Connections II

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Citlogo.png Connections II: Afosrlogo.png
Fundamentals of Network Science
14-18 August 2006
Pasadena, CA
Agenda Register Participants Travel Info CDS Home

The workshop will take place in Dabney Hall (campus map).


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.

Invited speakers (confirmed)

  • Samuel Buss, UC, San Diego
  • Mung Chiang, Princeton
  • Ali Jadbabaie, Penn
  • Neil Gershenfeld, MIT
  • Keith Glover, Cambridge
  • Bill Helton, UC, San Diego
  • Mustafa Khammash, UC, Santa Barbara
  • Sanjay Lall, Stanford
  • Nuno Martins, U. Maryland
  • Antonis Papachristodoulou, Oxford
  • Pablo Parrilo, MIT
  • Mihai Putinar, UC, Santa Barbara
  • Lawrence Saul, UC, San Diego
  • Christina Smolke, Caltech
  • Lin Xiao, Microsoft Research

Caltech organizers and speakers

  • Jean-Charles Delvenne, John Doyle, Maryam Fazel, Richard Murray, Ben Recht, Henrik Sandberg


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)
13:00   Early afternoon talks
14:30   Afternoon break
14:45   Late afternoon talks
16:00   Afternoon break until dinner
18:00   Dinner (buffet, Tue-Wed only)
18:30   Dinner talk (Tue-Wed only)
19:30   Dessert, wine, and...

Monday - Tutorial speaker list

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, Complexity and Fragility in Linear Programming
  Dennice Gayme, Complexity implies fragility
  Pablo Parrilo/John Doyle: Recap and wrapup
18:30   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: SAT Solvers and state of the art (zipped movies)]
  John Doyle: Layering architectures, examples
  Mung Chiang: Layering, optimization, and duality
  Parrilo: Recap and wrapup
18:30   Neil Gershenfeld: Math as computer programming

Thursday - Small Models

08:30   Ali J/ Sanj L/Antonis P: Networks and decentralized control
  Ali Jadbabaie, Flocking and consensus algorithms
  Sanjay Lall, Decentralized control
13:00   Lawrence Saul, Spectral methods in machine learning
  Ben Recht, Diffeomorphic Warping
  Lin Xiao, A Duality View of Spectral Methods for Dimensionality Reduction
  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:

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