This workshop on Mathematical Foundations of Open Systems explores new research directions towards a logical/mathematical foundation for modeling the behavior of dynamic open systems that evolve over time through self-organization, regulation, and adaptation to changing environments and structures. Such a framework should provide a unified approach for obtaining an advanced understanding of natural systems, the ability to fix and modify them, and to design cyber-physical systems (CPS) in principled ways using new notions of control and coordination. The workshop, held May 23-25, 2010, Philadelphia, PA, is supported by the NSF and other agency members of the interagency coordinating group on High Confidence Software and Systems.

Project Report

held at the Inn @ Penn in Philadelphia Pennsylvania, May 23-25, 2010. The goals of the workshop were to: * assess the current state-of-the art in system modeling and analysis; identify the limitations and critical gaps in existing theories and modeling formalisms, * develop benchmark challenge problems whose solutions could have high impact on the design, analysis, and maintainability of critical systems and the understanding of complex natural systems; * recommend a research agenda for developing new technologies to enable more rapid advance in areas such as biological science and the science of cyber-physical systems. * recommend new directions in education. Workshop participants included leading researchers in mathematics, biology, formal methods, computer science, chemistry, physics, control theory, and engineering. The workshop agenda included invited presentations on a variety of topics related to open systems, followed by several open discussion sessions probing issues raised and identifying potential grand challenge problems. The discussions are and recommendations are summarized below. 1 Summary of Talks Pat Lincoln: Discussed Formal/logical approaches to modeling and understanding complex systems. Ilya Nemenman: Discussed Information theory, what the Fly’s Eye tells the Fly’s Brain. Hong Qian: Gave a talk on Open Systems and Entropy. Kenneth Gollob: Discussed Issues in Immune System Modeling. Ashish Tiwari: Discussed Abstraction and Modeling. Bud Mishra: Gave a discussion of Model Checking Applications to Cancer Models. Ary Goldberger: Discussed Time Asymmetry properties of Human Physiologic Signals. John Doyle: Discussed Complexity and Network-Centric Infrastructures. 2 Emerging concepts Research emerged during discussions: the mathematics of rare events; complexity as an essential feature of healthy systems; complexity as a tool; thermodynamics -- irreversibility, energetics, mathematics of far from equilibrium systems; and networks everywhere. 3 Open Discussions There were robust discussions of rare events, biology as a model for cyber-physical systems, robustness, complexity as a tool, thermodynamics and far from equilibrium methods and networks. 4 Gaps: • Complexity leads to replacing models by data analysis • Overuse and ubiquitous abuse of statistics • The emerging ability to produce large quantities of data (in space and/or time), leads to over-determined systems. • Model-checking has proved to be useful in many applications, however there are serious limitations including scalability, and difficulty of application to hybrid systems or reaction-diffusion equations. • Linear methods have problems of scale while nonlinear methods have problems of compositionality. • Models should be compositional, adaptive, useful, predictive, insightful. Methods for validation are needed. • Fundamental mathematics and logic of stochastic/nonlinear dynamics is lacking. • Overuse of simulation and topological data analysis. • The infeasibility of universal models coupled with dynamically changing systems, e.g., internet and supply systems, limit the use of traditional techniques such as regression analysis. 5 Challenges and recommendations: towards a transformative agenda There is a need to develop a combined mathematical and logical framework for modeling the behavior of open dynamic networks that evolve over time. The framework would provide a unified approach to build diverse top down and bottom up models that are consistent with each other and with the system (biological, cyber-physical, or other) being modeled. 6 New Directions for Education were proposed 7 The Open CPS Website The purpose for the Open Systems Workshop was to initiate an ongoing discussion into the state and challenges of the field, as well as serve as an educational platform for the topics covered at the workshop. For this, we set up a website, www.istar.upenn.edu/osw/index.html which hosts post-workshop materials www.istar.upenn.edu/osw/postworkshop.html including PowerPoint presentations of the talks and position papers www.istar.upenn.edu/osw/positionpaper.html. 8.2 Contributors Gul Agha Professor in the Department of Computer Science University of Illinois at Urbana-Champaign David Axelrod Department of Genetics Rutgers University John Doyle Professor, California Institute of Technology Madalena Costa Instructor, Harvard Medical School Charles Epstein Professor of Mathematics , University of Pennsylvania James Faeder Associate Professor, University of Pittsburgh School of Medicine Helen Gill Program Director, Computer and Network Systems , National Science Foundation Ary Goldberger Professor, Harvard University Kenneth Gollob Senior Scientist, SRI International Mark Goulian Associate Professor, University of Pennsylvania Ali Jadbabaie Associate Professor, University of Pennsylvania Insup Lee Professor, University of Pennsylvania Pat Lincoln Director, SRI International Charlie Johnson Professor, University of Pennsylvania Max Mintz Professor, University of Pennsylvania Bud Mishra Courant Institute & New York University Jack Morava Professor, Johns Hopkins University Ilya Nemenman Associate Professor of Physics, Emory University Dusko Pavlovic Visiting Professor at University of Oxford Sylvan Pinsky Senior Computer Scientist, SRI International Hong Qian Professor. University of Washington Harvey Rubin Professor, University of Pennsylvania Carolyn Talcott Computer Scientist, SRI International Shin Teh Associate Director, ISTAR, University of Pennsylvania Ashish Tiwari Computer Scientist, SRI International Rajeev Alur Zisman Professor, University of Pennsylvania

Agency
National Science Foundation (NSF)
Institute
Division of Computer and Network Systems (CNS)
Type
Standard Grant (Standard)
Application #
1037877
Program Officer
David Corman
Project Start
Project End
Budget Start
2010-08-01
Budget End
2011-07-31
Support Year
Fiscal Year
2010
Total Cost
$34,850
Indirect Cost
Name
University of Pennsylvania
Department
Type
DUNS #
City
Philadelphia
State
PA
Country
United States
Zip Code
19104