Handling editor: Phanikrishna Thota

Cornell IGERT Program in Nonlinear Systems

John Guckenheimer

The Cornell IGERT Program in Nonlinear Systems is one of 125 Integrative Graduate Education and Research Traineeship Programs sponsored by the US National Science Foundation. The NSF states:

"The Integrative Graduate Education and Research Traineeship (IGERT) program has been developed to meet the challenges of educating U.S. Ph.D. scientists and engineers who will pursue careers in research and education, with the interdisciplinary backgrounds, deep knowledge in chosen disciplines, and technical, professional, and personal skills to become, in their own careers, leaders and creative agents for change. The program is intended to catalyze a cultural change in graduate education, for students, faculty, and institutions, by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. It is also intended to facilitate diversity in student participation and preparation, and to contribute to the development of a diverse, globally-engaged, science and engineering workforce."

The NSF IGERT awards provide five years of support, primarily for graduate student fellowships. The Cornell IGERT Program in Nonlinear Systems began in 1997, one of the first cohort of IGERTs, and received a renewal award in 2002. During the period 2003-08, the renewal award will fund 30 two-year fellowships. The fellowships are restricted to US citizens and permanent residents. Nationally, NSF makes approximately 20 new IGERT awards each year from over 500 proposals. The range of subjects encompassed is extremely broad, ranging from nanophotonics to inequality and social policy.

The nineteen current IGERT fellows in our program are also a diverse group, coming from fourteen different fields. (Graduate education at Cornell is organized into Fields of Study rather than by department, allowing for interdisciplinary Fields like Applied Mathematics that draw faculty from many different departments.) IGERT fellows commit to fulfilling several requirements: courses on nonlinear dynamics and computational methods for nonlinear systems, completion of a year-long project in nonlinear systems, a summer internship, participation in an IGERT seminar and attendance at IGERT-sponsored colloquia in diverse fields. Consistent with the NSF goals for IGERT, these activities broaden the graduate education of the fellows. This IGERT is a "disciplinary plus" program in that the IGERT requirements are an addition to the requirements for a PhD in a student's major Field.

The IGERT Seminar, Fall 2005
Seated: Derek Cabrera (Education), James Mandel (Ecology and Evolutionary Biology), David Ashley (Mechanical Engineering), Sam Arbesman (Computational Biology); Standing: Brett Streetman (Aerospace Engineering), John Guckenheimer (Director), Bret Hanlon (Statistics), Bryan Daniels (Physics), Richard Yamada (Applied Mathematics), Lauren Childs (Applied Mathematics), Gordon Berman (Physics), Mark Albert (Computational Biology), Heather Flores (Genetics and Development), Jordan Albert (Chemical Engineering), Daniel Brown (Mechanical Engineering) John Dietl (Mechanical Engineering) and Chris Cameron (Sociology). Not in the picture: Lydia Contreras (Chemical Engineering), Amina Kinkhabwala (Neurobiology and Behavior), Sam Walcott (Theoretical and Applied Mechanics).

There are four focus areas for the program, each with a lead faculty member.

Complex Networks (Steve Strogatz)

The 1998 paper Collective dynamics of 'small-world' networks by Duncan Watts and Steve Strogatz stimulated interest in the analysis of the statistical properties of complex networks of social interactions, power systems, world wide web links, and molecular interactions within a cell. Research activities on complex networks at Cornell include the 2005-08 theme project Getting Connected of the Institute for Social Sciences and an interdisciplinary Internet Archive Cybertools project led by sociologist Michael Macy with computer scientist participants Bill Arms, Dan Huttenlocher and Jon Kleinberg.

Gene Regulation (Jim Sethna)

The Cornell New Life Sciences Initiative includes an emphasis upon the interactions between the life sciences and physical sciences. Sethna, Rick Cerione, Kelvin Lee and Chris Myers have been leading a group of students exploring quantitative models for cell-signaling networks and related problems. The emphasis has been on parameter estimation for differential equations models of cellular networks from data. The group uses Monte-Carlo-Gibbs sampling methods and has developed the sloppy cell software for fitting models to data when the output of the model has large ranges of sensitivity to parameters.

Machines and Organisms - Locomotion and Manipulation (Francisco Valero-Cuevas)

The dexterity, efficiency and agility of movement and locomotion in animals surpasses the capabilities of machines that we build. Biology provides inspiration for machines we design and build while computational models and machines allow us to test our understanding of biology. Highlights of research in this area include insect flight (Jane Wang) and running (John Guckenheimer), efficient walking robots (Andy Ruina) and flying machines with flapping wings (Ephraim Garcia), manipulation (Francisco Valero-Cuevas), muscle biology (John Hermanson) and the use of evolutionary algorithms to design robots (Hod Lipson).

Pattern Formation (Robert Gilmour)

Waves of electrical action potentials drive the heartbeat. Heart rhythm disorders are frequently lethal. This focus group studies ionic mechanisms in heart cells and patterns of wave propagation in the heart. There is an emphasis on quantitative comparisons between models and data.

Students either choose projects in one of these focus areas or they recruit at least two faculty members in different research areas to jointly mentor their projects. One objective of the student projects is to bring together empirical data, theory and computation. The focus areas represent only a subset of research on nonlinear systems and dynamics at Cornell. Links from other faculty associated with the IGERT Program can be used to sample more. Additionally, complex dynamics is a strong area of research within the Field of Mathematics, led by senior faculty John Hubbard, Yulij Ilyashenko and John Smillie.

Applicants to PhD programs at Cornell are nominated for IGERT fellowships by their prospective Fields. They may indicate their interest in the program in their applications; field admissions committees also identify students whom they think will be interested in the program. The field system of graduate education allows students unusual flexibility in their academic programs and encourages interdisciplinary research. Joint mentorship of graduate students is welcomed as a mechanism for interdisciplinary collaborations among faculty.