introduction to complex systems

@anxosan

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

@anxosan

¿What are complex systems?

@anxosan

❖ Many interacting components / agents

@anxosan

❖ Many interacting components / agents❖ Emergent collective behavior

@anxosan

❖ 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)

@anxosan

❖ 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

@anxosan

(Physics Nobel Laureate) Phil Anderson, 1972

“More is different” (emergence)

@anxosan

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

@anxosan

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

@anxosan

which have emergent behavior (e.g. life)

@anxosan

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

@anxosan

MICRO: the relevant elementary agents

INTER: their basic, simple interactions

MACRO: the emerging collective objects

Complex Systems Paradigm:

@anxosan

MICRO: the relevant elementary agents

INTER: their basic, simple interactions

MACRO: the emerging collective objects

orders, transactions

traders

herds,crashes,booms

Economy:

@anxosan

Intrinsically (3x) interdisciplinary:

❖ MICRO belongs to one science

❖ MACRO to another science

❖ Mechanisms: a third science

@anxosan

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:

@anxosan

“More is different” (fluctuations)

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

@anxosan

“More is different” (fluctuaciones)

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

@anxosan

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

@anxosan

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

@anxosan

Water level vs. temperature

“More is different” (phase transition)

@anxosan

? Extrapolation?

@anxosan

Macroscopic linear extrapolation breaks down!

? Extrapolation?

@anxosan

Macroscopic linear extrapolation breaks down!

? Extrapolation?

(a single molecule

does not boil)Water level vs. temperature

@anxosan

Water level: economic index

@anxosan

95 97 99

@anxosan

95 97 99 101

Crash = result of collective behavior of

individual traders

@anxosan

Statistical Mechanics Phase Transition

@anxosan

Atoms,Molecules

Drops,Bubbles

Complexity MICRO

MACRO More is different

Anderson abstractization

@anxosan

Atoms,Molecules

Drops,Bubbles

Complexity MICRO

BiologySocial Science

Brain Science Economics and Finance

Business Administration ICT

Semiotics and Ontology

@anxosan

Atoms,Molecules

Drops,Bubbles

Complexity MICRO

Chemicals

E-pages

Neurons

Wordspeople

Customers

Traders

Cells,lifeMeaning

Social groups

Cognition, perception

Markets

Herds, Crashes

@anxosan

Atoms,Molecules

Drops,Bubbles

Complexity MICRO

Chemicals

E-pages

Neurons

Wordspeople

Customers

Traders

Cells,lifeMeaning

Social groups

Markets

Herds, Crashes

@anxosan

Atoms,Molecules

Drops,Bubbles

Complexity MICRO

Chemicals

E-pages

Neurons

Wordspeople

Customers

Traders

Cells,lifeMeaning

Social groups

Markets

Herds, Crashes

“More is different” (frontier science)

Chemicals

Ion channels

Neurons

Thoughts

Economy, Culture, Social groups

Chemicals

Ion channels

Neurons

Thoughts

Conceptual boundary between disciplines

Chemicals

Ion channels

Neurons

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

@anxosan

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

@anxosan

“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

@anxosan

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

@anxosan

Institutions in Spain

@anxosan

Asociación para el estudio de Sistemas Complejos Sociotecnológicos (COMSOTEC)

@anxosan

Complexitat.cat

@anxosan

Asociación Madrileña de Ciencias de la Complejidad (ComplejiMad)

@anxosan

Foundations

@anxosan

Foundations

❖ Statistical Mechanics (Boltzmann, Gibbs, 1900)

@anxosan

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)

@anxosan

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)

@anxosan

Cross-disciplinary (frontier) science

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

@anxosan

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

@anxosan

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

@anxosan

E. Moro, Leganés (2006)

@anxosan

E. Moro, Leganés (2006)

@anxosan

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

@anxosan

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

@anxosan

M. San Miguel, Palma de Mallorca (2005)

@anxosan

M. San Miguel, Palma de Mallorca (2005)

@anxosan

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

@anxosan

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

@anxosan

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

@anxosan

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

@anxosan

Innovation between Science and Technology

@anxosan

❖ Bottom-up approximation

@anxosan

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

@anxosan

❖ 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

@anxosan

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

@anxosan

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

@anxosan

Mathematics

@anxosan

Mathematics

❖ Graph theory (Complex networks)

@anxosan

Mathematics

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

@anxosan

Mathematics

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

@anxosan

Mathematics

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

@anxosan

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

@anxosan

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”

@anxosan

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)

@anxosan

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

@anxosan

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

@anxosan

Applications

@anxosan

Applications

@anxosan

Applications

@anxosan

Applications

@anxosan

Applications

@anxosan

Applications

@anxosan

The Sicomoro course

@anxosan

The Sicomoro course

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

@anxosan

The Sicomoro course

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

@anxosan

The Sicomoro course

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

@anxosan

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)

@anxosan

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)

@anxosan

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)

@anxosan

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)

@anxosan

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)

@anxosan

Examples

@anxosan

Examples

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

@anxosan

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?

@anxosan

• Important problem

Examples: Traffic

@anxosan

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

❖10% asphalt land (Netherlands)

❖ Billions of lost hours (Spain)

Examples: Traffic

@anxosan

❖ Billions of euros in gas (Europe)

• Difficult solution

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

Examples: Traffic

@anxosan

❖ 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

@anxosan

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

@anxosan

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)

@anxosan

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

4. Motion

Parallel updating (important)

@anxosan

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

4. Motion

Parallel updating (important)

@anxosan

Empirical findings: “Fundamental diagram”

@anxosan

Empirical findings: Phantom jams

@anxosan

Simulation results: Good agreement

@anxosan

What can be inferred?

@anxosan

• 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”

@anxosan

BML Automata (Biham, Middleton & Levine, 1992)

• Traffic lights even instants

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

City traffic: 2D models

@anxosan

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

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

@anxosan

Main result: Phase diagram

@anxosan

• 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

@anxosan

Generalization: particle flow

@anxosan

Generalization: particle flow

@anxosan

Examples: Opinion formation

Question: How can the minority win?

@anxosan

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

@anxosan

Social inertia: Ties favor the “no” option

@anxosan

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

@anxosan

(Taken from Maxi San Miguel, IFISC, Mallorca)

@anxosan

(Taken from Maxi San Miguel, IFISC, Mallorca)

@anxosan

S. Galam: Le Monde, 26 February, 2005

@anxosan

S. Galam: Le Monde, 26 February, 2005

@anxosan

Binary opinion, either yellow or blue, about reform

Galam´s model

@anxosan

For Against

Galam´s model

@anxosan

For Against

Initially, there is a blue minority

Galam´s model

@anxosan

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

Galam´s model

@anxosan

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

@anxosan

Galam´s modelInteraction: Majority convinces minority in a cell

@anxosan

Every agent becomes yellow

@anxosan

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

@anxosan

Galam´s modelEvolution: Random reshuffling in cells

@anxosan

Phase diagram: Initial minority vs max cell size

p: initial minority population

Threshold

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

Galam´s model

M: max

cell size

@anxosan

• 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

@anxosan

By way of conclusion

@anxosan

❖ Complexity Science is here to stay

@anxosan

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

(cf. Examples)

@anxosan

(cf. Examples)❖ Key concept: Emergence

@anxosan

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

Mathematics and Computation

@anxosan

Mathematics and Computation❖ Requires working and thinking about frontiers

@anxosan

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

introduction to complex systems

Education

1. introduction 2. a complex systems sampler 3...

complex lives complex needs complex service systems...

introduction to and measurement of complexity frst 532c –...

what makes complex systems complex?

the analysis of complex tonal systems: motivations,...

academic course: 04 introduction to complex systems and...

introduction to bioinformatics - indiana university...

modeling of complex systems and environments july 17th, 2007...

statistical physics of complex networks · i. introduction:...

simulating complex systems - complex system theories

investing in complex systems regulated infrastructure by dr...

river basins: water and complex adaptive systems · river...

an introduction to complex systems science - unibo.it ·...

advanced design for complex systems - 중앙대학교...

introduction to bioinformatics · 1 introduction to...

1. introduction 2. a complex systems...

introduction to complex systems and social network analysis

evolution of complex systems lecture 1: introduction peter...

complex social systems - lecture 5 in introduction to...

an introduction to intelligent transportation systems 1 ·...