### Spring 2015

**CS 206/CSYS 295 Evolutionary Robotics****CS/CSYS 302 Modeling Complex Systems****Math/CSYS 266 Chaos, Fractals, and Dynamical Systems****CE/CSYS 359 Applied Artificial Neural Networks****PA 306 Policy Systems****PA 317 Systems Analysis & Strategic Management**

### All Courses

Below are all Complex Systems courses organized alpha-numerically by course department and number. Click the link to find out more about the course listed.

BIOL 271 |
Evolution: Basic concepts in evolution will be covered, including the causes of evolutionary change (selection, mutation, migration and genetic drift), speciation, phylogenetics, and the history of life.Prerequisites:Biol 102 or instructor permission There is an implied prerequisite of Math 19 (Calculus) Methodologies:Evolutionary/adaptive computing/simulation |

CE 359 |
Applied Artificial Neural Networks: A practical hands-on introduction to the theory and implementation of a variety of architectures of artificial neural networks, including back-propagation, hopfield networks, counter-propagation networks, recurrent networks, self-organizing maps, and more.Prerequisites:Computer programming Methodologies:Pattern recognition/classification/data mining, Statistical modeling |

CE 369 |
Applied Geostatistics: Introduction to the theory of regionalized variables, geostatistics (kriging techniques): special topics in multivariate analysis; Applications to real data subject to spatial variation are emphasized.Prerequisites:Stat 223 (multivariate statistics) or 225 (applied regression analysis); CS16/CE11 (Matlab programming) or permission. Methodologies:Multi-scale modeling, Pattern recognition/classification/data mining, Statistical modeling |

CS 251 |
Artificial Intelligence:Introduction to methods for realizing intelligent behavior in computers. Knowledge representation, planning, and learning. Selected applications such as natural language understanding and vision.Prerequisites:CS 103 (programming languages), CS 104 (data structures), STAT 153 (probability & statistics) or equivalent. Methodologies:Agent-based simulation / cellular automata, Evolutionary/adaptive computing/simulation, Pattern recognition/classification/data mining |

CS 256 |
Neural Computation:Introduction to artificial neural networks, their computational capabilities and limitations, and the algorithms used to train them. Statistical capacity, convergence theorems, backpropagation, reinforcement learning, generalization.Prerequisites:Math 124 (or 271), Stat 153 or equivalent, computer programming. Methodologies:Pattern recognition/classification/data mining, Statistical modeling |

CS 295 |
Information and Complexity:Information and Complexity describe a broad theoretical framework that can be applied to a variety of problems in computer science, engineering, statistics, and other disciplines. Claude Shannon extended Ludwig Boltzmann’s concept of entropy to describe the amount of computer memory that is required to store a random message, as well as the maximum rate at which it can be reliably transmitted over a given communication channel.Andrey Nikolaevich Kolmogorov (1903–1987) developed algorithmic information theory to measure the complexity of a message as the “size” of the smallest computer program that generates it. This course will develop, analyze, and apply these and other measures of information and complexity in a variety of contexts, including communication theory, computer science, finance, physics, statistics, and complex systems. Prerequisites:A course in probability or statistics. E.g., stat 141, 143, 151, or 153. Methodologies:Information Theory |

CS 302 |
Modeling Complex Systems:Integrative breadth-first introduction to computational methods for modeling complex systems; numerical methods, cellular automata, agent-based computing, game theory, genetic algorithms, artificial neural networks, and complex networks.Prerequisites:Computer programming (in any language, but Matlab is the language that we use in the course), calculus. Linear algebra is recommended. Methodologies: Agent-based simulation / cellular automata, Chaos theory, Evolutionary/adaptive computing/simulation, Game Theory, Nonlinear dynamic differential equations, Pattern recognition/classification/data mining |

CS 352 |
Evolutionary Computation:Evolutionary computation is a class of biologically-inspired computational search strategies based on the principles of Darwinian evolution (heritability+variation+selection).Applications of EAs span a variety of disciplines, including solving design and optimization problems in engineering, architecture, computer chip design, scheduling, drug design, biotechnology, and bioinformatics, and basic research in evolution and ecology.Prerequisites:Some familiarity with computer programming (in any language, either through coursework or experience) and fundamental probability and statistics. A basic understanding of genetics & evolution is useful, but is not required. Multi-disciplinary teams will match students with complementary backgrounds. Bring your curiosity and a desire to experience interdisciplinary research! Methodologies:Agent-based simulation / cellular automata, Evolutionary/adaptive computing/simulation |

CS 355 |
Statistical Pattern Recognition Prerequisites:Stat 241 or 251 or instructor permission.Methodologies:Pattern recognition/classification/data mining, Statistical modeling |

CS 395 |
Evolutionary Robotics:This course will explore the automated design of autonomous machines using evolutionary algorithms. The course will cover relevant topics in evolutionary computation, artificial neural networks,robotics, biomechanics, and simulation. Students will conduct a major programming project that will span the course and thus provide hands-on experience with the topics covered. Undergraduates will use their developed system to perform a pre-specified evolutionary robotics experiment; graduate students will formulate their own research hypothesis and use their system to test that hypothesis. Prerequisites:Junior standing and programming experience, or instructor permission Methodologies:Distributed control, Evolutionary/adaptive computing/simulation, Nonlinear dynamic differential equations, Numerical optimization |

ENVS 295 |
Modeling Environmental Systems: In this socially relevant course, you will learn to use computer simulation models to create sustainable environmental policies from a Systems Thinking perspective. Systems Thinking is the art and science of making reliable inferences about the behavior of complex systems. Based on class interest, you will study four of these six enduring and profound environmental models: (1) predator-prey interdependency, (2) consumption of scarce resources, (3) population dynamics, (4) spread of epidemics, (5) limits to growth, and (6) global warming. For each of these models, you will analyze the underlying assumptions on which they are built, and then use computer simulation to create policies that make them sustainable over the long-term. These models will provide you with a wealth of knowledge about how complex environmental systems behave.Prerequisites:It is preferred, but not required, that you have taken ENVS 195–Systems Thinking Methodologies: STELLA simulation modeling |

MATH 266 |
Chaos, Fractals, and Dynamical Systems: We discuss orbits, stability, sinks, sources, saddles, chaos, lyapunov exponents, fractals, mandelbrot and julia sets, strange attractors, and manifolds.Methodologies:Chaos theory, Nonlinear dynamic differential equations |

MATH 268 |
Mathematical Biology & Ecology:Mathematical modeling in the life sciences. Topics include population modeling, dynamics of infectious diseases, reaction kinetics, wave phenomena in biology, and biological pattern formation.Prerequisites:Math 124 (linear algebra) and Math 230 (differential equations) or instructor’s permission. Methodologies:Agent-based simulation / cellular automata, Nonlinear dynamic differential equations |

MATH 300 |
Principles of Complex Systems: Many of the problems we face in the modern world revolve around comprehending, controlling, and designing multi-scale, interconnected systems. Networked systems, for example, facilitate the diffusion and creation of ideas, the physical transportation of people and goods, and the distribution and redistribution of energy. Complex systems such as the human body and ecological systems are typically highly balanced, flexible, and robust, but are also susceptible to systemic collapse. These complex problems almost always have economic, social, and technological aspects.So what do we know about complex systems? The basic aim of this introductory interdisciplinary course is to present a suite of theories and ideas that have evolved over the last couple of decades in the pursuit of understanding complex systems. The central focus will be on understanding small-scale mechanisms that give rise to observed systemic phenomena. Students will be encouraged to see how different areas connect to each other and, just as importantly, where analogies break down. Prerequisites:Familiarity with the following would be good but not completely necessary: standard calculus, differential equations, difference equations, linear algebra, statistical physics, and statistical methods.Computing: Proficiency in coding (C, Matlab, perl, python) will be beneficial (and indeed necessary) for certain projects but is not required. Methodologies:Agent-based simulation / cellular automata, Multi-scale modeling, Network/graph science, Statistical modeling |

MATH 303 |
Complex Networks: Complex networks crucially underpin much of the real and synthetic world. Networks distribute and redistribute information, water, food, and energy. Networks can be constituted by physical pipes, embodied in relationships carried in people’s minds, or manifested by economic interdependencies.In the past decade, building on work in a wide range of disciplines, many (but certainly not all) advances have been made in understanding all manner of complex networks such as the World Wide Web, social and organizational networks, biochemical networks, and transportation networks. In this special topics course, we will explore this evolving field of complex networks by reading and discussing seminal and recent papers, and developing mathematical and algorithmic results where they exist. The level will be graduate/advanced undergraduate. Prerequisites:Math/Csys 300 Familiarity with differential equations, difference equations, standard calculus, linear algebra, statistical methods. Proficiency in coding (C, Matlab, Perl, Python) will be beneficial (and indeed necessary) for certain projects but is not required. Methodologies:Network/graph science |

ME 295 |
Systems and Synthetic Biology:The course will focus on applying engineering tools to the study of molecular biology to (a) analyze complex gene regulatory networks and (b) design novel gene circuits using principles from electrical circuits and mechanical design. We will discuss mathematical modeling techniques, molecular biology methods, and recent literature in the fields of systems and synthetic biology.Prerequisites:differential equations, linear algebra, programming (class assignments will use Matlab) Methodologies:Distributed control, Multi-scale modeling, Network/graph science, Nonlinear dynamic differential equations, Statistical modeling |

ME 312 |
Multi-scale Bioengineering: Advanced bioengineering design and analysis for current biomedical problems spanning molecular, cell, tissue, organ, and whole body systems including their interactions and emergent behaviors.Methodologies:multiscale phenomena |

ME 350 |
Multiscale Modeling: Atomistic modeling techniques (i.e., molecular dynamics, etc.) and related multiscale methods (i.e., coarse-graining, quasicontinuum, etc.) applicable to the modeling of fluid and solid matter.Methodologies:Multi-scale modeling |

PA 308 |
Decision Making Models: This course focuses on systems level thinking to impart problem-solving skills in complex decision-making contexts. Individual, inter-personal, organizational and inter-organizational decision making contexts will be analyzed with varying levels of complexity. The emphasis will be placed on imparting cutting edge skills to the students to develop intelligent decision support systems, including agent based simulation models; artificial intelligence (AI)-based technologies such as logic rule-based systems, neural networks, fuzzy logic, case-based reasoning, genetic algorithms, data-mining algorithms; and deliberative decision making models such as mediated modeling and collaborative management techniques.Prerequisites:Graduate Standing Methodologies: Agent-based simulation / cellular automata, Chaos theory, Distributed control, Evolutionary/adaptive computing/simulation, Game Theory, Multi-scale modeling, Network/graph science, Nonlinear dynamic differential equations, Numerical optimization, Pattern recognition/classification/data mining, Statistical modeling, Other: Scenario analysis, Judgemental Decision Making |

PA 317 |
Systems Analysis and Strategic Management: By applying complexity, network and systems analysis to the study of organized responses to wicked problems, it is possible to “harness complexity” in such a way as to generate effective results. This means that effective leaders, modelers and policy analysts must be attentive to the inputs (human, social, financial, political, cultural , knowledge, and physical capital), the processes (inter & intra-organizational and inter-personal dynamics), the outputs (the tangible measures and product of collective action) and the outcomes (the long term goals and objectives) associated with their environments. In addition, they must understand the broader environmental factors that impact their organizations. These externals factors may include: market trends, funder priorities, policy developments, etc.Prerequisites:Basic understanding of social organizations, social network dynamics. Interest in the policy process and social systems modeling. Methodologies:Agent-based simulation / cellular automata, Evolutionary/adaptive computing/simulation, Game Theory, Multi-scale modeling |

PBIO 295 |
Ecological and Environmental Modeling:Prerequisites: Introductory calculus or permission of the instructor. Methodologies:Statistical modeling |

STAT 253 |
Applied Time Series & Forecasting: Autoregressive moving average (Box-Jenkins) models, autocorrelation, partial correlation, differencing for nonstationarity, computer modeling. Forecasting, seasonal or cyclic variation, transfer function and intervention analysis, spectral analysis.Prerequisites:Stat 211 or 225; or 141 or 143 with instructor’s permission. Methodologies:Pattern recognition/classification/data mining, Statistical modeling |

STAT 330 |
Bayesian Statistics: This is a course in Bayesian statistics. Bayesian inference is a powerful and increasingly popular statistical approach, which allows one to deal with complex problems in a conceptually simple and unified way. The recent introduction of Markov Chain Monte Carlo (MCMC) simulation methods has made possible the solution of large problems in Bayesian inference that were formerly intractable. This course will introduce the student to the basic methods and techniques of modern Bayesian inference, including parameter estimation, MCMC simulation, hypothesis testing, and model selection/model averaging in the context of practical problems.Prerequisites:STAT 241 or 251 or instructor permission. Methodologies:Statistical modeling, Other: Markov chain Monte Carlo (MCMC) |