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Details of Grant 

EPSRC Reference: GR/R29628/01
Title: Digital Descriptions For Serial Data Streams
Principal Investigator: Lyons, Professor T
Other Investigators:
Hambly, Professor B
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Institute
Organisation: University of Oxford
Scheme: Standard Research (Pre-FEC)
Starts: 01 October 2001 Ends: 30 June 2005 Value (£): 142,278
EPSRC Research Topic Classifications:
Algebra & Geometry Information & Knowledge Mgmt
Software Engineering
EPSRC Industrial Sector Classifications:
Creative Industries No relevance to Underpinning Sectors
Communications
Related Grants:
Panel History:  
Summary on Grant Application Form
Sampling a continuously varying data stream and then reproducing the signal adequately, is a frequent computing challenge? An audio recording should reproduce the sounds created in the studio. A recording of wind patterns should allow one to test the design of a bridge. What data should one collect?The traditional approach would be to take linear samples from the data stream. If the data is vector valued, the theory of systems driven by rough paths suggests it might be more sensible to use more complex algebraic proxies for the data stream over short time intervals.We want to develop the maths arising from this novel perspective that the incremental path segments of a continuous data stream can be coded efficiently using elements chosen from a nilpotent Lie group labelled via their Lie representation. Open questions of strategic importance include: Does the iterated integral sequence determine the path? (Cf. identification problem for Fourier Series). How should one extrapolate back from increments to a continuous stream (invert the transform)? We will keep this project informed and focussed through computational examples such as the compression of stereo sound.
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Organisation Website: http://www.ox.ac.uk