Connections II

	Connections II:
	Fundamentals of Network Science
	14-18 August 2006 Pasadena, CA

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Description

The Connections workshop series pulls together researchers in mathematics, science and engineering who bring together novel ideas and tools from outside their traditional training to influence problems in areas as diverse as networking protocols, systems biology, ecology, geophysics, finance, fluid mechanics, and multiscale physics. An underlying theme of this workshop is to look forward to ways in which future scientists can be educated in mathematical, computational, and quantitative methods, to prepare them to interact broadly from the time they are students and throughout their academic careers.

The first Connections workshop, held at Caltech in July 2004, brought together over 200 researchers in the fields of mathematics, biology, physics, engineering and other disciplines to participate in a 3 day conference exploring the connections between diverse applications and common underlying mathematics, particularly with regard to the role of uncertainty and robustness in complex systems. For the second Connections workshop, we plan to focus on the connections within the mathematics that would form the foundation of a theoretical framework for network science, still motivated by the diverse applications in science and technology that were focus of Connections I.

We are organizing the activities around three main themes (roughly one each day) of Hard Limits, Short Proofs, and Small Models, together with the crosscutting theme of Architecture:

• Hard limits - a major challenge in network science is to understand the fundamental limits on networks due to their components and their interconnection. One challenge is unifying and extending the previously fragmented hard limit theories that arise in thermodynamics, control, communications, and computing, and are often associated with the names Carnot, Bode, Shannon, and Turing. There are encouraging pairwise connections, like the Bode-Shannon theory developed by Martins et al and others, and this theme will explore the progress and potential for further integration. Also encouraging is the opportunity for overcoming hard limits when new connections are made, such as the relationship between proof complexity and problem fragility.

• Short proofs - in general, overcoming the apparent computational intractability of analysis and design of complex networks is a central challenge, from formal verification of programs and protocols to the robustness analysis of the dynamics of biological networks and advanced technologies. Here the apparent asymmetry between NP/coNP is as significant as that between P/NP, and moving from analysis to synthesis involves higher complexity classes in fundamental ways. Substantial progress has been made recently in creating frameworks to systematically search for short proofs, but the research communities involved and the results are again somewhat fragmented. Fortunately there is also encouraging progress in creating a more unified framework, motivated by new connections within mathematics, the pervasive role of duality, and the concept of "complexity implies fragility" from the first theme.

• Small models - an important route to short proofs is finding small models of complex phenomena through model identification from data, and model reduction. Again, there has been substantial recent progress within relatively fragmented research communities, with encouraging results that suggest the potential for a richer and more unified framework.

• Architecture - a cross-cutting theme in the background throughout the workshop will be the challenge of a theory of architecture, as in the claim that "the architecture of the cell and the Internet have enabled their robustness and evolvability." Despite its widespread usage, there is little formalization of the concept and essentially no theory. The existing hard limits theories all assume architectures a priori which are incompatible and incomparable, and thus offer little guidance in the tradeoffs associated with architecture design. Short proofs and small models also arise only in the context of a priori specified proof and modeling architectures. A diverse set of examples of successful and unsuccessful architectures in technology and biology are now available, and motivate the study of a theory. More unified theories of hard limits, short proofs, and small models appear to be essential first steps towards a theory of architecture.

Confirmed speakers

• Samuel Buss, University of California, San Diego
• Mung Chiang, Princeton University
• John Doyle, California Institute of Technology
• Keith Glover, Cambridge University
• Bill Helton, University of California at San Diego
• Mustafa Khammash, Univeristy of California, Santa Barbara
• Nuno Martins, U. Maryland
• Pablo Parrilo, Massuchusetts Institute of Technology
• Mihai Putinar, University of California, Santa Barbara
• Ben Recht, California Institute of Technology
• Lawrence Saul, University of California, San Diego
• Lin Xiao, Microsoft Research

Agenda

Mon(Tutorial), Tue-Thur (workshop), Fri(Student talks)

Mon-Thur (workshop) - Daily schedule 08:00   Breakfast (buffet) 08:30   Early morning talks 10:15   Morning break 10:45   Late morning talks 12:15   Lunch (buffet) 13:00p   Early afternoon talks 14:30   Afternoon break 14:45   Late afternoon talks   John Doyle: Recap and wrapup 16:00   Afternoon break 18:00   Dinner (buffet) 18:30   Dinner talk (Tue-Wed only) 19:30   Dessert, wine, and...

Monday - Speaker list Schedule TBD: Pablo Parrilo, John Doyle, Maryam Fazel, Xin Liu, Nuno Martins, Ben Recht, Lijun Chen

Tuesday - Hard Limits 08:30   John Doyle, Workshop Overview   Henrik Sandberg/Jean-Charles Delvenne: Control, information, and statistical mechanics   Nuno Martins: Communications and control   Pablo Parrilo: Intro to computational complexity 13:00   Pablo Parrilo: Computational complexity and formal methods   Mustafa Khammash: Complexity of the chemical master equation   Maryam Fazel, Dennice Gayme, Ben Recht: Complexity implies fragility   Pablo Parrilo/John Doyle: Recap and wrapup 18:30   Dinner presentation: Christina Smolke: Regulatory mechanisms in natural and synthetic biology

Wednesday - Short Proofs 08:30   Pablo Parrilo, Day Overview   Mihai Putinar: Polynomial proofs and operator theory   Samuel Buss: Proof systems   Bill Helton: Scale-independent proofs in systems and control 13:00   Carla Gomes/Bart Selman: SAT Solvers and state of the art   John Doyle: Layering architectures, examples   Mung Chiang: Layering, optimization, and duality   Parrilo: Recap and wrapup 16:30   Neil Gershenfeld: Math as computer programming

Thursday - Small Models 08:30   Ben Recht, Lin Xiao: Day Overview   Ali J/ Sanj L/Antonis P: Networks and decentralized control   Keith Glover, Model reduction and system ID 13:00   Lawrence Saul, Spectral methods in machine learning   Ben Recht, Lin Xiao: Convex optimization approaches and recap   Parrilo: Recap and wrapup 16:00   Adjourn, dinner on own

Friday - Student talks 09:00   Breakfast (buffet) 09:30   Morning talks and break 12:00   Lunch (buffet) 13:00   Afternoon talks and break 16:00   End

Additional Information

The main workshop will be held on 15-17 August 2006 in Pasadena, CA, with additional sessions on Monday and Friday for interested participants:

• Monday: tutorial sessions
• Tuesday: Hard Limits
• Wednesday: Short Proofs
• Thursday: Small Models
• Friday: student presentations
  
• Register to attend
  
• Participants (restricted page)

The Connections workshop is sponsored by Caltech and the Air Force Office of Scientific Research.