Research Groups and Projects
Bruch, Elizabeth—Dynamic Models of Racial Residential Segregation
Deegan, Robert—The Deegan Group: Nonlinear Science Laboratory
Doering, Charlie—Systematic Search..Fluid Dynamics
Newman, Mark—Large-scale structure in complex networks
Page, Scott—Creating Wise Crowds
Page, Scott—Games Theory, Culture and Institutional Path Dependence
Page, Scott—Teaching Computational Thinking
Page, Scott—Complex Systems Advanced Academic Workshop
The Center for the Study of Complex Systems supports a diverse body of research, training and educational initiatives. The following is a list of our active research groups and projects.
A list of projects from previous years can be found in the Research Archive section.
Research Groups and Projects
Dynamic Models of Racial Residential Segregation
Principal Investigator: Elizabeth Bruch
Co-PI: Rick Riolo
Source of Funding: National Institutes of Health
This project outlines a plan of research to better understand the causes of racial and economic residential segregation in American cities. We propose to develop data-based models of household residential mobility and to use these models as a basis for a realistic, agent-based model of neighborhood formation and residential segregation.
Current methods used to study residential segregation have examined specific single processes linked to segregation. These methods usually rely on intuitive judgments to draw conclusions about how these processes aggregate to form segregated neighborhoods. This is problematic because stylized simulation models show feedback and constraints in residential systems produce relations of inputs and outcomes that are highly interactive and non-linear. Our alternative approach is based on discrete choice models of destination selection in residential relocation and an agent-based simulation. We estimate the discrete choice models using the data on mobility from the Panel Study of Income Dynamics matched with data from the decennial censuses.
Our proposed basic model incorporates race and neighborhood racial composition, income and housing cost, neighborhood income composition, and tenure (owner or renter). We also propose an extension to the model that incorporate wealth, housing market discrimination, and impacts of neighborhood change in the residential neighborhood and adjacent neighborhoods. The base model we propose could incorporate other future refinements toward greater realism and usefulness. The model has two uses. The first use is to address basic science questions regarding the causes of segregation. The second use is to evaluate the effects of spatially targeted housing policies on race and income segregation. We use the model to evaluate the effects of the shift from traditional fixed-site public housing to housing vouchers and mixed-income housing on race and income segregation.
The Deegan Group: Non Linear Science Laboratory
Principal Investigator: Robert Deegan
Sources of Funding: James S. McDonnell Foundation, NSG, Among Others
Simple systems driven from equilibrium will spontaneously form patterns. A classic demonstration is a pot of water on a stove. If the stove is not turned on, the water remains still. The fluid is in equilibrium, and all parts behave the same; there is no structure. But if the heat is turned on, the water begins to move in an organized manner. The water rises along the walls of the pot and falls in the middle. From initially homogeneous conditions the water has developed an organized dynamical structure. The world is filled with countless examples of this general phenomenon from the mundane-the ornate architecture of a snow flake, the crown-like splash of a drop, the dark ring around a coffee strain-to the exotic-the Earth's magnetic field, sunspots, the large scale structure of the universe.
Is all the structure in world around us an inevitable product of the forcing? Is life itself a generic manifestation of driven systems? These are fascinating issues that research on nonequilibrium systems and pattern formation will hopefully one day answer.
My research focus is patterns in fluids and solids. Lately, I've been working on drop impact, vibrated shear thickening fluids, vibrated drops, the statistics of caustic networks, and exploding seed pods. Some past projects include the fracture of rubber and silicon, and the formation of rings from a drying drop.
Web site: http://www-personal.umich.edu/~rddeegan/index.html.
Systematic Search for Extreme and Singular Behavior in Some Fundamental Models of Fluid Mechanics
Principal Investigator: Charlie Doering
Source of Funding: National Science Foundation, Division of Mathematical Sciences
This project utilizes methods of modern applied mathematics and scientific computation to systematically search for extreme behavior in some of the fundamental equations of physical fluid mechanics. Mathematical measures of mixing introduced by the investigator and collaborators are utilized in optimal control analyses of the advection and advection-diffusion equations in order to place absolute limits on passive tracer mixing by incompressible flows, and to illuminate key features of particularly effective stirring strategies. Computational control and applied analysis are employed to construct incompressible fluid flows optimizing transport between impenetrable surfaces and produce new transport bounds for buoyancy-driven Rayleigh-Bénard convection and the outstanding problem of turbulent convection. Optimal control techniques are developed and deployed to determine maximal enstrophy production in the incompressible three-dimensional Navier-Stokes equations over finite time intervals. Extremal solutions provide new insight into fully nonlinear vorticity amplification in unforced flows, and this component of the project is a novel and promising framework for the study of one of the signal challenges for 21st century applied mathematics: the regularity question for the 3D Navier-Stokes equations.
Large-scale structure in complex networks
Principal Investigator: Mark Newman
Source of Funding: National Science Foundation
This group is conducting research on the structure and function of networked systems such as the Internet, the web, social networks, and biological and epidemiological networks, employing a combination of empirical data, mathematical theory, and computer simulation. For more information about the Networks project, please visit Professor Newman's web site: http://www.umich.edu/~mejn/
Creating Wise Crowds: Diversity Maintenance Through Incentives
Principal Investigator: Scott Page
Source of Funding: National Science Foundation, Innovation and Organizational Sciences (IOS) Program
Effective management of organizations requires the ability to make forecasts of the future. These forecasts guide day-to-day decisions such as the allocation of resources and can warn of busts and identify booms. In this research, we are constructing a new framework that demonstrates the contributions of individual cognitive depth and collective diversity on forecast accuracy. We then explore the ability of incentive structures to maintain that depth and diversity.
Games Theory, Culture and Institutional Path Dependence
Principal Investigator: Scott Page
Source of Funding: Dept. of Defense, Army Research Office (ARO)
In the proposed research we combine analytic, computational and experimental methods to study the relationship between cultural and institutional performance. In our framework, cultural factors influence the success of institutions and institutions, in turn, influence culture. This interplay between institutions and culture creates the potential for institutional and cultural path dependence. Our proposed research identifies explicit behavioral patterns produced by institutions and describes them with mathematical formalism. We then explore whether and how these behaviors transfer across domains using computational and experimental methods. Our research has implications for the design and choice of restoration programs after military interventions or government upheavals. Our research can show how new governing institutions can leverage existing patterns of behavior to produce more efficient and robust outcomes.
Teaching Computational Thinking Through Integration of Dynamic Systems Modeling
Principal Investigator: Scott Page
Source of Funding: National Science Foundation Sub-award from Oberlin College
Enormous progress in computational technology has generated a new methodology for learning about and advancing traditional sciences such as physics, chemistry, and biology, as well as social sciences like economics and cross-disciplinary fields such as environmental studies. Computational Modeling (CM) applies numerical methods, models, and algorithms to complex problems that are intractable by purely analytical or experimental techniques. It is distinct from computer science, which studies computers and computation, and it is different from the traditional scientific methods of theory and experimentation, but interacts closely with them.
We propose to collaborate with the University of Michigan's Center for the Study of Complex Systems (CSCS) to demonstrate how computational modeling can transform many areas of the undergraduate curriculum. Computational Modeling makes frontier problems accessible, and it can be introduced with a minimum of mathematical background. This allows rapid start-up for students who are eager to explore exciting content in a discipline. Once so engaged, they will have incentive to deepen their understanding of the mathematical and algorithmic basics underpinning the CM tools that they are using.
Complex Systems Advanced Academic Workshop (CSAAW)
Source of Funding: UM Rackham Interdisciplinary Workshop Grant
The goal of CSAAW is to support students who are writing dissertations that involve the interdisciplinary ideas and techniques of complex systems research. Through a series of regular meetings, students will discuss their own work and receive feedback from other students, faculty and researchers. Other meetings will consist of talks by and discussions with invited speakers who are active in complex systems research. These speakers, many of whom will be recent graduates, will discuss their own work, provide advice on how to successfully complete a complex systems (interdisciplinary) dissertation, and how to navigate through the post-graduate job market.
Computational Models for Belief Revision, Group Decisions and Cultural Shifts
Principal Investigators: Scott Page, Jenna Bednar
Source of Funding: U.S. Air Force Office of Scientific Research
This project, in collaboration with a team at the Massachusetts Institute of Technology (MIT), is developing and comparing a variety of computational models, grounded in previous and future studies of cultural differences. The aim of the models is to predict intent and patterns of behavior, given new concepts. A further objective is to study the dynamics of the different models, when perturbed by unexpected external forces that put pressure on existing belief structures. Although much of the modeling will be through simulations, some grounding will be possible using either lab-based mockups, data currently available or anticipated and media reports that trigger reactions among elements of a population.