Presentación utilizada por Anxo Sanchez (@anxosan) en la primera sesión del Curso de Introducción a los Sistemas Complejos de la Fundacion Sicomoro y ComplejiMad
1. @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
8. @anxosan
When there are MORE
than one simple agent (e.g. molecule)
(Physics Nobel Laureate) Phil Anderson, 1972
“More is different” (emergence)
9. @anxosan
When there are MORE
than one simple agent (e.g. molecule)
those agents may self-organize in collective objects (e.g. cells)
(Physics Nobel Laureate) Phil Anderson, 1972
“More is different” (emergence)
10. @anxosan
When there are MORE
than one simple agent (e.g. molecule)
those agents may self-organize in collective objects (e.g. cells)
which have emergent behavior (e.g. life)
(Physics Nobel Laureate) Phil Anderson, 1972
“More is different” (emergence)
11. @anxosan
When there are MORE
than one simple agent (e.g. molecule)
those agents may self-organize in collective objects (e.g. cells)
which have emergent behavior (e.g. life)
that
IS DIFFERENT
from the behavior of the simple agent (e.g. chemical reactions)
(Physics Nobel Laureate) Phil Anderson, 1972
“More is different” (emergence)
12. @anxosan
MICRO: the relevant elementary agents
INTER: their basic, simple interactions
MACRO: the emerging collective objects
“More is different” (emergence)
Complex Systems Paradigm:
13. @anxosan
MICRO: the relevant elementary agents
INTER: their basic, simple interactions
MACRO: the emerging collective objects
orders, transactions
“More is different” (emergence)
Complex Systems Paradigm:
traders
herds,crashes,booms
Economy:
14. @anxosan
Intrinsically (3x) interdisciplinary:
❖ MICRO belongs to one science
❖ MACRO to another science
❖ Mechanisms: a third science
“More is different” (emergence)
Complex Systems Paradigm:
15. @anxosan
Intrinsically (3x) interdisciplinary:
❖ MICRO belongs to one science
❖ MACRO to another science
❖ Mechanisms: a third science
Decision making, psychology
Financial economics
Statistical mechanics, Physics
Mathematics
“More is different” (emergence)
Complex Systems Paradigm: Economy:
16. @anxosan
“More is different” (fluctuations)
• Role of fluctuations: many, but not infinite,
agents / interactions
17. @anxosan
“More is different” (fluctuations)
• Role of fluctuations: many, but not infinite,
agents / interactions
18. @anxosan
“More is different” (fluctuations)
• Role of fluctuations: many, but not infinite,
agents / interactions
19. @anxosan
“More is different” (fluctuaciones)
• Role of fluctuations: many, but not infinite,
agents / interactions
• Nonlinear systems with instabilities
20. @anxosan
“More is different” (fluctuaciones)
• Role of fluctuations: many, but not infinite,
agents / interactions
• Nonlinear systems with instabilities
• External influences: noise, disorder
21. @anxosan
“More is different” (fluctuaciones)
• Role of fluctuations: many, but not infinite,
agents / interactions
• Nonlinear systems with instabilities
• External influences: noise, disorder
• Creative effects, e.g., stochastic resonance
22. @anxosan
“More is different” (fluctuaciones)
• Role of fluctuations: many, but not infinite,
agents / interactions
• Nonlinear systems with instabilities
• External influences: noise, disorder
• Creative effects, e.g., stochastic resonance
23. @anxosan
“More is different” (fluctuaciones)
• Role of fluctuations: many, but not infinite,
agents / interactions
• Nonlinear systems with instabilities
• External influences: noise, disorder
• Creative effects, e.g., stochastic resonance
32. @anxosan
95 97 99 101
Crash = result of
collective behavior of
individual traders
“More is different” (phase transition)
Water level:
economic index
35. @anxosan
Statistical Mechanics
Phase Transition
Atoms,Molecules
Drops,Bubbles
Complexity
MICRO
MACRO More is
different
Biology
Social Science
Brain Science
Economics and
Finance
Business
AdministrationICT
Semiotics and
Ontology
Anderson abstractization
36. @anxosan
Statistical Mechanics
Phase Transition
Atoms,Molecules
Drops,Bubbles
Complexity
MICRO
MACRO More is
different
Biology
Social Science
Brain Science
Economics and
Finance
Business
AdministrationICT
Semiotics and
Ontology
Chemicals
E-pages
Neurons
Words
people
Customers
Traders
Cells,life
Meaning
Social groups
WWW
Cognition,
perception
Markets
Herds,
Crashes
Anderson abstractization
37. @anxosan
Statistical Mechanics
Phase Transition
Atoms,Molecules
Drops,Bubbles
Complexity
MICRO
MACRO More is
different
Biology
Social Science
Brain Science
Economics and
Finance
Business
AdministrationICT
Semiotics and
Ontology
Chemicals
E-pages
Neurons
Words
people
Customers
Traders
Cells,life
Meaning
Social groups
WWW
Cognition,
perception
Markets
Herds,
Crashes
Anderson abstractization
38. @anxosan
Statistical Mechanics
Phase Transition
Atoms,Molecules
Drops,Bubbles
Complexity
MICRO
MACRO More is
different
Biology
Social Science
Brain Science
Economics and
Finance
Business
AdministrationICT
Semiotics and
Ontology
Chemicals
E-pages
Neurons
Words
people
Customers
Traders
Cells,life
Meaning
Social groups
WWW
Cognition,
perception
Markets
Herds,
Crashes
Anderson abstractization
42. Chemicals
Ion channels
Neurons
Brain
Thoughts
Economy, Culture, Social groups
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.
“More is different” (frontier science)
Conceptual boundary between disciplines
43. @anxosan
Santa Fe Institute for Complex Systems
“... a private, non-profit, multidisciplinary research and education center”
44. @anxosan
Santa Fe Institute for Complex Systems
“... a private, non-profit, multidisciplinary research and education center”
“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
45. @anxosan
Santa Fe Institute for Complex Systems
“... a private, non-profit, multidisciplinary research and education center”
46. @anxosan
Santa Fe Institute for Complex Systems
“... a private, non-profit, multidisciplinary research and education center”
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
70. @anxosan
M. San Miguel, Palma de Mallorca (2005)
❖Sociology
❖Norms and institutions, cultural dynamics, cooperation,…
Cross-disciplinary (frontier) science
71. @anxosan
M. San Miguel, Palma de Mallorca (2005)
❖Sociology
❖Norms and institutions, cultural dynamics, cooperation,…
Cross-disciplinary (frontier) science
72. @anxosan
A. Arenas, Tarragona (2002)M. San Miguel, Palma de Mallorca (2005)
❖Sociology
❖Norms and institutions, cultural dynamics, cooperation,…
Cross-disciplinary (frontier) science
83. @anxosan
Innovation between Science and Technology
❖ 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
84. @anxosan
Innovation between Science and Technology
❖ 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
❖ Basis for new technologies (ICT, transport, …)
85. @anxosan
Innovation between Science and Technology
❖ 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
❖ Basis for new technologies (ICT, transport, …)
❖ ¿A paradigm shift?
89. @anxosan
Mathematics
❖ Graph theory (Complex networks)
❖ Stochastic processes and statistics (Disorder, noise)
❖ Functional analysis (Phase transitions)
90. @anxosan
Mathematics
❖ Graph theory (Complex networks)
❖ Stochastic processes and statistics (Disorder, noise)
❖ Functional analysis (Phase transitions)
❖ Control theory and signal theory
91. @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
92. @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”
93. @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)
94. @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
95. @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
105. @anxosan
The Sicomoro course
❖ Intro (this lecture, not over yet, examples coming)
❖ Sociophysics
❖ Econophysics (Bartolo Luque, May 3)
106. @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)
107. @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)
108. @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)
109. @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)
110. @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)
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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
❖ 82% travellers and 53% commercial transport (Germany)
❖10% asphalt land (Netherlands)
❖ Billions of lost hours (Spain)
Examples: Traffic
116. @anxosan
• Important problem
❖ 82% travellers and 53% commercial transport (Germany)
❖10% asphalt land (Netherlands)
❖ Billions of lost hours (Spain)
❖ Billions of euros in gas (Europe)
• Difficult solution
❖ Wrong traditional answer (new roads don’t fix it)
Examples: Traffic
117. @anxosan
• Important problem
❖ 82% travellers and 53% commercial transport (Germany)
❖10% asphalt land (Netherlands)
❖ Billions of lost hours (Spain)
❖ 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
118. @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
119. @anxosan
1. Acceleration: if possible, increase speed by 1; vmax=5
7.5
2. Braking: slow down to the fastest possible speed
1D Nagel-Schreckenberg model (1992)
120. @anxosan
1. Acceleration: if possible, increase speed by 1; vmax=5
7.5
2. Braking: slow down to the fastest possible speed
1D Nagel-Schreckenberg model (1992)
121. @anxosan
1. Acceleration: if possible, increase speed by 1; vmax=5
7.5
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)
1D Nagel-Schreckenberg model (1992)
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3. Randomization: with probability p, brake (no apparent cause)
4. Motion
Parallel updating (important)
1D Nagel-Schreckenberg model (1992)
129. @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”
What can be inferred?
134. @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
What can be inferred?
138. @anxosan
Serge Galam has proposed a mechanism, social inertia,
that leads to a democratic rejection of social reforms initially
favored by the majority
Examples: Opinion formation
Question: How can the minority win?
139. @anxosan
Serge Galam has proposed a mechanism, social inertia,
that leads to a democratic rejection of social reforms initially
favored by the majority
Social inertia: Ties favor the “no” option
Examples: Opinion formation
Question: How can the minority win?
140. @anxosan
Serge Galam has proposed a mechanism, social inertia,
that leads to a democratic rejection of social reforms initially
favored by the majority
Social inertia: Ties favor the “no” option
Examples: Opinion formation
Question: How can the minority win?
! Conservative reaction to the risk of change
! Keep the social “statu quo”
141. @anxosan
Serge Galam has proposed a mechanism, social inertia,
that leads to a democratic rejection of social reforms initially
favored by the majority
Social inertia: Ties favor the “no” option
Examples: Opinion formation
Question: How can the minority win?
! Conservative reaction to the risk of change
! Keep the social “statu quo”
(Taken from Maxi San Miguel, IFISC, Mallorca)
142. @anxosan
Serge Galam has proposed a mechanism, social inertia,
that leads to a democratic rejection of social reforms initially
favored by the majority
Social inertia: Ties favor the “no” option
Examples: Opinion formation
Question: How can the minority win?
! Conservative reaction to the risk of change
! Keep the social “statu quo”
(Taken from Maxi San Miguel, IFISC, Mallorca)
149. @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
159. @anxosan
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
161. @anxosan
What can be inferred?
• 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
164. @anxosan
By way of conclusion
❖ Complexity Science is here to stay
❖ Relevant to real life problems of different nature
(cf. Examples)
165. @anxosan
By way of conclusion
❖ Complexity Science is here to stay
❖ Relevant to real life problems of different nature
(cf. Examples)
❖ Key concept: Emergence
166. @anxosan
By way of conclusion
❖ Complexity Science is here to stay
❖ Relevant to real life problems of different nature
(cf. Examples)
❖ Key concept: Emergence
❖ Involves many sciences, but strongly based on
Mathematics and Computation
167. @anxosan
By way of conclusion
❖ Complexity Science is here to stay
❖ Relevant to real life problems of different nature
(cf. Examples)
❖ Key concept: Emergence
❖ Involves many sciences, but strongly based on
Mathematics and Computation
❖ Requires working and thinking about frontiers
168. @anxosan
By way of conclusion
❖ Complexity Science is here to stay
❖ Relevant to real life problems of different nature
(cf. Examples)
❖ Key concept: Emergence
❖ Involves many sciences, but strongly based on
Mathematics and Computation
❖ Requires working and thinking about frontiers
❖ Key for future R+D+i