The project will develop the mathematical theories of asynchronous and adaptive networks as part of a general scheme for pattern recognition, visualization of complex dynamics and 'qualitative' computing. The work will combine ideas on adaptive networks inspired by computational neuroscience, notably Spike-Timing Dependent Plasticity (STDP), with mathematical techniques developed in the study of statistical properties of dynamical systems with multiple time scales. We allow for asynchronous dynamics (no global clock); specifically, nodes of the network may not be updated synchronously (at each time step). Of special interest is the further development of a very promising Globally Asynchronous Locally Synchronous (GALS) network architecture that combines randomness (coming from node dynamics) with a loose (sloppy) asynchronous logic. Overall, the research will use mathematical techniques developed in the study of statistical properties of dynamical systems with the mathematics of network dynamics and be guided by numerical simulation and experimentation.
Many physical, electrical and biological systems can be modeled by networks of interacting differential equations and maps. The most realistic models allow for randomness, discontinuity, time delays and asynchrony - there may be no global clock and so the nodes of the network may not be updated synchronously (by way of contrast, the motion of the planets round the sun is synchronous: all the planets continually move and interact, via gravity, with all the other planets). Asynchrony is a characteristic feature of much recent technology as well as of complex biological systems, such as the brain. The project will develop new models for network dynamics that involve a mix of random, asynchronous and deterministic dynamics. As part of the work, it is proposed to refine and develop existing novel visualization tools with the aim of identifying key dynamical features in complex network dynamics, such as patterns of synchronization in large networks. Of great potential significance in applications is the development of new adaptive methods for high speed pattern recognition and learning.
