introduction to complex systems

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Anxo Sánchez

Grupo Interdisciplinar de Sistemas Complejos Departamento de Matemáticas

Institute UC3M-BS for Financial Big Data (IFiBiD) Universidad Carlos III de Madrid

Instituto de Biocomputación y Física de Sistemas Complejos (BIFI) Universidad de Zaragoza

Introduction to complex systems

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¿What are complex systems?

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❖ Many interacting components / agents

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❖ Many interacting components / agents❖ Emergent collective behavior

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❖ Many interacting components / agents❖ Emergent collective behavior❖ Examples:

❖ Water (molecules vs phases) (more later) ❖ Proteins (aminoacids vs molecule / structure) ❖ Brain (neurons vs intelligence) ❖ Society (people vs institutions /norms) ❖ Biosphere (species vs ecosystem) (more later)

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❖ Many interacting components / agents❖ Emergent collective behavior❖ Examples:

❖ Water (molecules vs phases) (more later) ❖ Proteins (aminoacids vs molecule / structure) ❖ Brain (neurons vs intelligence) ❖ Society (people vs institutions /norms) ❖ Biosphere (species vs ecosystem) (more later)

❖ Frontier between sciences or subjects

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(Physics Nobel Laureate) Phil Anderson, 1972

“More is different” (emergence)

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When there are MORE than one simple agent (e.g. molecule)



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those agents may self-organize in collective objects (e.g. cells)



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which have emergent behavior (e.g. life)



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which have emergent behavior (e.g. life) that IS DIFFERENT from the behavior of the simple agent (e.g. chemical reactions)



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MICRO: the relevant elementary agents

INTER: their basic, simple interactions

MACRO: the emerging collective objects


Complex Systems Paradigm:

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MICRO: the relevant elementary agents

INTER: their basic, simple interactions

MACRO: the emerging collective objects

orders, transactions



traders

herds,crashes,booms

Economy:

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Intrinsically (3x) interdisciplinary:

❖ MICRO belongs to one science

❖ MACRO to another science

❖ Mechanisms: a third science



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Intrinsically (3x) interdisciplinary:

❖ MICRO belongs to one science

❖ MACRO to another science

❖ Mechanisms: a third science

Decision making, psychology

Financial economics

Statistical mechanics, PhysicsMathematics


Complex Systems Paradigm: Economy:

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“More is different” (fluctuations)

• Role of fluctuations: many, but not infinite, agents / interactions

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“More is different” (fluctuaciones)

• Role of fluctuations: many, but not infinite, agents / interactions• Nonlinear systems with instabilities

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• Role of fluctuations: many, but not infinite, agents / interactions• Nonlinear systems with instabilities • External influences: noise, disorder

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• Role of fluctuations: many, but not infinite, agents / interactions• Nonlinear systems with instabilities • External influences: noise, disorder• Creative effects, e.g., stochastic resonance

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950C

1Kg

1cm

Water level vs. temperature

“More is different” (phase transition)

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950C

1Kg

1cm

970C

1cm

1Kg



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950C

1Kg

1cm

970C

1cm

1Kg

990C

1Kg



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950C

1Kg

1cm

970C

1cm

1Kg

990C

1Kg

? Extrapolation?



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950C

1Kg

1cm

970C

1cm

1Kg

990C

1Kg

1010C

Macroscopic linear extrapolation breaks down!

? Extrapolation?



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950C

1Kg

1cm

970C

1cm

1Kg

990C

1Kg

1010C

Macroscopic linear extrapolation breaks down!

? Extrapolation?

(a single molecule

does not boil)Water level vs. temperature


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Water level: economic index

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95 97 99



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95 97 99 101

Crash = result of collective behavior of

individual traders



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Statistical Mechanics Phase Transition

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Atoms,Molecules

Drops,Bubbles

Complexity MICRO

MACRO More is different

Anderson abstractization

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Atoms,Molecules

Drops,Bubbles

Complexity MICRO


BiologySocial Science

Brain Science Economics and Finance

Business Administration ICT

Semiotics and Ontology


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Atoms,Molecules

Drops,Bubbles

Complexity MICRO


BiologySocial Science

Brain Science Economics and Finance

Business Administration ICT

Semiotics and Ontology

Chemicals

E-pages

Neurons

Wordspeople

Customers

Traders

Cells,lifeMeaning

Social groups

WWW

Cognition, perception

Markets

Herds, Crashes


“More is different” (frontier science)

Chemicals

Ion channels

Neurons

Brain

Thoughts

Economy, Culture, Social groups


Chemicals

Ion channels

Neurons

Brain

Thoughts



Conceptual boundary between disciplines

Chemicals

Ion channels

Neurons

Brain

Thoughts


It helps to bridge them by addressing within a common conceptual framework the fundamental problems of one of them in terms of the collective phenomena of another.


Conceptual boundary between disciplines

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Santa Fe Institute for Complex Systems “... a private, non-profit, multidisciplinary research and education center”

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“Since its founding in 1984, the Santa Fe Institute (SFI) has devoted itself to fostering a multidisciplinary scientific research community pursuing frontier science. SFI seeks to catalyze new research activities and serve as an "institute without walls.” Topics • Physics and Computation of Complex Systems • Human Behavior, Institutions and Social Systems • Living Systems: Emergence, Hierarchy and Dynamics

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Research projects

• A theory of invention and innovation • Theory of embodied intelligence • Biology, behavior, and disease • Social networks, big data, and physics-powered inference • Information, thermodynamics, and the evolution of complexity in biological systems • Neighborhoods, slums, & human development • Emergence of complex societies • Hidden laws in biological and social systems • Evolution of complexity on earth • Cities, scaling, & sustainability

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Institutions in Spain

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Asociación para el estudio de Sistemas Complejos Sociotecnológicos (COMSOTEC)

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Complexitat.cat

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Asociación Madrileña de Ciencias de la Complejidad (ComplejiMad)

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Foundations

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Foundations

❖ Statistical Mechanics (Boltzmann, Gibbs, 1900)

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Foundations

❖ Statistical Mechanics (Boltzmann, Gibbs, 1900)❖ Nonlinear Science

❖ Chaos (Lorenz, 1963) ❖ Coherents Structures (Fermi, Pasta y Ulam, 1955) ❖ Patterns (Bénard, 1900; Belusov, 1951; Winfree, 1967) ❖ Evolutionary Dynamics (Maynard-Smith, 1974)

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Foundations

❖ Statistical Mechanics (Boltzmann, Gibbs, 1900)❖ Nonlinear Science

❖ Chaos (Lorenz, 1963) ❖ Coherents Structures (Fermi, Pasta y Ulam, 1955) ❖ Patterns (Bénard, 1900; Belusov, 1951; Winfree, 1967) ❖ Evolutionary Dynamics (Maynard-Smith, 1974)

❖ Computation (1990)

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Cross-disciplinary (frontier) science

❖ Physics ❖ Statistical and nonlinear physics ❖Nanotechnology, quantum computation, astronomy,…

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J. Muñoz, R. Cuerno & M. Castro (2006)


❖ Physics ❖ Statistical and nonlinear physics ❖Nanotechnology, quantum computation, astronomy,…

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❖Economy ❖Micro vs macro, financial markets, management, …


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E. Moro, Leganés (2006)



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E. Moro, Leganés (2006) P. Richmond, Dublin (2006)



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❖Sociology ❖Norms and institutions, cultural dynamics, cooperation,…


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M. San Miguel, Palma de Mallorca (2005)



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A. Arenas, Tarragona (2002)M. San Miguel, Palma de Mallorca (2005)



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❖ Biology ❖ Ecology, inmune system, genetic networks, biofilms, …


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❖ Biology ❖ Ecology, inmune system, genetic networks, biofilms, ……

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Innovation between Science and Technology

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❖ Bottom-up approximation

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❖ Bottom-up approximation❖ Robust, self-organized systems

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❖ Bottom-up approximation❖ Robust, self-organized systems❖ Control of complex systems

❖ Internet ❖ Agent-based software ❖ Design of organization ❖ Risks: spam, SIDA/SARS/Avian flu ❖ New drugs / genetic therapy

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❖ Basis for new technologies (ICT, transport, …)

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❖ Basis for new technologies (ICT, transport, …)❖ ¿A paradigm shift?

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Mathematics

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Mathematics

❖ Graph theory (Complex networks)

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory ❖ Evolutionary dynamics and game theory

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory ❖ Evolutionary dynamics and game theory❖ A “discrete analysis”

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory ❖ Evolutionary dynamics and game theory❖ A “discrete analysis”❖ New simulation techniques (Agents, OOP)

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory ❖ Evolutionary dynamics and game theory❖ A “discrete analysis”❖ New simulation techniques (Agents, OOP)❖ Computational complexity

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Mathematics

❖ Graph theory (Complex networks)❖ Stochastic processes and statistics (Disorder, noise)❖ Functional analysis (Phase transitions)❖ Control theory and signal theory ❖ Evolutionary dynamics and game theory❖ A “discrete analysis”❖ New simulation techniques (Agents, OOP)❖ Computational complexity❖ Data mining, data analysis

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Applications

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The Sicomoro course

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)❖ Fractals and scale invariance (Bartolo Luque, May 3)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)❖ Fractals and scale invariance (Bartolo Luque, May 3)❖ The game of evolution (José A. Cuesta, May 9)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)❖ Fractals and scale invariance (Bartolo Luque, May 3)❖ The game of evolution (José A. Cuesta, May 9)❖ Genes and human genealogies (Susanna Manrubia, May 9)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)❖ Fractals and scale invariance (Bartolo Luque, May 3)❖ The game of evolution (José A. Cuesta, May 9)❖ Genes and human genealogies (Susanna Manrubia, May 9)❖ Complex networks (Javier Galeano, May 17)

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The Sicomoro course

❖ Intro (this lecture, not over yet, examples coming)❖ Sociophysics❖ Econophysics (Bartolo Luque, May 3)❖ Fractals and scale invariance (Bartolo Luque, May 3)❖ The game of evolution (José A. Cuesta, May 9)❖ Genes and human genealogies (Susanna Manrubia, May 9)❖ Complex networks (Javier Galeano, May 17)❖ Complexity in biology (Ester Lázaro, May 17)

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Examples

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Examples

❖ Traffic • Question 1: How are jams formed in highways? • Question 2: How are jams formed in cities?

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Examples

❖ Traffic • Question 1: How are jams formed in highways? • Question 2: How are jams formed in cities?

❖ Opinion formation • Question: How can a minority win?

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• Important problem

Examples: Traffic

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❖ 82% travellers and 53% commercial transport (Germany)

❖10% asphalt land (Netherlands)

❖ Billions of lost hours (Spain)

Examples: Traffic

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❖ Billions of euros in gas (Europe)

• Difficult solution

❖ Wrong traditional answer (new roads don’t fix it)

Examples: Traffic

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❖ Billions of euros in gas (Europe)

• Difficult solution

❖ Wrong traditional answer (new roads don’t fix it)

Wider applicability: other transports, pedestrians, internet,…

Examples: Traffic

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Simulation work needed:❖ Discrete models suited to simulation and amenable to analytics (at least to some extent)❖ Need for predictions: realistic models impossible

❖ Controlled experiments and identification of relevant parameters❖ Monitor global variables

Examples: Traffic

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1. Acceleration: if possible, increase speed by 1; vmax=57.5

2. Braking: slow down to the fastest possible speed

1D Nagel-Schreckenberg model (1992)

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3. Randomization: with probability p, brake (no apparent cause)

4. Motion

Parallel updating (important)


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Empirical findings: “Fundamental diagram”


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Empirical findings: Phantom jams

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Simulation results: Good agreement

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What can be inferred?

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• The NaSch is a good (stylized) description of highway traffic • (Can be extended to more complicated situations/geometries) • Averages are not very relevant • New interesting magnitudes to monitor: “throughput” vs “volatility”


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BML Automata (Biham, Middleton & Levine, 1992)

• Traffic lights even instants

odd instants • No overlap • Parallel update • Periodic B.C.

City traffic: 2D models

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Aleatoriedad: Probabilidad g de giro, g < 0.5 (BML g=0)

g

1-g


CMMS Automata (Cuesta, Martínez, Molera & Sánchez, 1993)

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Main result: Phase diagram

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• The phase transition picture applies to traffic as well as to molecules • Phase diagram similar to water; g similar to temperature • Additional info by analytical means (low density limit, other approaches) • Note interaction through excluded volume


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Generalization: particle flow

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Examples: Opinion formation

Question: How can the minority win?

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Serge Galam has proposed a mechanism, social inertia, that leads to a democratic rejection of social reforms initially favored by the majority



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Social inertia: Ties favor the “no” option



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! Conservative reaction to the risk of change ! Keep the social “statu quo”

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! Conservative reaction to the risk of change ! Keep the social “statu quo”

(Taken from Maxi San Miguel, IFISC, Mallorca)

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S. Galam: Le Monde, 26 February, 2005


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Binary opinion, either yellow or blue, about reform

Galam´s model

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For Against

Galam´s model

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For Against

Initially, there is a blue minority

Galam´s model

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Social life: Discussion in groups (e.g., at work, at the bar, at the church,…)

Galam´s model

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Social life: Discussion in groups (e.g., at work, at the bar, at the church,…)

Example,k=16

M, maximum cell size

Cells defined by their size k

Galam´s model

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Galam´s modelInteraction: Majority convinces minority in a cell

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6

10


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Every agent becomes yellow

6

10


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Galam´s modelSocial inertia: Ties resolved in favor of blue

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8

8

Galam´s modelSocial inertia: Ties resolved in favor of blue

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Galam´s modelEvolution: Random reshuffling in cells

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Phase diagram: Initial minority vs max cell size

p: initial minority population

Threshold

line

Eur. Phys. J. B 39, 535 (2004)

Galam´s model

M: max

cell size

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• There is a threshold value pc<½ such that for p>pc the minority becomes a majority • For the effect to happen far from ½ M needs to be small • Time to consensus T ~ ln N • Note that this is a proposal for a mechanism but not a proof that this mechanism is the correct one • Models can be used to verify or falsify intuitions in social problems

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By way of conclusion

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❖ Complexity Science is here to stay

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❖ Complexity Science is here to stay❖ Relevant to real life problems of different nature

(cf. Examples)

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(cf. Examples)❖ Key concept: Emergence

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(cf. Examples)❖ Key concept: Emergence❖ Involves many sciences, but strongly based on

Mathematics and Computation

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Mathematics and Computation❖ Requires working and thinking about frontiers

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Mathematics and Computation❖ Requires working and thinking about frontiers❖ Key for future R+D+i

introduction to complex systems

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