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Asynchronous Networks

Final Report Summary - ASYNCNET (Asynchronous Networks)

Asynchronous Networks

In the first year of the project, a transparent and powerful mathematical model was developed for asynchronous networks that incorporates most of the features seen in contemporary network problems. A key advance was formalizing the idea of a functional asynchronous network: a network with a specific function (for example, a transport network or neural network performing pattern recognition).

A major breakthrough was obtained in the second year of the project when a foundational result was obtained that clarified the structure of functional asynchronous networks and went far beyond the original goals of the project. A large class of functional asynchronous networks was identified for which one can describe the function of the network in terms of the function of constituent subnetworks. The result answers a question raised by the systems biologist Uri Alon in connection with gene transcription networks (from page 27 of Alon's 2007 book on systems biology):

“Ideally, we would like to understand the dynamics of the entire network, based on the dynamics of the individual building blocks”.

The underlying premise behind Alon's comment is that a modular, or engineering, approach to network dynamics is feasible: identify building blocks, connect together to form networks and describe the dynamical properties of the resulting network in terms of the dynamics of its components.

Articles describing these results, general theory, and applications, have been submitted for publication and are listed and available on the project website.