The Santa Fe Institute is an independent, nonprofit theoretical research institute located in Santa Fe and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive ...
The Foundations & Applications of Humanities Analytics course is aimed at a broad range of humanities scholars. The course aims to empower scholars in the humanities by eliminating the “black box” of computational text analysis. Participants will gain a theoretical and practical understanding of text analysis methods, and will learn how to extract content and derive meaning from digital sources, enabling new humanities scholarship.This online course will comprise two modules. Foundations will impart conceptual skills and computational thinking through a study of the principles behind contemporary artificial intelligence. Applications will employ those skills to develop meaningful accounts of literary, historical, and cultural artifacts. A supplementary online tutorial will introduce the necessary steps to get started with Python programming and Jupyter notebooks.The project Foundations and Applications of Cultural Analytics in the Humanities has been made possible in part by a major grant from the National Endowment for the Humanities: Exploring the human endeavor, under Federal Award ID Number HT-272418-20. Any views, findings, conclusions, or recommendations expressed in this course do not necessarily represent those of the National Endowment for the Humanities.
Introduction to Computation Theory is an overview of some basic principles of computation and computational complexity, with an eye towards things that might actually be useful without becoming a researcher. Students will examine the formal mathematics for foundational computation proofs, as well as gain tools to analyze hard computational problems themselves. Students who take this course should have basic knowledge of the principles of graphs. Some tutorial material references linear algebra, but familiarity is not necessary. This tutorial uses proofs, and requires understandings of formal math notations.
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'sbehavior.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.
This course explores computational complexity, from search algorithms and solution landscapes to reductions and universality. We explore problems ranging from easy (polynomial time) to hard (NP-complete) to impossible (undecidable). These ideas form one of the most beautiful fields of modern mathematics, and they are increasingly relevant to sciences ranging from physics to biology. The aim of this course is to help participants gain an understanding of the deep ideas of theoretical computer science in a clear and enjoyable fashion, making those ideas accessible both to non-computer scientists and to computer scientists who want to revisit these ideas in a broader and deeper way.
This tutorial introduces students to essential ideas related to vectors and matrices. These mathematical structures form the foundations for many key topics in complex systems, such as dynamical systems, stochastic processes, and network science. The prerequisite for this tutorial is knowledge of high-school algebra. The content of the tutorial is built, in a self-contained fashion, starting with basic notions of real numbers and elementary set theory. Ideas of vectors and vector operations are developed next, in an intuitive way, by appealing, simultaneously to their algebraic and geometric underpinnings. Next, the tutorial explores matrices and vector spaces, determininants and eigenvalues with, again, an eye toward understanding the intuitive geometric and algrebraic connections that tie these notions together. Finally, the tutorial concludes with a survey of applications of matrix algebra, including diagnolization, recursion, geometric transformations, differential operators and Markov Chains. Importantly, the content and emphasis of this material differs significantly from a standard university course in linear algebra. Instead of solving and analyzing systems of linear equations of the form Ax=b, as is conventional from the perspective of linear algebra, students will instead be exposed to the fundamental ideas of matrix algebra in a less restrictive and more conceptually-integrated way. At the conclusion of this tutorial, students will be equipped with a core understanding of the breadth and power of matrix algebra as an essential tool for complex systems research.
This course aims to push the field of Origins of Life research forward by bringing new and synthetic thinking to the question of how life emerged from an abiotic world.This course begins by examining the chemical, geological, physical, and biological principles that give us insight into origins of life research. We look at the chemical and geological environment of early Earth from the perspective of likely environments for life to originate.Taking a look at modern life we ask what it can tell us about the origin of life by winding the clock backwards. We explore what elements of modern life are absolutely essential for life, and ask what is arbitrary? We ponder how life arose from the huge chemical space and what this early 'living chemistry' may have looked like.We examine phenomena, that may seem particularly life like, but are in fact likely to arise given physical dynamics alone. We analyze what physical concepts and laws bound the possibilities for life and its formation.Insights gained from modern evolutionary theory will be applied to proto-life. Once life emerges, we consider how living systems impact the geosphere and evolve complexity. The study of Origins of Life is highly interdisciplinary - touching on concepts and principles from earth science, biology, chemistry, and physics. With this we hope that the course can bring students interested in a broad range of fields to explore how life originated. The course will make use of basic algebra, chemistry, and biology but potentially difficult topics will be reviewed, and help is available in the course discussion forum and instructor email. There will be pointers to additional resources for those who want to dig deeper.This course is Complexity Explorer's first Frontiers Course. A Frontiers Course gives students a tour of an active interdisciplinary research area.The goals of a Frontiers Course are to share the excitement and uncertainty of a scientific area, inspire curiosity, and possibly draw new people into the research community who can help this research area take shape!
Machine Learning is a fast growing, rapidly advancing field that touches nearly everyone's lives. There has recently been an explosion of successful machine learning applications - in everything from voice recognition to text analysis to deeper insights for researchers. While common and frequently talked about, most people have only a vague concept of how machine learning actually works.In this tutorial, Dr. Artemy Kolchinsky and Dr. Brendan Tracey outline exactly what it is that makes machine learning so special in an accessible way. The principles of training and generalization in machine learning are explained with ample metaphors and visual intuitions, an extended analysis of machine learning in games provides a thorough example, and a closer look at the deep neural nets that are the core of successful machine learning. Finally, it addresses when it's appropriate to use (and not use) machine learning in problem solving, as well as an example of scientific research incorporating machine learning principles.Students of all levels should be able to follow this reasonably-paced introduction to one of the most important engineering breakthroughs of our time.
This tutorial will present you with the basics of how to use NetLogo to create an agent-based modeling. During the tutorial, we will briefly discuss what agent-based modeling is, and then dive in to hands-on work using the NetLogo programming language, which is developed and supported at Northwestern University by Uri Wilensky. No programming background or knowledge is required, and the methods examined will be useable in any number of different fields.
This course provides a broad introduction to the field of nonlinear dynamics, focusing both on the mathematics and the computational tools that are so important in the study of chaotic systems.The course is aimed at students who have had at least one semester of college-level calculus and physics, and who can program in at least one high-level language.After a quick overview of the field and its history, we review the basic background that students need in order to succeed in this course.We then dig deeper into the dynamics of maps—discrete-time dynamical systems—encountering and unpacking the notions of state space, trajectories, attractors and basins of attraction, stability and instability, bifurcations, and the Feigenbaum number.We then move to the study of flows, where we revisit many of the same notions in the context of continuous-time dynamical systems.Since chaotic systems cannot, by definition, be solved in closed form, we spend several weeks thinking about how to solve them numerically and what challenges arise in that process.We finish by learning about techniques and tools for applying all of this theory to real-world data.
This course covers several mathematical techniques that are frequently used in complex systems science. The techniques are covered in independent units, taught by different instructors. Each unit has its own prerequisites. Note that this course is meant to introduce students to various important techniques and to provide illustrations of their application in complex systems. A given unit is not meant to offer complete coverage of its topic or substitute for an entire course on that topic. The units included during this offering of the course are:(1) Introduction to differential equations (David Feldman)(2) Ordinary differential equations (ODEs) and numerical ODE solvers (Liz Bradley)(3) Functions and iteration (David Feldman)(4) Maximum entropy methods (Simon DeDeo)(5) Random Walks (Sid Redner)(6) Vector and matrix algebra (Anthony Rhodes)(7) Introduction to information theory (Seth Lloyd)(8) Game Theory I - Static Games (Justin Grana) (9) Game Theory II - Dynamic Games (Justin Grana) (10) Introduction to Renormalization (Simon DeDeo) (11) Fundamentals of Machine Learning (Artemy Kolchinsky) (12) Introduction to Computation Theory (Josh Grochow) (13) Fundamentals of NetLogo (Bill Rand) Other units to be developed over time.
Game theory is the standard quantitative tool for analyzing the interactions of multiple decision makers. Its applications extend to economics, biology, engineering and even cyber security. Furthermore, many complex systems involve multiple decision makers and thus a full analysis of such systems necessitates the tools of game theory. This course is designed to provide a high-level introduction to static, non-cooperative game theory. The main goal of this course is to introduce students to the idea of a Nash Equilibrium and how the Nash Equilibrium solution concept can be applied to a number of scenarios. Students are assumed to be familiar with the concept of expected value and the basics of probability. While calculus is not required for the majority of the course, lesson 7 focuses on an example that employs calculus. However, lesson 7 can be skipped without any harm in understanding lessons 8 − 10.