Difference between revisions of "Connections II"

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== Description ==
== Description ==


The ''Connections'' workshop series pulls together researchers mathematics, science and engineering who brought together novel ideas and tools from outside their traditional
The ''Connections'' workshop series pulls together researchers in mathematics,
training to influence problems in areas as diverse as Internet protocols, fluid
science and engineering who bring together novel ideas and tools from
mechanics, biologic signal transduction, ecology, systems biology,
outside their traditional training to influence problems in areas as diverse
finance, and multiscale physics. An
as networking protocols, systems biology, ecology, geophysics, finance,
underlying theme of this workshop is to look forward to ways in which
fluid mechanics, and multiscale physics. An underlying theme of this
future scientists can be educated in computation and quantitative
workshop is to look forward to ways in which future scientists can be
methods, to prepare them to interact broadly from the time they are
educated in mathematical, computational, and quantitative methods, to
students and throughout their academic careers.
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,
The first Connections workshop, held at Caltech in July 2004, brought
brought together over 200 researchers in the fields of biology,
together over 200 researchers in the fields of mathematics, biology,
mathematics, physics, engineering and other disciplines to participate
physics, engineering and other disciplines to participate in a 3 day
in a 3 day conference exploring the the role of uncertainty and
conference exploring the connections between diverse applications and common
robustness in complex systems. For the second ''Connections'' workshop, we plan to organize the activities around three main themes (roughly one each day):
underlying mathematics, particularly with regard to the role of uncertainty
* ''Hard limits'' - a major challenge in network science is to define the fundmantal limits associated with limits.  This thread would be about unifying the previously disconnected hard limits that arise due to thermodynamics, control, communications, and computingThere are now some pairwise connections, like the Bode-Shannon theory developed by Martins, Dahleh, Doyle and others.
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.   


* ''Simple models'' - one of the key techniques in dealing with complex, network systems is to identify simple models that capture essential phenomena.  The CDS community has developed many techniques for doing such modeling, including basic input/output representations for systems and explicit model reduction techniques with undertainty guarantees.  Other results include multiscale modeling, learning and ID from data, and model  invalidation.
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:


* ''Short proofs'' - a key element of any successful theory for large scale networked systems is an understanding of how to generate proofs for complex phenomenaLots continues to happen around proof automationIt connects with the first thread in that simple models help short proofs.  The big win will probably be when model simplification and proof search are coupled through systematic relaxations that exploit symmetriesThere are some nice starting points here, and lots of mathematicians are working on aspects of this problemThe tie with 1) is something that is not yet exploited as much as it could be.
* ''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 waysSubstantial 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
fragmentedFortunately there is also encouraging progress in creating a
more unified framework, motivated by new connections within mathematics, and
in part by 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
reductionAgain, 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 theoryThe 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 theoryMore unified theories of hard limits, short proofs, and
small models appear to be essential first steps towards a theory of
architecture.


== Agenda ==
== Agenda ==

Revision as of 15:21, 7 June 2006

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

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, and in part by 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.

Agenda

Monday - tutorial sessions

  • Schedule TBD

Tuesday - Hard Limits

9:00a   John Doyle, Workshop Overview
10:00a  
11:00a   Break
11:30a  
12:30p   Lunch
2:00p  
3:00p  
4:00p   Afternoon break
6:30p   Reception and cocktails
7:00p   Dinner presentation

Wednesday - Simple Models

9:00a   Laurence Saul, Machine Learning
10:00a   Keith Glover, Model reduction
11:00a   Break
11:30a   Jean Carlson, Eco/Geo systems
12:30p   Lunch
2:00p  
3:00p  
4:00p   Afternoon break
6:30p   Reception and cocktails
7:00p   Dinner presentation

Thursday - Short Proofs

9:00a   Pablo Parrilo, Semi-algebraic proofs
10:00a  
11:00a   Break
11:30a  
12:30p   Lunch
2:00p  
3:00p  
4:00p   Afternoon break
6:30p   Reception and cocktails
7:00p   Dinner presentation

Friday - Student talks

  • Schedule TBD

Additional Information

The main workshop will be held on 13-15 August 2006 in Pasadena, CA, with additional sessions on Monday and Friday for interested participants: