Unit 10 – Wrap Up
What are Complex Systems? – Large networks of simple interactive elements which, following simple rules, produce emergent, collective, complex behaviour.
Core disciplines of the science of complexity:
- Dynamics – the study of continually changing structure and behaviour of systems
- Information – the study of representation, symbols and communication.
- Computation – the study of how systems process information and act on the results
- Evolution/Learning – the study of how systems adapt to constantly changing environments
Goals of the course
- To give you a sense of how these topics are integrated in the study of complex systems
- To give you a sense how idealized models can be used to study the field of complex systems (using netlogo as simulator)
Quick review of the course:
Research projects on complexity systems in Santa Fe Institute
Unit 9 is about Networks. Examples of networks in human beings, nature and technology:
A Neural network
US Internet network
US Power Grid
Social Network – friendship links in Facebook
The science of networks crosses many fields. It is concerned with common properties. Can we formulate a theory of structure, evolution and dynamics of networks?
Networks common properties
Terminoly related to networks: nodes and links; cluster of nodes (to what extent are your frienfs also friends of one another)
Dimensions of networks:
Small world network (network of family or friends)
Scale-free and Long-Tailed Distribution Networks
Distribution scale in random and WWW networks
Scale-free networks are like fractals
Scale-free and long-tailed netwaors are vulnerable when atacked. For instance, when an energy power grid fails tends to overburden the next grid with a cascade effect; or when malware is spread in the web may damage computers; or whem a disease spreads bacause of mobility of people across the world, like the flu.
When a personal website goes down it may not affect many people but when an important online service goes down (financial portal) it affects many people and can be quite disturbing.
Cascading failure may affect many fields like the banking system with systemic impacts on each other
Proportionality is a linear concept
Scaling: How do attributes of bodies change as their body mass increases? (rat vs. elephant) – How do attributes of cities change as their population increases?
Theories of Metabolic Scaling
A fourth dimension (fractal dimension) is considered in this model, beyond the usual 3D
Critique to the model
Unit 8 is about Models of Cooperation in Social Systems
Cooperation works on the assumption that individuals act in order to maximize their utility (in biology, social science and economics systems). Individuals are assumed to be selfish, yet cooperation and altruism is evident at all levels of biology and society.
Two Models of Social Cooperation: The Prisoner’s Dilemma and El Farol
Unit 7 is about Models of Biological Self-Organization
Self-organization definition: production of organized patterns, resulting from localized interactions within the components of the system, without any central control.
Self organization of ANTS, building a bridge with their bodies:
Self-organization of FISH to defend themselves from predators:
Flocking – self organization without leader or general information about the flock
Reasons to flock:
Why do fireflies synchronize their flashing
Prof. Doyne Farmer (Oxford Univ. ) considers that Economics is a self-organized system. The system adapts and evolves.
Unit 6 is about Cellular Automata, which is defined in Wikipedia:
«A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.
A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t=0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton.»
Some simulations in Netlogo were made:
A link for Wolfram Math World was provided – http://mathworld.wolfram.com/ElementaryCellularAutomaton.html
It defined Computation and the notion of Universal Computation
John von Newman was one of the first scientist to look at cellular automata as models of complex systems and the idea of self-reproduction in machines or automata.
Significance of Cellular Automata as Complex Systems
Unit 5 focus on Genetic Algorithms that have been applied to different fields as the slides show. Examples were given in simulations of netlogo to programme a robot.
And genetic programming (John Koza, 1990) is also applied to art and computer graphics – syntactic trees. Some images that resulted from this kind of programming by Karl Sims:
The same artist and researcher, Karl Sims, developed another project «Evolving Virtual Creatures» in 1994:
«The Koch snowflake (also known as the Koch star and Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled “On a continuous curve without tangents, constructible from elementary geometry” (original French title: Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire) by the Swedish mathematician Helge von Koch. (Wikipedia)
Prof. Mellanie explains it, but I found another Khan video on the subject:
Fractal dimension is explained in this alternative video:
To address fractal dimensions methods applied to earthquake forecast, Prof. John Rundell (professor of Physics and Geology) engages in a dialogue with Prof. Merrill to discuss how fractal dimensions can be applied to other fields such as earthquake forecast or financial crisis. How data, statistics and probabilities can help to predict natural disasters or financial crashes.
He refers a website http://openhazards.com/ that aims at, through advances in forecasting and sensor technology, as well as an open, web-based approach to public information availability and sharing, enable a more sustainable human society in the face of severe, recurring natural disasters.
In Portugal there was a huge earthquake (8.75 Richter), followed by a tsunamy and fires that destroyed most of Lisbon and killed thousands of people. There are predictions of similar ones in the far future.
Fractals are objects with «self-similarity» at different scales.
Prof. Melanie Mitchell explains how fractals can be found in nature in his introductory video to the topic.
Fractals are an amazing subject that have always fascinated me. I remenber a fabulous documentary in the 90’s by Arthur C. Clark about fractals «The colours of Infinity», interviewing some scientists and mathematicians, namely Benoit Mandelbrot, famous for his Mandelbrot set.
Amazing videos can be found in the Internet, 3D trips, such as «Like a Dream»
I’ve created a Livebinders with the literature on all topics of Complexity MOOC – http://www.livebinders.com/play/play?id=1066771
The topic of Dynamics and Chaos offered a definition for Dynamics – «the general study of how systems change» – a general field with many examples:
- Planetary dynamics – movement of planets, orbits, gravity, eclipses…
- Fluid dynamics – ocean flows, hurricanes, air turbulence…
- Electrical dynamics – flow of electricity and circuits…
- Climate dynamics – climate changes, temperature, pressure…
- Crowd dynamics – how crowds of people act, panic situations…
- Population dynamics – population variation over time…
- Social dynamics – conflicts between nations, cooperation…
Complex equations have been developed to analyse these complex phenomena and Dynamic Systems Theory is the branch of mathematical area that describes how systems change over time (includes algebra, calculus, iterated maps…)
Brief history of Dynamic Systems Theory in Capzles – History Dynamic Systems Theory
Chaos has the common meaning of «disorder», but in scientific terms means one particular type of dynamics of a system, «sensitive dependence on initial conditions». Examples of chaos in nature: climate change, brain activity (EEG), heart activity (EKG), computer networks, population growth, financial data…
What is the difference between chaos and randomness? Notion of deterministic chaos. Iteration – doing something again and again.
Analysing a graphic of population growth and a netlogo simulation (ex. of bunnies) an equation is produced to calculate the growth of population year after year – exponential equation/function.
Linear and non-linear systems/equations were addressed in this topic and several simulations in netlogo. So, after these simulations chaos result as seemingly random behavior with sensitive dependence on initial conditions.
The logistic map is a simple, completely deterministic equation that, when iterated, can display chaos.
Deterministic chaos as a perfect prediction is impossible (Laplace deterministic clockwork universe), even in principle if we’re looking to a chaotic system.
Prof. Garland is a guest in one of the videos of the topic and explains that most of transistors in a computer are non-linear dynamics, electrons are moving around silicon. She says that many years ago computers were very simple and predictable, but in the last decade systems became a lot more complex. Tools of non-linear dynamics have been used to understand computers. The way a computer uses its processing and memory is chaotic, that is, sensible to initial conditions.
Prof. Garland recommends that participants search for «The Morning Glory Cloud» , a rare meteorological phenomenon occasionally observed in different locations around the world, not yet scientifically explained, the southern part of Northern Australia’s Gulf of Carpentaria is the only known location where it can be predicted and observed on a more or less regular basis due to the configuration of land and sea in the area (http://en.wikipedia.org/wiki/Morning_glory_cloud )
An article co-authored by Prof. Garland «On the importance of nonlinear modeling in computer performance prediction»
The MOOC «Introduction to Complexity» started on the 30th September 2013 – http://www.complexityexplorer.org/online-courses/3/segments/1018. It will extend through December.
It is promoted by the Santa Fe Institute and moderated by Prof. Mellanie Mitchell,a researcher of Portland University in the field of artificial intelligence and machine learning, and also very active in developing educational materials and courses related to complex systems.
Eleven Units with videos, quizzes, assignments per week. Can be followed in Twitter. Netlogo will be used as the simulation platform.
There’s a Youtube channel for the course and the opening video explains how the course will work