What is Chaos Theory?
The Secret Life of Chaos
Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand.
It turns out that chaos theory answers a question that mankind has asked for millennia – how did we get here?
In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science – how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder?
It’s a mind bending, counter intuitive and for many people a deeply troubling idea. But Professor Jim Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern.
The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans – after watching this film you’ll never be able to look at the world in the same way again.
http://documentarystorm.com/the-secret-life-of-chaos/~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Complexity Explorer
Complexity Explorer is a web-based repository of educational materials related to complex systems science. Currently under development by researchers and educators at the Santa Fe Institute and Portland State University, Complexity Explorer will host SFI’s online courses, as well as an extensive complex systems glossary and easily searchable databases of syllabi, citations, and other resources related to complex systems topics. Complexity Explorer will also host a “Virtual Laboratory” consisting of open-source simulation programs illustrating complex systems ideas, theories, and tools, accompanied by curricula designed for both teachers and independent learners who want to take advantage of these simulations. All content of the Complexity Explorer website will be open to anyone.
The Complexity Explorer website is currently hosting SFI’s first online course, “Introduction to Complexity”. During 2013 other components of the site will be rolled out as they become ready, and the user community will be solicited to submit additional materials for inclusion.
About the Santa Fe Institute
The Santa Fe Institute is a private, not-for-profit, independent research and education center, founded in 1984, where leading scientists grapple with some of the most compelling and complex problems of our time.
Researchers come to the Santa Fe Institute from universities, government agencies, research institutes, and private industry to collaborate across disciplines, merging ideas and principles of many fields -- from physics, mathematics, and biology to the social sciences and the humanities -- in pursuit of creative insights that improve our world.
The Institute's scientific and educational missions are supported by philanthropic individuals and foundations, forward-thinking partner companies, and government science agencies.
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http://www.complexityexplorer.org/"Introduction to Complexity" course, with some new material, homework, and exams.
In this course you'll learn about the tools used by scientists to understand complex systems. The topics you'll learn about include dynamics, chaos, fractals, information theory, self-organization, agent-based modeling, and networks. You’ll also get a sense of how these topics fit together to help explain how complexity arises and evolves in nature, society, and technology. There are no prerequisites. You don't need a science or math background to take this introductory course; it simply requires an interest in the field and the willingness to participate in a hands-on approach to the subject.
Next course offerings will be:
September 30, 2013: Introduction to Complexity (a second offering, with improvements)
January 2014: Introduction to Dynamics and Chaos (algebra only; taught by David Feldman)
Spring 2014: Agent-Based Modeling in Netlogo
Summer 2014: Mathematics for Complex Systems
Fall 2014: Nonlinear Dynamics (with calculus; taught by Liz Bradley)
Introduction to Dynamical Systems and Chaos
In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:
1. Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's
behavior.
2. Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
3. Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
4. Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
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Agent Based Modeling of Complex Adaptive Systems (Basic)
Our human society consists of many intertwined Large Scale Socio-Technical Systems (LSSTS), such as infrastructures, industrial networks, the financial systems etc. Environmental pressures created by these systems on Earth’s carrying capacity are leading to exhaustion of natural resources, loss of habitats and biodiversity, and are causing a resource and climate crisis. To avoid this sustainability crisis, we urgently need to transform our production and consumption patterns. Given that we, as inhabitants of this planet, are part of a complex and integrated global system, where and how should we begin this transformation? And how can we also ensure that our transformation efforts will lead to a sustainable world?
LSSTS and the ecosystems that they are embedded in are known to be Complex Adaptive Systems (CAS). According to John Holland CAS are "...a dynamic network of many agents (which may represent cells, species, individuals, firms, nations) acting in parallel, constantly acting and reacting to what the other agents are doing. The control of a CAS tends to be highly dispersed and decentralized. If there is to be any coherent behavior in the system, it will have to to arise from competition and cooperation among the agents themselves. The overall behavior of the system is the result of a huge number of decisions made every moment" by many individual agents.
Understanding Complex Adaptive Systems requires tools that themselves are complex to create and understand. Shalizi defines Agent Based Modeling as "An agent is a persistent thing which has some state we find worth representing, and which interacts with other agents, mutually modifying each other’s states. The components of an agent-based model are a collection of agents and their states, the rules governing the interactions of the agents and the environment within which they live."
This course will explore the theory of CAS and their main properties. It will also teach you how to work with Agent Based Models in order to model and understand CAS.
http://ocw.tudelft.nl/courses/tpm-minors-and-electives/agent-based-modeling-of-complex-adaptive-systems-basic/course-home/http://wiki.tudelft.nl/bin/view/Education/SPM955xABMofCAS/WebHome~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Complex analysis is the study of functions that live in the complex plane, i.e. functions that have complex arguments and complex outputs. In order to study the behavior of such functions we’ll need to first understand the basic objects involved, namely the complex numbers. We’ll begin with some history: When and why were complex numbers invented? Was it the need for a solution of the equation x^2 = -1 that brought the field of complex analysis into being, or were there other reasons? Once we’ve answered these questions we’ll devote some time to learn about basic properties of complex numbers that will make it possible for us to use them in more advanced settings later on. We will learn how to do basic algebra with these numbers, how they behave in limiting processes, etc. These facts enable us to begin the study of complex functions, and at this point we can already understand the basics about the construction of the Mandelbrot set and Julia sets (if you have never heard of these that’s quite alright, but do look at
http://en.wikipedia.org/wiki/Mandelbrot_set for example to see some beautiful pictures).
When studying functions we are often interested in their local behavior, more specifically, in how functions change as their argument changes. This leads us to studying complex differentiation – a more powerful concept than that which we learned in calculus. Don’t worry! We’ll help you remember facts from calculus in case you have forgotten. After this exploration we will be ready to meet the main players: analytic functions. These are functions that possess complex derivatives in lots of places, a fact which endows these functions with some of the most beautiful properties mathematics has to offer. We’ll explore these properties!
Who would want to differentiate without being able to undo it? Clearly we’ll have to learn about integration as well. But we are in the complex plane, so what are the objects we’ll integrate over? Curves! We’ll study these as well, and we’ll tie everything together via Cauchy’s beautiful and all encompassing integral theorem and formula.
Throughout this course we'll tell you about some of the major theorems in the field (even if we won't be able to go into depth about them) as well as some outstanding conjectures....
http://www.coursera.org/course/complexanalysis~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Announcing the Opening of the Network Analysis in Systems Biology Course
Module 1 - Complex Systems
Module 2 - Introduction to Biology for Engineers
Module 3 - Network Evolution Models
Module 4 - Types of Biological Networks
Module 5 - Network and Gene Set Analyses
Module 6 - Deep Sequencing Data Analysis
Module 7 - PCA, GSEA and HC
Module 8 - Finding Differentially Expressed Genes with Python
Module 9 - Crowdsourcing
https://class.coursera.org/netsysbio-001/class/index~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Automata Theory is a course based on the material has been taught periodically at Stanford in the course CS154. Students have access to screencast lecture videos, are given quiz questions, assignments and exams, receive regular feedback on progress, and can participate in a discussion forum. Those who successfully complete the course will receive a statement of accomplishment. You will need a decent Internet connection for accessing course materials, but should be able to watch the videos on your smartphone.
The course covers four broad areas: (1) Finite automata and regular expressions, (2) Context-free grammars, (3) Turing machines and decidability, and (4) the theory of intractability, or NP-complete problems.
http://online.stanford.edu/course/automata-fall-2013~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Popularized by movies such as "A Beautiful Mind", game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call 'games' in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE. How could you begin to model eBay, Google keyword auctions, and peer to peer file-sharing networks, without accounting for the incentives of the people using them? The course will provide the basics: representing games and strategies, the extensive form (which computer scientists call game trees), Bayesian games (modeling things like auctions), repeated and stochastic games, and more. We'll include a variety of examples including classic games and real-world applications.
http://online.stanford.edu/course/game-theory-fall-2013~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Nonlinear Dynamics I: Chaos - lecture notes only
http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-006j-nonlinear-dynamics-i-chaos-fall-2006/index.htm~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
March 22, 2007, 08:59:30 PM
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