Welcome to the homepage for the Workshop on 'Mathematical Foundations for Open Systems', a conference organized by ISTAR of the University of Pennsylvania and co-sponsored by the National Science Foundation and the National Security Agency. The workshop was held at Penn from May 23rd - 25th, 2010.
The workshop hoped to address the need for 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.
Please visit our Post-Workshop site for workshop-related content and products.
Rationale for the Workshop
Open systems continually interact with their environment through exchanges of energy, materials, and information to reach a steady state and can evolve towards states of greater complexity and differentiation. They maintain themselves in an ongoing build up and break down of components and are capable of self-regulation and adapting to circumstances by changing the structure and process of their internal components. Biological systems are open, non-equilibrium systems that are embedded in a changing and often-times hostile environment exchanging energy and molecular species with its surroundings. The study of open systems was recommended by the ”2004Models of Thought Workshop”. Our candidate systems include the immune system, CPSs such as pervasive spaces, smart buildings, robotics swarms, sensor/actor systems, medical devices, and metabolic and regulatory networks for dormancy and persistence in bacteria. A mathematical framework provides improved modeling and analysis tools to gain a more comprehensive understanding of open systems and the ability to fix or modify existing systems and design CPSs in principled ways using new notions of control and coordination. There are computational challenges in developing protection strategies and designing and building control systems to defend against external attack. A recent JASON report suggests a risk assessment approach that includes the very interesting idea of splitting entropy into extensive and a non-extensive components and using the techniques of nonextensive statistical mechanics to compute risk.
Approaches to this Challenge
The approach is to develop a mathematical framework that provides a unified foundation to build diverse top down and bottom up models and facilitates the derivation of macroscopic behavior based on microscopic properties such as those developed in physics using statistical mechanics and thermodynamics. We propose to merge formal methods techniques with classical mathematics to develop new mathematical concepts that enable modeling and prediction of behavior. The integrative nature of the logic, mathematics, and formal methods will focus attention on the selection and limitation of the models by identifying basic subsystems, their local and global environments, and theories that characterize the interdependencies and interactions with other subsystems and structures organized at multiple levels. An important goal is to build diverse models that extract and organize crucial information, discover hidden structures, and integrate models with varying timescales. Identifying a family of properties and functions of open systems that can account for the organization and ability for self-regulation, maintainability, and adaptability to environmental changes will play a central role in the principled design and analysis of such systems.
Goals of the workshop
The workshop hosted leading researchers in mathematics, biology, formal methods, computer science, chemistry, physics, control theory, and engineering to assess the current state-of-the art, identify the hard problems in open systems, and will recommend a research agenda to develop a new kind of technology to enable more rapid advance in biological science.
The goals of the workshop was to identify the limitations and critical gaps in existing theories and modeling formalisms, build new research collaborations, and develop bench mark challenge problems whose solutions have high impact on the design, analysis, and maintainability of critical systems. Also, the identification of fundamental questions, next steps, new research directions, and recommendations for new directions in education will be given.
