger systems the effect is even more dramatic

55%

If lowering the price, or increasing quality, or decreasing taxes or subsidizing adopters (or affecting credit rate) etc one gains 5% more potential adopters Then density of potential adopters = 60% How much will this increase the actual adoption?

55%

60%55%

60%55%

60%55%

60% potential adopters 55% potential adopters

60% potential adopters 55% potential adopters 0%adoption 55% 60% 59.3 Theorem

55% density 61% Potential Adopters Adopters fraction 0% sales Percolation transition infinitely sharp at infinite size Fractal Sales: Prediction Tool for product success (15/17)

fractal space distribution Prediction of campaign success (15/17) Goldenberg Air-view of a sub-urban neighborhood; crosses on the roofs indicate air-conditioner purchase

Stock market shock explained Physicists model recent trading frenzy. Market 'spikes' are seen by traders as freak events. Physicists expect them Small changes in product quality, price, external conditions can produce large effects (e.g. large market fluctuations) Small deterioration in credit market can trigger large waves of bankruptcies

Stock market shock explained Physicists model recent trading frenzy. Market 'spikes' are seen by traders as freak events. Physicists expect them Lev Muchnik Phys. Scripta

“ Levy, Solomon and Levy's Microscopic Simulation of Financial Markets points us towards the future of financial economics. If we restrict ourselves to models which can be solved analytically, we will be modeling for our mutual entertainment, not to maximize explanatory or predictive power." --HARRY M. MARKOWITZ, Nobel Laureate in Economics

-emergence of High-Tech communities -start-ups connections to previous businesses -entrepreneurs emerging from old businesses -partners having previous common institutions

- map the interdisciplinary cooperation network (- people are nodes - cooperations and common papers, are links). - give priority to people with high interdisciplinarity rather then high rank / disciplinary authority Discipline 2 Discipline 1 Subjects that need synthesis Objective Algorithm to Evaluate Interdisciplinary researchers relevance Discipline3

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This was a Particular case of Logistics dynamics (with Corrections!!); Other : technological change; innovations diffusion (Rogers) new product diffusion / market penetration (Bass) social change diffusion X = number of people that have already adopted the change and N -X = number of remaining customers dX/dt ~ X(N – X ) Potential Adopters Adopters 0% sales Percolation transition infinitely sharp at infinite size Logarithmic scale Naïve logistic