Complexity Research; Why and How

Complexity Research; Why and How

Sorin Solomon Racah Institute of Physics HUJ Israel

Director, Complex Multi-Agent Systems Division, ISI TurinDirector, Lagrange Interdisciplinary Laboratory

for Excellence In Complexity

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


Racah Institute of Physics HUJ Israel and

Director of the Complex Multi-Agent Systems Division, ISI Turin


Complex “Macroscopic” properties may be the collective effect of many simple “microscopic” components


Lagrange Laboratory for Excellence In Complexity at ISI Torino support for students and researchersGeneral Integration Action in Complexity Science + 12 Specific Targeted Research Projects in Complexity (CO3)

The Multi-Agent Complex Systems Paradigm

MICRO - the relevant microscopic degrees of freedom

INTER - their fundamental interactions

MACRO - the macroscopic emerging collective objectsIntrinsically (3x) interdisciplinary:

-MICRO belongs to one science

-MACRO to another science

-Mechanisms: statistical mechanics (?) phase transitions, scale invariance,

The challenge : transcend traditional disciplinary research Complexity Research: More than a juxtaposition of expertises:

a new grammar with new interrogative forms allowing the formulation of new questions. Grow a new generation of bi- or multi-lingual scientists.

“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, physicsmath, game theory, info


Racah Institute of Physics HUJ Israel Complex Multi-Agent Systems Division, ISI Turin

Lagrange Interdisciplinary Lab for Excellence In Complexity


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’. we need to free ourselves from ‘average’ thinking.”

950C

1Kg

1cm

97

1cm

1Kg

99

1Kg

101

The breaking of macroscopic linear extrapolation

?Extrapolation?

BOILING PHASE TRANSITIONMore is different: a single molecule does not boil at 100C0

Simplest Example of a “More is Different” Transition

Water level vs. temperature

95 97 99 101

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

Chemicals almost free particles

DNA chains, proteins reproduction,evolution,synthesis

Cells chemotaxis, metabolism

Systems, Organisms health, perception self-non-self recognition

CONCEPTUAL AND DISCIPLINARY JUMPS

of the

MORE IS DIFFERENT

type

Statistical Mechanics

Phase Transition

Atoms,Molecules

Drops,Bubbles

Anderson abstractization

Complexity MICRO

MACRO More is different

BiologySocial Science

Brain ScienceEconomics and

Finance

BusinessAdministration ICT

Semiotics and Ontology

Chemicals

E-pages

Neurons

Words

people

Customers

Traders

Cells,lifeMeaning

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 1895-1930

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



VCR

Extrapolation

Actual sales

Product Propagation

BASS

VCR

SALES



VCR

Extrapolation

Actual sales

Also Belief Propagation

Reality curves

DVD

VCR

CARS in USA 1895-1930

Extrapolation

Product Propagation



Actual sales

Also Belief Propagation

- Microscopic Customers and Macroscopic Sales

MICRO – Customers, products / ideas / information

INTER – purchase, inform, learn, hear-say

MACRO – global trends, waves of sales (e.g. Tamaguchi), hits, flops, market fluctuations, anomalous diffusion

demarketing

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

PotentialAdopters

RejectorsThe Square Lattice is

just for clarityThe 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 %

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%

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 0%adoption55%

60%

59.3

Theorem

55%density

61%

Potential Adopters

Adopters fraction

0% salesPercolation transition

infin

itely

sha

rp

at in

finite

siz

e

Fractal Sales: Prediction Tool for product success (15/17)

fractal space distributionPrediction of campaign success (15/17) Goldenberg

Air-view of a sub-urban neighborhood;

crosses on the roofs indicate air-conditioner purchase

Stock market shock explainedPhysicists 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

http://www.nature.com/


Stock market shock explainedPhysicists 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

Percolation transition

From non-sales at all to a lot of sales

Infinitely sharp at infinite size system

ALSO: effects of

Expectations Adaptation

Self tunning to criticality

Fractal fluctuations

and correlations

ALSO: effects of

Expectations Adaptation

Fractal space-time fluctuationsProduct Success prediction (15/ 17)

Resistance

Resistance

Resistance

Resistance

“ANTI-Percolation”

Antivirus

Figure 1 Comparing infection process evolution with (bottom) and without (top)immunization edges. On the top the network is being infected fully by the virus. Onthe bottom the virus cluster is reduced by more than half by introducing immunization edges. The blue (dark green) edges represent the original network (further immunization) edges. During the spread, an edge is coloured in red (turquoise) if it was used to infect (immunize) a node. In both cases we present foursnapshots of each network in different times. In addition, we present the time (t )varying graphs for the cluster development over time.

The blue, red and green lines are used to present the size of the susceptible, infected and immunized clusters,respectively. Note that in the bottom set, initially in snapshots 1 and 2, the virus cluster develops uninterruptedly until the immunization agent manages to escape the border of the virus cluster, in snapshot 3, and start immunizing the network; therefore the agent manages to immunize most of the network even though the virus had a head start.

Figure 2 Relative virus cluster size as a function of immunization link density(log–log scale). The dependence of the relative infected cluster size on the relative edge addition q, resulting from simulations over uncorrelated, scale-free networks with power exponent −3, mean degree 4 and network size 50,000–200,000 nodes. The ratio dependence shows a power-law form, with an exponent close to −4/3. The error bars present the 95% confidence interval.

Figure 5 Comparison of virus cluster sizes for the random-edge and thehoney-pot architectures. The different sets present different relative edge additions, q. The clusters in the random case are always larger than the clusters in the honey-pot case; as the network size grows, so does the gap between the two architectures. The reason behind this is that, whereas in the random case the cluster size remains fairly constant as we vary the network size, in the honey-pot case as the network grows, so does the effectiveness of the honey pots. This effect is mostly noted in the middle range of the density values where the immunization has an effect but the virus cluster is not extremely small. The error bars present the 95% confidence interval. show a power-law ratio dependence

Figure 6 The dependence of the virus cluster on the degree distribution powerexponent. We ran a sensitivity analysis where we varied the power exponent of thePareto degree distribution characterizing the underlying topology between 1.8 and 3,which includes all degree distributions found in real scale-free networks. As can be

seen, the effectiveness of the immunization process grows with the powerexponent, owing to the fact that lower exponents entail a higher density of edges,

which allows the virus to advance faster. However, this variation is still minorcompared with variations in the relative edge addition, q, and in the architecturetype, which are illustrated by the different data sets presented. The error bars

present the 95% confidence interval. HP = honey pot.

Parallel Networks

Consumption;

home

Expectations

work

- Microscopic Investors and Macroscopic Crashes /Power Laws

MICRO - Investors, individual capital ,shares

INTER - sell/buy orders, gain/loss

MACRO - social wealth distribution, market price fluctuations (cycles, crushes, booms, stabilization by noise)

-Microscopic Concepts and Macroscopic Ideas

MICRO - concepts, connections between concepts

INTER - creating/deleting/activating connections between concepts

- Microscopic Seers and Macroscopic Sight

MICRO - motion visual sensors for points and line elements.

INTER - time and space local data integration.

MACRO - Perception of 3 Dimensional global structure.

- Microscopic Picassos and Macroscopic Drawings

MICRO - local line / motion features, mental states, mental eventsINTER - line breaks and mind events(changes) vs line/mind inertia.MACRO - drawing shapes, emergence of representational meaning - Microscopic Doctors and Macroscopic Health

MICRO - Cells, Enzimes, Antigens, Antibodies INTER - producing, destroying, changing state of a cell/enzime, MACRO - immunity, health, infection, sickness, inflamation. -Microscopic Drivers / police and Macroscopic Jams

MICRO - carsINTER - go ahead/give way at intersections.MACRO - traffic flow, jamming; self-organization; useless police

Microscopic Grimm Brothers and Macroscopic Stories

MICRO – persons, relationsINTER – change in relations ; actingMACRO –plot, story, meaning

Internet study along the same lines1. physical,2. information flow and 3. emergent / cognitive.

LAYERS

Micro Macro

1. Cognitive / Social Layer Self-Organization

Content based servicerelationships, ringsPeer-To-Peer nets

Emergence of Collective

Complex Institutions with personality and

interests

2. WEB Information Layer

Sites, links, information storage and flow

Distributed Information

storage, processing retrieval, control, trust

3.INTERNETHardware Layer

Nodes, cables, data packets

Connectivity, robustness

• We exemplify this by studying two types of networks: Genetic networks and the World Wide Web. In the first case we formulate a model including only random unbiased gene duplications and mutations. In the second case, the basic moves are website generation and rapid surf-induced link creation (/ destruction). In both cases we do reproduce the experimental observations at all scales.

• For the genetic network our model predicts a slow convergence toward a directed structure composed roughly of a core directing toward a periphery. By contrast, the WWW presents rapidly changing non-stationary bi-directionally linked clusters.

• In the genetic case the rough picture outside the core is of a tree-like structure with arrows preferentially directed towards the branches. In the WWW case, the hierarchy is rather in the form of strongly linked clusters-within clusters and the connections between clusters are generically pointing in both directions.

Louzoun-LevA

B

C

DC

A

36546, Z=46

B

253270, Z=23

826, Z=2.83 442, Z=2.22

browse

link

Gene network

Internet network

Figure 1 - Mechanisms of individual node evolution: the 3 elementary processes defining our genetic model. Their effect is demonstrated on the configuration of the left upper corner (only links and nodes relevant for the explanation are explicitly shown). The effect of a Node copying elementary event is shown in A) . The blue node is “duplicated” by introducing the new brown node that has the same targets for its out-going links (and no incoming links at all). The Node removal is illustrated in B). The green node and all its links are deleted. The drawing C) illustrates the elementary operation of Link Mutation: the pink link is “copied”. i.e. a new link with the same origin but different target is created . These 3 elementary operations turn out to be sufficient for the formation of a steady state directional hierarchical scale free network, with the experimentally observed sub-motif distribution.

Microscopic Links, Macroscopic NetworksMICRO – Nodes, connections INTERACTIONS - Local changes (node / link (dis-) appearance)MACRO- Global connectivity, percolation, topologyNew generation of network studies:Instead of study generic properties that are not specific to any particular system, Study specific macroscopic collective properties implied by specific elementary interactions..

site links

Copied site /gene

links

site

Transitive link

browse

Gene activation

WWW linking

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

1

2

3

4

5

6

log10

(Number of Nodes)

log 10

(Ran

k)IncomingOutgoing

Figure 2 Node degree distribution in the genetic model- Incoming (empty circles) and outgoing (full squares) link distributions. The outgoing link distribution is normal (as experimentally observed). The incoming link distribution is scale free over more than three orders of magnitude (10-50,000). The straight line corresponds on this double logarithmic graph to a power law with exponent -2.2 (the value actually observed in most genetic networks). Increasing the network size has no effect on the exponent of the power distribution; it only increases its validity range.

Figure 3. Measures of the Small World character of the genetic network. The main graph represents the clustering coefficient (C) as a function of the degree k. The clustering coefficient of the node i, with a degree ki is defined as as Ci = 2ni/ki(ki - 1), where ni denotes the number of direct links connecting its ki nearest neighbors among themselves. Ci is equal to 1 if the neighbors of i are all connected one to the other. A random (Erdos-Renyi) graph would produce a flat very small clustering coefficient. One sees from the graph that the actual distribution, far from being a small constant is fitted by a straight line that represents on the double logarithmic scale a power law with exponent -1 as observed in genetic networks (and in contrast with the preferential attachment dynamics). The fit is excellent with no free parameters. The inset plots the distribution of distances between arbitrary pairs of nodes in the network. A regular one dimensional lattice would produce a distance proportional to the network size (50,000). The combination of a distance of the order of the log of the network size (inset) and the existence of high clustering coefficient are the hallmark of a "small world network".

1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

log10

(Number of nodes)

log 10

(Ran

k)

Nodes rank distribution

IncomingOutgoing

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 40.6

0.65

0.7

0.75

0.8

0.85

log10(Network Size)

log

10(<

d>)

IncomingPower law fitOutgoingPower law fit

Figure 6: Double logarithmic histogram of the nodes rank distribution in the WWW model. Results show a power law for both incoming (empty circles; exponent

2.1+/-0.1) and outgoing links (full squares; exponent 3.1 +/- 0.2). These exponents are in perfect agreement with the experimental data.

The inset shows the average node distance as predicted by the WWW model. The distance grows as the log of the network size, and thus the network is indeed a

small world network in agreement with the experiments.

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.

- map the interdisciplinary cooperation network(- people are nodes - cooperations andcommon 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

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% salesPercolation transition

infin

itely

sha

rp

at in

finite

siz

e

10

1

100Logarithmic scale

Naïve logistic

• Insert LSS book

POSTEXT

Shalit A. Erez T. Deters A. Hershberg U. Shir E. Solomon S.

My papers

I am here

Clusters automatically formed by elastic

connectionsand repelling forces

New (Dynamic, Distributed, Open, Free, Self-Org, Ontology

My papers

I am here

Clusters automatically formed by elastic

connectionsand repelling forces

New (Dynamic, Distributed, Open, Free, Self-Org, Ontology

EMPTY SHELLS

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

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

Realistic macroscopic simulations require a new causal framework:

discrete / delayed/ conditional / nested causality instead of the usual Markov infinitesimal one

TimeTime

New mathematical concept: Markov Webs

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Complexity Research; Why and How

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